CHAPTER
2
Motion
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Video
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Audio
Assessment
Review
Concepts in Motion
g
Inquiry
Multilingual eGlossary
Launch Lab
Animal Race
A cheetah can run at a speed of almost 120 km/h. It is the
fastest runner in the world. A horse can reach a speed of
64 km/h, an elephant’s top speed is about 40 km/h, and a
tortoise walks at a speed of about 0.3 km/h. The speed of an
object is calculated by dividing the distance that the object
travels by the time it takes it to move that distance. How does
your speed compare to the speeds of these animals?
For a lab worksheet, use your StudentWorks™ Plus Online.
?
Inquiry
Launch Lab
Make a three-tab book.
Label it as shown. Use it
to organize your notes
on motion.
Displacement
Velocity
Acceleration
Motion
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THEME FOCUS
Motion and Forces
Section 1 • Describing Motion
Objects are in motion all around us.
Section 2 • Velocity and
BIG Idea Motion occurs when an object changes its
position.
Momentum
Section 3 • Acceleration
Chapter 2 • Motion
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SC.912.P.12.2: Analyze the motion of an object in terms of its position, velocity, and acceleration (with respect to
a frame of reference) as functions of time. ALSO COVERS MA.912.S.1.2
Section 1
Reading Preview
Describing Motion
Essential Questions
MAIN Idea Position describes where an object is, and speed
◗ How are distance and
describes how fast the object is moving.
displacement different?
◗ How is an object’s speed
calculated?
◗ What information does a
distance-time graph provide?
Real-World Reading Link How would you describe the trip from your
home to your school? You might include whether you walked or rode a
bus, how far away the school was, and how long it took to get there.
Scientists describe motion in a similar, but very specific way.
Review Vocabulary
Motion and Position
meter: the SI unit of length,
abbreviated m
You do not always need to see something move to know that
motion has taken place. For example, suppose you look out a
window and see a mail truck stopped next to a mailbox, as
shown in Figure 1. One minute later, you look out again and
see the same truck stopped farther down the street. Although
you did not see the truck move, you know it moved because its
position relative to the mailbox changed.
New Vocabulary
motion
displacement
speed
g
Multilingual eGlossary
■ Figure 1 As the mail truck follows
its route, it stops at each mailbox
along the street.
Explain How do you know the mail
truck has moved?
9:00 A.M.
44
Reference points A reference point is needed to determine the position of an object. In Figure 1, the reference point
might be a mailbox. Motion is a change in an object’s position
relative to a reference point. How you describe an object’s motion
depends on the reference point that is chosen. For example, the
description of the mail truck’s motion in Figure 1 would be
different if the reference point were a tree instead of a mailbox.
After a reference point is chosen, a frame of reference can be
created. A frame of reference is a coordinate system in which
the position of the object is measured. The x-axis and y-axis
of the reference frame are drawn so that they are perpendicular
to each other and intersect the reference point.
9:01 A.M.
Chapter 2 • Motion
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Coordinate systems Figure 2 shows a map of the city
where the mail truck is delivering mail with a coordinate system drawn on it. The x-axis is in the east-west direction, the
y-axis is in the north-south direction, and each division represents a city block. The post office is located at the origin. The
mail truck is located at 3 blocks east (x = 3) and 2 blocks north
(y = 2) of the post office.
2
Change in Position
-2
Have you ever run a 50-m dash? Describing how far and in
what direction you moved was an important part of describing
your motion.
-3
4
N
0m
10 m
20 m
40 m
Post
office
0
-1
-4
-4
-3
-2
-1
0
1
2
3
4
■ Figure 2 A coordinate system is
like a map. The reference point is at
the origin, and each object’s position
can be described with its coordinates.
Identify the position of the
orange car.
VOCABULARY
SCIENCE USAGE V. COMMON USAGE
Position
Science usage
the location of an object in relation to
a reference point
The cat’s position was 3 meters west of
the house.
Common usage
a point of view; a job or rank
After graduation, I accepted a teller
position at the bank.
50 m
30 m
S TA R T
FINISH
20 m
30 m
N
1
Distance In a 50-m dash, each runner travels a total distance of 50 m. The SI unit of distance is the meter (m). Longer
distances are measured in kilometers (km). One kilometer is
equal to 1,000 m. Shorter distances are measured in centimeters (cm) or millimeters (mm). One meter is equal to 100 cm
and to 1,000 mm.
Displacement Suppose a runner jogs to the 50-m mark
and then turns around and runs back to the 20-m mark, as
shown in Figure 3. The runner travels 50 m in the original
direction (east) plus 30 m in the opposite direction (west), so
the total distance that she ran is 80 m. How far is she from the
starting line? The answer is 20 m. Sometimes, you may want
to know the change in an object’s position relative to the starting point. An object’s displacement is the distance and direction of the object’s change in position. In Figure 3, the runner’s
displacement is 20 m east.
The length of the runner’s displacement and the total distance traveled would be the same if the runner’s motion were in
a single direction. For example, if the runner ran east from the
starting line to the finish line without changing direction, then
the distance traveled would be 50 m and the displacement
would be 50 m east.
Mail
truck
3
50 m
■
Figure 3 An object’s displacement
is not the same as the total distance
that the object traveled. The runner’s
displacement is 20 m east of the
starting line. However, the total
distance the runner traveled is 80 m.
Describe the difference between
the total distance traveled and the
displacement.
Section 1 • Describing Motion
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5m
east
5m
east
10 m east
Displacements in the same direction can
be added.
■ Figure 4 These arrows represent
the students’ walks. The green arrows
show the first part of the walk and the
purple arrows show the second part.
The red arrows show the students’
displacements.
FOLDABLES
Incorporate information
from this section into
your Foldable.
5m
east
st
ea
10 m east
h
ort
5 m west
Displacements in opposite directions
can be subtracted.
n
5m
4 m east
3 m north
Displacements that are not in the same
direction or opposite directions cannot
be directly added or subtracted.
Adding displacements You know that you can add
distances together to get the total distance. For example,
2 m + 3 m = 5 m. But how would you add the displacements
5 m east and 10 m east? Directions in math problems are much
like units: you can add numbers with like directions. For example, suppose a student walks 5 m east, stops at a crosswalk, and
then walks another 5 m east, as shown on the left in Figure 4.
His displacement is
5 m east + 5 m east = 10 m east
But what if the directions are not the same? Then compare
the two directions. If the directions are exactly opposite, the
distances can be subtracted. Suppose a student walks 10 m east,
turns around, and walks 5 m west, as shown in the center of
Figure 4. The size of the displacement would be
10 m − 5 m = 5 m
Rules for
Table 1 Adding
Displacements
The direction of the total displacement is always the direction
of the larger displacement. In this case, the larger displacement
is east, so the total displacement is 5 m east.
Now suppose the two displacements are not in the same
direction or in opposite directions, as illustrated on the right in
Figure 4. Here, the student walks 4 m east and then 3 m north.
The student walks a total distance of 7 m, but the displacement
is 5 m in a roughly northeast direction. 4 m east and 3 m north
cannot be directly added or subtracted, and they should be discussed separately. The rules for adding displacements are summarized in Table 1.
1. Add displacements in the same
Speed
direction.
2. Subtract displacements in
opposite directions.
3. Displacements that are not in the
same or in opposite directions
cannot be directly added
together.
46
Think back to the mail truck moving down the street. You
could describe the movement by the distance traveled or by the
displacement. You might also want to describe how fast the
truck is moving. To do this, you need to know how far it travels
in a given amount of time. To describe how fast an object
moves, scientist use the object’s speed. Speed is the distance an
object travels per unit of time.
Chapter 2 • Motion
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Calculating speed Any change over time is called a rate.
For example, you could describe how quickly water is leaking
from a tank by stating how many liters are lost each hour. This
would be the rate of water leakage. If you think of distance as
the change in position, then speed is the rate of change in position. Speed can be calculated from this equation.
Speed Equation
distance (in meters)
time (in seconds)
speed (in meters/second) = __
d
s=_
t
Table 2
Common
Speeds
Motion
Speed (m/s)
Olympic
100-m dash
10 m/s
Car on city street
(35 mph)
16 m/s
Car on interstate
highway (65 mph)
30 m/s
Commercial
airplane
250 m/s
In SI units, distance is measured in meters and time is measured in seconds. Therefore, the SI unit for speed is meters per
second (m/s). Sometimes, it is more convenient to express speed
in other units, such as kilometers per hour (km/h). Table 2
shows the speeds of some common objects.
?
Inquiry
Virtual Lab
SC.912.P.12.2: Analyze the motion of an object in terms of its position, velocity, and acceleration
(with respect to a frame of reference) as functions of time. MA.912.S.1.2: Determine appropriate
and consistent standards of measurement for the data to be collected in a survey or experiment.
EXAMPLE Problem 1
Calculate Speed A car traveling at a constant speed covers a distance of
750 m in 25 s. What is the car’s speed?
Identify the Unknown:
speed: s
List the Knowns:
distance: d = 750 m
time: t = 25 s
Set Up the Problem:
Solve the Problem:
Check the Answer:
PRACTICE Problems
750 m
s = _td= _
25 s
750 m
_
s=
= 30 m/s
25 s
30 m/s is approximately the speed limit on a U.S.
interstate highway, so the answer is reasonable.
Find Additional Practice Problems in the back of your book.
1. A passenger elevator travels from the first floor to the 60th floor, a distance
of 210 m, in 35 s. What is the elevator’s speed?
Review
Additional Practice Problems
2. A motorcycle is moving at a constant speed of 40 km/h. How long does it
take the motorcycle to travel a distance of 10 km?
3. How far does a car travel in 0.75 h if it is moving at a constant speed of
88 km/h?
4. Challenge A long-distance runner is running at a constant speed of 5 m/s.
How long does it take the runner to travel 1 km?
Section 1 • Describing Motion
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■ Figure 5 The cyclist’s speed varies
from 0 km/h to 30 km/h during his trip.
Speed Changing over Distance
Explain how you can describe the
Speed (km/h)
speed of an object when the speed
is changing.
30
Going downhill
25
Climbing
steep hill
Stopping for
red light
20
15
Constant speed
10
5
0
Gaining
speed
1
2
3
4
5
Distance (km)
SC.912.P.12.2: Analyze the motion of an object in
terms of its position, velocity, and acceleration (with
respect to a frame of reference) as functions of time.
?
Inquiry
MiniLab
Measure Average
Speed
Procedure
1. Read the procedure and safety
2.
3.
4.
5.
information, and complete the
lab form.
Mark a point on the floor with
tape. Place a toy car at this
point.
Give the toy car a gentle push
forward. At the same time, start
a stopwatch.
Record the time it takes for the
car to come to a stop.
Use a meterstick to measure
the distance the car traveled.
Analysis
1. Calculate the average speed of
the car in m/s.
2. Infer How would the average
speed change if you gave the
car a harder push? Try it.
48
Constant speed Suppose you are in a car traveling on a
nearly empty freeway. You look at the speedometer and see that
the car’s speed hardly changes. If the car neither slows down
nor speeds up, the car is traveling at a constant speed. If you are
traveling at a constant speed, you can calculate your speed by
dividing any distance interval over the time it took you to
travel that distance. The speed you calculate will be the same
regardless of the interval you choose.
Changing speed Usually, speed is not constant. Think
about riding a bicycle for a distance of 5 km. The bicycle’s speed
will vary, as in Figure 5. As you start out, your speed increases
from 0 km/h to 20 km/h. You slow down to 10 km/h as you
pedal up a steep hill and speed up to 30 km/h going down the
other side of the hill. You stop for a red light, speed up again,
and move at a constant speed for a while. Finally, you slow
down and come to a stop.
Checking your watch, you find that the trip took 15 min.
How would you express your speed on such a trip? Would you
use your fastest speed, your slowest speed, or some speed
between the two? Two common ways of expressing a changing
speed are average speed and instantaneous speed.
Average speed Average speed is one way to describe the speed
of the bicycle trip. Average speed is the total distance traveled
divided by the total time of travel. It can be calculated using the
relationships between speed, distance, and time. For the bicycle
trip just described, the total distance traveled was 5 km and the
1
h, or 0.25 h. Therefore, the average speed was
total time was _
4
d
5 km
=_
= 20 km/h
s=_
t
0.25 h
Chapter 2 • Motion
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Instantaneous speed Suppose you watch a car’s speedometer,
like the one in Figure 6, go from 0 km/h to 80 km/h. A speedometer shows how fast a car is going at one point in time, or at
one instant. The speed shown on a speedometer is the instantaneous speed. Instantaneous speed is the speed at a given point
in time. When something is speeding up or slowing down, its
instantaneous speed is changing. The speed is different at every
point in time. If an object is moving with constant speed, the
instantaneous speed does not change. The speed is the same at
every point in time.
Reading Check Identify two examples of motion in which an object’s
■ Figure 6 A speedometer gives the
car’s instantaneous speed. Instantaneous speed is the speed at one
instant in time.
instantaneous speed changes.
Graphing Motion
The motion of an object over a period of time can be shown
on a distance-time graph. For example, the graph in Figure 7
shows the distance traveled by three swimmers during a
30-minute workout. Time is plotted along the horizontal axis of
the graph, and the distance traveled is plotted along the vertical
axis of the graph.
Each axis must have a scale that covers the range of numbers
to be plotted. In Figure 7, the distance scale must range from
0 to 2,400 m and the time scale must range from 0 to 30 min.
Next, the x-axis is divided into equal time intervals, and the
y-axis is divided into equal distance intervals.
Once the scales for each axis are in place, the data points can
be plotted. In Figure 7, there is a data point plotted for each
swimmer every two and a half minutes. After plotting the data
points, a line is drawn connecting the points.
Distance-Time Graph
Mary
2,400
2,200
Distance (m)
2,000
Kathy
1,800
1,600
Animation
1,400
Julie
1,200
1,000
800
600
400
200
0
Concepts in Motion
0
10
20
Time (min)
30
■ Figure 7 This graph shows how far
each girl swam during a 30 minute
workout. Time is divided into 2.5-minute intervals along the x-axis. Distance
swam is divided into 200-m intervals
along the y-axis.
Examine the graph and determine
which girl swam the farthest during
the workout.
Section 1 • Describing Motion
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Distance-Time Graph
Mary
2,400
2,200
Distance (m)
2,000
Kathy
1,800
v = 80 m/min
1,600
1,400
v = 60 m/min
1,200
Julie
1,000
800
v = 0 m/min
600
v = 80 m/min
400
200
0
0
v = 40 m/min
10
20
30
Time (min)
■ Figure 8 An object’s speed is equal to the slope
of the line on a distance-time graph.
Identify the part of the graph that shows one of
the swimmers resting for 10 min.
Section 1
Review
Section Summary
◗ Motion occurs when an object changes its
position relative to a reference point.
◗ Displacement is the distance and direction
of a change in position from the starting
point.
◗ Speed is the rate at which an object’s
position changes.
◗ On a distance-time graph, time is the
Speed on distance-time graphs If an
object moves with constant speed, the increase in
distance over equal time intervals is the same. As a
result, the line representing the object’s motion is a
straight line. For example, look at the graph of the
swimmers’ workouts in Figure 8. The straight red
line represents the motion of Mary, who swam with
a constant speed of 80 m/min. The green line represents the motion of Julie, who did not swim with
a constant speed. She swam with a constant speed
of 40 m/min for 10 minutes, rested for 10 minutes,
and then swam with a constant speed of 80 m/min
for 10 minutes.
The graph shows that the line representing the
motion of the faster swimmer is steeper. The
steepness of a line on a graph is the line’s slope.
The slope of a line on a distance-time graph
equals the object’s speed. Because Mary has a
greater speed (80 m/min) than Kathy (60 m/min),
the line representing her motion has a larger slope.
Now look at the green line representing Julie’s
motion. During the time she is resting, her line is
horizontal. A horizontal line on a distance-time
graph has zero slope and represents an object
at rest.
SC.912.P.12.2, MA.912.S.1.2
5.
MAIN Idea
Describe the trip from your home to school using the
words position, distance, displacement, and speed.
6. Explain whether the size of an object’s displacement could be
greater than the distance the object travels.
7. Describe the motion represented by a horizontal line on a distancetime graph.
8. Describe the difference between average speed and constant speed.
9. Think Critically During a trip, can a car’s instantaneous speed ever
be greater than its average speed? Explain.
x-axis and distance is the y-axis.
◗ The slope of a line plotted on a distance-
time graph is the speed.
Apply Math
10. Calculate Speed Michiko walked a distance of 1.60 km in 30 min.
Find her average speed in m/s.
11. Calculate Distance A car travels at a constant speed of 30.0 m/s for
0.80 h. Find the total distance traveled in km.
50
Chapter 2 • Motion
0044_0050_C02S1_894583.indd 50
Assessment
Online Quiz
5/7/10 9:43 AM
SC.912.P.12.2: Analyze the motion of an object in terms of its position, velocity, and acceleration (with respect to
a frame of reference) as functions of time. ALSO COVERS: MA.912.S.1.2
Section 2
Reading Preview
Velocity and Momentum
Essential Questions
MAIN Idea An object’s velocity describes the object’s speed and
◗ What is the difference between
direction of motion.
speed and velocity?
◗ How is the motion of two objects
relative to each other described?
◗ How can an object’s momentum
be calculated?
Real-World Reading Link Cars, trucks, and many other vehicles can
go both backward and forward. The driver must put the car in the proper
gear for each direction. What could happen if the driver put the car into
reverse instead of forward?
Review Vocabulary
Velocity
speed: rate of change of position
You turn on the radio and hear a news story about a hurricane. The storm, traveling at a speed of 20 km/h, is located
500 km east of your location. Should you worry?
Unfortunately, you do not have enough information to
answer that question. Knowing only the speed of the storm is
not much help. Speed describes only how fast something is moving. To decide whether you need to move to a safer area, you also
need to know the direction that the storm is moving. In other
words, you need to know the velocity of the storm. Velocity
includes the speed of an object and the direction of its motion.
Velocity has the same units as speed, m/s. If you had been told
that the hurricane was traveling straight toward your house at
20 km/h, you would have known to evacuate.
New Vocabulary
velocity
momentum
g
Multilingual eGlossary
FOLDABLES
Incorporate information
from this section into
your Foldable.
Velocity and speed Because velocity depends on direction as well as speed, the velocity of an object can change even
if the speed of the object remains constant. For example, the
race cars in Figure 9 have constant speeds through the turn.
Even though the speeds remain constant, their velocities
changes because they change direction thoughout the turn.
Reading Check Describe how velocity and speed are different.
Figure 9 These cars travel at
constant speed, but not with constant
velocity. The cars’ velocities change
because their direction of motion
changes.
■
Section 2 • Velocity and Momentum
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Same speed, different velocities It is possible for two objects
to have the same speed but different velocities. For example, the
two escalators pictured in Figure 10 are moving at the same
speed but in opposite directions. The speeds of the two sets of
passengers are the same, but their velocities are different
because they are moving in different directions. Cars traveling
in opposite directions on a road with the same speed also have
different velocities.
Motion of Earth’s Crust
■
Figure 10 The two escalators
move with a speed of 0.5 m/s. But
the left escalator’s velocity is 0.5 m/s
downward and the right escalator’s
velocity is 0.5 m/s upward.
VOCABULARY
WORD ORIGIN
Velocity
from the Latin veloci– meaning fast,
swift, or rapid.
The students found that the velociraptor’s velocity was 10 m/s north.
Concepts in Motion
Animation
■
Figure 11 Geologic evidence suggests that Earth’s surface is changing.
The continents have moved slowly over
time and are still moving today.
Can you think of something that is moving so slowly that
you cannot detect its motion, but you can see evidence of its
motion over long periods of time? As you look around the
surface of Earth from year to year, its basic structure seems
the same. Mountains, plains, and oceans seem to remain
unchanged. Yet, if you examined geologic evidence of what
Earth’s surface looked like over the past 250 million years, you
would see that large changes have occurred. Figure 11 shows
how, according to the theory of plate tectonics, the positions of
landmasses have changed during this time. Changes in the
landscape occur constantly as continents drift slowly over
Earth’s surface.
These moving plates cause geologic changes, such as the
formation of mountain ranges, earthquakes, and volcanic
eruptions. The movement of the plates changes the size of the
oceans. The Pacific Ocean is getting smaller, and the Atlantic
Ocean is getting larger. The plates’ movement also changes the
shape of the continents as they collide and spread apart.
Plates move so slowly that their speeds are given in units of
centimeters per year. Along the San Andreas Fault in California, two plates move past each other with an average speed of
about 1 cm per year. The Australian Plate moves faster and
pushes Australia north at an average speed of about 17 cm/y.
Therefore, the velocity of the Austrailian plate is 17 cm/y north.
About 250 million years ago, the continents formed a supercontinent called Pangaea.
52
Pangaea separated into smaller pieces. About 66 million years
ago, the continents looked like the figure above.
Chapter 2 • Motion
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60 km
70 km
20 km/h
20 km/h
10 km/h
10 km/h
10 km
20 km
60 km
West
40 km
30 km 20 km 10 km 0 km 10 km 20 km 30 km 40 km 50 km 60 km
30 km 20 km 10 km 0 km 10 km 20 km 30 km 40 km 50 km 60 km
West
East
East
2:00 P.M.
3:00 P.M.
■
Relative Motion
Have you ever watched cars pass you on the highway? Cars
traveling in the same direction often seem to creep by, while
cars traveling in the opposite direction seem to zip by. This
apparent difference in speeds is because the reference point—
your vehicle—is also moving.
The choice of a moving reference point affects how you
describe motion. For example, the motion of a hurricane can be
described using a stationary reference point, such as a house.
Figure 12 shows the locations and velocities of a hurricane and
a car relative to a house at 2:00 p.m. and 3:00 p.m. The distance
between the hurricane and the house is decreasing at a rate of
20 km/h. The distance between the house and the car is
increasing at a rate of 10 km/h.
How would the description of the hurricane’s motion be different if the reference point were a car traveling at 10 km/h
west? Figure 13 shows the motion of the hurricane and the
house relative to the car. A person in the car would say that the
hurricane is approaching with a speed of 10 km/h and that the
house is moving away at a speed of 10 km/h. It is important to
notice that Figure 12 and Figure 13 show the same changes, but
they use different reference points. Velocity and position always
depend on the point of reference chosen.
Figure 12 If the house is chosen
for the reference point, the car
appears to be traveling 10 km/h west
and the hurricane appears to be traveling 20 km/h west.
■ Figure 13 If the car is chosen as
the reference point, the hurricane
appears to be moving towards the car
at 10 km/h and the house is moving
away from the car at 10 km/h.
60 km
70 km
10 km/h 10 km/h
10 km/h
10 km
10 km/h
20 km
60 km
West
West
East
2:00 P.M.
40 km
10 km 0 km 10 km 20 km 30 km 40 km 50 km 60 km 70 km 80 km
10 km 0 km 10 km 20 km 30 km 40 km 50 km 60 km 70 km 80 km
East
3:00 P.M.
Section 2 • Velocity and Momentum
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Typical
Table 3
Momentums
Momentum
(kg·m/s)
Object
Tossed baseball
0.15
Person walking
100
Car on interstate
?
Inquiry
45,000
Momentum
An object is moving at 2 m/s toward a glass vase. Will the
vase be damaged in the collision? If the object has a small mass,
like a bug, a collision will not damage the vase. But if the object
has a larger mass, like a car, a collision will damage the vase.
A useful way of describing both the velocity and mass of an
object is to state its momentum. The momentum of an object is
the product of its mass and velocity. Momentum is usually represented by the symbol p.
Momentum Equation
Video Lab
momentum (in kg·m/s) = mass (in kg) × velocity (in m/s)
What’s PHYSICAL and
EARTH SCIENCE Got To Do With It?
p = mv
Video
EXAMPLE Problem 2
The unit for momentum is kg·m/s. Like velocity, momentum
has a size and a direction. An object’s momentum is always in
the same as the direction as its velocity. Table 3 shows the sizes
of the momentums of some common objects.
SC.912.P.12.2: Analyze the motion of an object in terms of its position, velocity, and acceleration
(with respect to a frame of reference) as functions of time. MA.912.S.1.2: Determine appropriate
and consistent standards of measurement for the data to be collected in a survey or experiment.
Solve for Momentum At the end of a race, a sprinter with a mass of 80.0 kg
has a velocity of 10.0 m/s east. What is the sprinter’s momentum?
Identify the Unknown:
momentum: p
List the Knowns:
mass: m = 80.0 kg
velocity: v = 10.0 m/s east
Set Up the Problem:
p = mv = (80.0 kg) × (10.0 m/s) east
Solve the Problem:
p = (80.0 kg)(10.0 m/s) east = 800.0 kg·m/s east
Check the Answer:
Our answer makes sense because it is greater than
the momentum of a walking person, but much
smaller than the momentum of a car on the highway.
PRACTICE Problems
Find Additional Practice Problems in the back of your book.
12. What is the momentum of a car with a mass of 1,300 kg traveling north at
a speed of 28 m/s?
Review
Additional Practice Problems
13. A baseball has a momentum of 6.0 kg·m/s south and a mass of 0.15 kg.
What is the baseball’s velocity?
14. Find the mass of a person walking west at a speed of 0.8 m/s with a
momentum of 52.0 kg·m/s west.
15. Challenge The mass of a basketball is three times greater than the mass of a
softball. Compare the momentums of a softball and a basketball if they
both are moving at the same velocity.
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Chapter 2 • Motion
0051_0055_C02S2_894583.indd 54
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30 m/s
30 m/s
900,000 kg·m/s
45,000 kg·m/s
30,000 kg
1,500 kg
■ Figure 14 Both the car and the
truck have a velocity of 30 m/s west,
but the truck has a much larger
momentum.
Comparing momentums Think about the car and the
truck in Figure 14. Which has the larger momentum? The
truck does because it has more mass. When two objects travel
at the same velocity, the object with more mass has a greater
momentum. A difference in momentums is why a car traveling
at 2 m/s might damage a porcelain vase, but an insect flying at
2 m/s will not.
Now consider two 1-mg insects. One insect flies at a speed of
2 m/s, and the other flies at a speed of 4 m/s. The second insect
has a greater momentum. If two objects have the same mass,
the object with the larger velocity has the larger momentum.
Section 2
Review
Section Summary
◗ The velocity of an object includes the
object’s speed and its direction of motion
relative to a reference point.
◗ An object’s motion is always described rel-
ative to a reference point.
◗ The momentum of an object is the product
of its mass and velocity: p = mv.
SC.912.P.12.2, MA.912.S.1.2
16.
Describe a car’s velocity as it goes around a track at a
constant speed.
MAIN Idea
17. Explain why streets and highways have speed limits rather than
velocity limits.
18. Identify For each of the following news stories, determine whether the object’s speed or velocity is given: the world record for the
hundred-meter dash is about 10 m/s; the wind today is 30 km/h
from the north-west; a 200,000 kg train was traveling north at
70 km/h when it derailed; a car was issued a ticket for traveling at
140 km/h on the interstate.
19. Think Critically You are walking toward the back of a bus that is
moving forward with a constant velocity. Describe your motion
relative to the bus and relative to a point on the ground.
Apply Math
20. Calculate Momentum What is the momentum of a 100-kg football
player running north at a speed of 4 m/s?
21. Compare the momentums of a 6,300-kg elephant walking 0.11 m/s
and a 50-kg dolphin swimming 10.4 m/s.
Assessment
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Online Quiz
Section 2 • Velocity and Momentum
55
5/3/10 12:21 PM
SC.912.P.12.2: Analyze the motion of an object in terms of its position, velocity, and acceleration (with respect to a
frame of reference) as functions of time. ALSO COVERS: SC.912.N.4.1, MA.912.S.1.2, MA.912.S.3.2
Section 3
Reading Preview
Acceleration
Essential Questions
MAIN Idea Acceleration describes how the velocity of an object
◗ How are acceleration, time, and
velocity related?
◗ What are three ways an object
can accelerate?
◗ How can an object’s acceleration
be calculated?
◗ What are the similarities and
differences between straight line
motion, circular motion, and
projectile motion?
Review Vocabulary
velocity: describes the speed and
direction of a moving object
New Vocabulary
acceleration
centripetal acceleration
g
Multilingual eGlossary
Video
BrainPOP
is changing with time.
Real-World Reading Link If you have ever ridden on an airplane, you
know that the plane taxis at a slow speed. Once on the runway, you are
pressed back against your seat as the plane speeds up until it is going fast
enough to take off. When the plane speeds up, it is accelerating.
Velocity and Acceleration
You are sitting in a car at a stoplight when the light turns
green. The driver steps on the gas pedal and the car starts
moving faster and faster. Just as speed is the rate of change of
position, acceleration is the rate of change of velocity. When
the velocity of an object changes, the object is accelerating.
Remember that velocity includes the speed and direction of
an object. Therefore, a change in velocity can be either a change
in speed or a change in direction. Acceleration occurs when an
object changes its speed, its direction, or both.
When you think of acceleration, you probably think of
something speeding up. However, an object that is slowing
down also is accelerating, as is an object that is changing direction. Figure 15 shows the three ways an object can accelerate.
Reading Check Identify three ways that an object can accelerate.
Figure 15 An object, such as this
car, is accelerating if it is speeding up,
slowing down, or changing direction.
■
Acceleration
Like velocity and momentum, acceleration has a direction.
If you look at the car in Figure 15, you will see that when it is
speeding up, its acceleration and velocity are in the same
direction. When the car is slowing down, its acceleration is in
the opposite direction of its velocity. When the car changes
direction, the acceleration is not in the same direction or
opposite direction as the car’s velocity.
Acceleration
Velocity
Velocity
Velocity
Acceleration
Speeding Up
56
Slowing Down
Changing Direction
Chapter 2 • Motion
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■ Figure 16 For objects that are
speeding up and slowing down, the
slope of the line on a speed-time
graph is the acceleration.
Speed of Tamara’s Car
Moving at a
constant speed
Speed (km/h)
25
20
Slowing down at
a red light
10
0
1
Parking
Stopped at
red light
Pulling out
of driveway
5
0
Slowing down to
enter parking lot
Speeding up
15
Identify the time intervals when
Tamara’s car is not accelerating.
2
3
4
5
6
7
Time (min)
Speed-time graphs and acceleration When an
object travels in a straight line and does not change direction, a
graph of speed versus time can provide information about an
object’s acceleration. Figure 16 shows the speed-time graph of
Tamara’s car as she drives to the store. Just as the slope of a line
on a distance-time graph is the object’s speed, the slope of a
line on a speed-time graph is the object’s acceleration. For
example, when Tamara pulls out of her driveway, the car’s
acceleration is 0.33 km/min2, which is equal to the slope of the
line from t = 0 to t = 0.5 min.
Calculating acceleration Acceleration is the rate of
change in velocity. To calculate the acceleration of an object,
the change in velocity is divided by the length of the time interval over which the change occurred. The change in velocity is
final velocity minus the initial velocity. If the direction of
motion does not change and the object moves in a straight line,
the size of the change in velocity can be calculated from the
change in speed. Then, the acceleration of an object can be calculated from the following equation.
SC.912.P.12.2: Analyze the motion of an object in
terms of its position, velocity, and acceleration (with
respect to a frame of reference) as functions of time.
?
Procedure
1. Read the procedure and safety
2.
3.
4.
5.
acceleration
change in velocity (in meters/second)
time (in seconds)
vf - vi
_
a= t
= ____
In SI units, velocity has units of m/s and time has units of s,
so the SI unit of acceleration is m/s2. In some cases, your calculations will result in a negative acceleration. The negative sign
means in the opposite direction. For example, an acceleration of
−10 m/s2 north is the same as 10 m/s2 south.
MiniLab
Determine the Direction
of Acceleration
Acceleration Equation
(in meters/second2)
Inquiry
information, and complete the
lab form.
Tape a bubble level onto the
top of a laboratory cart and
center the bubble. Tie a string
to the front of the cart.
Pull the cart forward, and
observe the direction of the
motion of the bubble.
Move the cart at a constant
speed, and observe the direction of the motion of the
bubble.
Allow the cart to coast to a
stop, and observe the direction
of the motion of the bubble.
Analysis
1. Relate the motion of the bubble to the acceleration of the
cart.
2. Predict how the bubble would
move if you tie the string to the
back of the cart and repeat the
experiment in the opposite
direction. Try it.
Section 3 • Acceleration
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5/7/10 10:06 AM
SC.912.P.12.2: Analyze the motion of an object in terms of its position, velocity, and acceleration
(with respect to a frame of reference) as functions of time. MA.912.S.1.2: Determine appropriate
and consistent standards of measurement for the data to be collected in a survey or experiment.
EXAMPLE Problem 3
Calculate Acceleration A skateboarder has an initial velocity of 3 m/s west and
comes to a stop in 2 s. What is the skateboarder’s acceleration?
Identify the Unknown:
acceleration: a
List the Knowns:
initial velocity: v i = 3 m/s west
final velocity: v f = 0 m/s west
time: t = 2 s
(v - v )
Set Up the Problem:
(0 m/s - 3 m/s)
f
i
a=_
= __ west
t
Solve the Problem:
(0 m/s - 3 m/s)
a = __
= -1.5 m/s2 west
2s
2s
The acceleration has a negative sign, so the direction
is reversed.
a = 1.5 m/s2 east
Check the Answer:
PRACTICE Problems
The magnitude of the acceleration (1.5 m/s2) is
reasonable for a skateboard that takes 2 s to slow
from 3 m/s to 0 m/s. The acceleration is in the
opposite direction of the velocity, so the skateboard
is slowing down, as we expected.
Find Additional Practice Problems in the back of your book.
22. An airplane starts at rest and accelerates down the runway for 20 s. At the
end of the runway, its velocity is 80 m/s north. What is its acceleration?
Review
Additional Practice Problems
23. A cyclist starts at rest and accelerates at 0.5 m/s2 south for 20 s. What is
the cyclist’s final velocity?
24. Challenge A ball is dropped and falls with an acceleration of 9.8 m/s2
downward. It hits the ground with a velocity of 49 m/s downward. How long
did it take the ball to fall to the ground?
Motion in Two Dimensions
So far, we have only discussed motion in a straight line. But
most objects are not restricted to moving in a straight line.
Recall that we cannot add measurements that are not in the
same or opposite directions. So, we will discuss motion in each
direction separately. For example, suppose a student walked
three blocks north and four blocks east. The trip could be
described this way: the student walked north for three blocks
at 1 m/s and then walked east for four blocks east at 2 m/s.
Recall that objects that change direction are accelerating.
For an object that is changing direction, its acceleration is not
in the same or opposite direction as its velocity. This means
that we cannot use the acceleration equation. Just as with displacement and velocity, accelerations that are not in the same
or opposite directions cannot be directly combined.
58
Chapter 2 • Motion
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5/7/10 10:07 AM
Circular motion Think about a horse’s horizontal motion
on a carousel, such as the one in Figure 17. The horse moves in
a circular path. Its speed remains constant, but it is accelerating
because its direction of motion changes. The change in the
direction of the horse’s velocity is toward the center of the
carousel. The horse’s velocity is perpendicular to the inward
acceleration. Acceleration toward the center of a curved or circular path is called centripetal acceleration. In the same way,
Earth experiences centripetal acceleration as it orbits the Sun in
a nearly circular path.
Reading Check Define the term centripetal acceleration.
Projectile motion If you have tossed a ball to someone,
you have probably noticed that thrown objects do not travel in
straight lines. They curve downward. That is why quarterbacks,
dart players, and archers aim above their targets. Anything that
is thrown or shot through the air is called a projectile. Earth’s
gravity causes projectiles to follow a curved path.
■
Figure 17 The horizontal speed of
the horses in this carousel is constant,
but the horses are accelerating because
their direction is changing constantly.
The acceleration of each horse is toward
the center of the circular carousel.
Horizontal and vertical motion When you throw or shoot an
object, such as the rubber band in Figure 18, the force exerted by
your hand gives the object a horizontal velocity. For example,
after releasing the rubber band, its horizontal velocity is constant. The rubber band does not accelerate horizontally. If there
were no gravity, the rubber band would move along the straight
dotted line in Figure 18.
However, when you release a rubber band, gravity causes it
to accelerate downward. The rubber band has an increasing
vertical velocity. The result of these two motions is that the
rubber band travels in a curve, even though its horizontal and
vertical motions are completely independent of each other.
vh = 2.0 m/s
VOCABULARY
ACADEMIC VOCABULARY
Constant
not varying or changing over time; a
quantity that does not vary
The constant hum of the fan made it
difficult to sleep.
vh = 2.0 m/s
vv = 0.0 m/s
vh = 2.0 m/s
vv = 0.5 m/s
vv = 1.0 m/s
■ Figure 18 The student gives the
rubber band a horizontal velocity. The
horizontal velocity of the rubber band
remains constant, but gravity causes
the rubber band to accelerate downward. The combination of these two
motions causes the rubber band to
move in a curved path.
Section 3 • Acceleration
0056_0060_C02S3_894583.indd 59
59
5/7/10 10:07 AM
Throwing and dropping If you were to throw a ball as hard as
you could in a perfectly horizontal direction, would it take longer to reach the ground than if you dropped a ball from the
same height? Surprisingly, it will not. A thrown ball and a
dropped ball will hit the ground at the same time. Both balls in
Figure 19 travel the same vertical distance in the same amount
of time. However, the ball thrown horizontally travels a greater
horizontal distance than the ball that is dropped.
■
Figure 19 The dropped ball and
the thrown ball in this multiflash photograph have the same downward
acceleration.
Concepts in Motion
Animation
Section 3
Amusement park acceleration Riding roller coasters
in amusement parks can give you the feeling of danger, but
these rides are designed to be safe. Engineers use the laws of
physics to design amusement park rides that are thrilling but
harmless. Roller coasters are constructed of steel or wood.
Because wood is not as strong as steel, wooden roller coasters
do not have hills that are as high and as steep as some steel
roller coasters have.
The highest speeds and accelerations are usually produced
on steel roller coasters. Steel roller coasters can offer multiple
steep drops and inversion loops, which give the rider large
accelerations. As riders move down a steep hill or an inversion
loop, they will accelerate toward the ground due to gravity.
When riders go around a sharp turn, they are also accelerated.
This acceleration makes them feel as if a force is pushing them
toward the side of the car.
Review
Section Summary
◗ Acceleration is the rate of change of
velocity.
◗ The speed of an object increases if the
acceleration is in the same direction as the
velocity.
◗ The speed of an object decreases if the
acceleration and the velocity of the object
are in opposite directions.
◗ If an object is moving in a straight line, the
size of the change in velocity equals the
final speed minus the initial speed.
◗ Acceleration toward the center of a curved
or circular path is called centripetal
acceleration.
SC.912.P.12.2, MA.912.S.1.2
25.
MAIN Idea Describe the acceleration of your bicycle as you ride it
from your home to the store.
26. Determine the change in velocity of a car that starts at rest and
has a final velocity of 20 m/s north.
27. Describe the motion of an object that has an acceleration of 0 m/s2.
28. Think Critically Suppose a car is accelerating so that its speed is
increasing. First, describe the line that you would plot on a speedtime graph for the motion of the car. Then describe the line that
you would plot on a distance-time graph.
Apply Math
29. Calculate Time A ball is dropped from a cliff and has an acceleration of 9.8 m/s2. How long will it take the ball to reach a speed
of 24.5 m/s?
30. Calculate Speed A sprinter leaves the starting blocks with an acceleration of 4.5 m/s2. What is the sprinter’s speed 2 s later?
60
Chapter 2 • Motion
0056_0060_C02S3_894583.indd 60
Assessment
Online Quiz
5/7/10 10:07 AM
LAB
Motion Graphs
SC.912.P.12.2: Analyze the motion of an object in terms of its position, velocity, and acceleration (with respect to a
frame of reference) as functions of time. MA.912.S.3.2: Collect, organize, and analyze data sets, determine the best
format for the data and present visual summaries from the following: bar graphs, line graphs, stem and leaf plots,
circle graphs, histograms, box and whisker plots, scatter plots, cumulative frequency (ogive) graphs.
Objectives
n Measure the position of a moving object.
n Create a distance-time graph.
n Use a distance-time graph to explain how an
object is changing speeds.
Background: Cars are equipped with speedometers that allow the driver to monitor the car’s speed.
Toy cars, however, do not have speedometers. How
would you determine the speed of a toy car? In this
activity, you will graph the motion of a toy car. Your
distance-time graph will allow you to determine
whether the toy car is speeding up, slowing down, or
moving at a constant speed.
Question: How is the changing speed of an object
represented on a distance-time graph?
Preparation
6. Use the camera to record a video of the toy car’s
motion.
7. Set the camera to play the video frame by frame.
Replay the video for 0.5 s, stopping to take a
measurement every 0.1 s.
8. Determine the toy car’s position for each 0.1 s
time interval by reading the meterstick in the
video. Record it in the data table.
Materials
Conclude and Apply
camera with video capabilities
windup toy car
meterstick
1. Draw a distance-time graph for the toy car using
the data that you collected.
2. Calculate the toy car’s speed for each interval.
3. Rank the speeds of each 0.1 s interval. On your
graph, label the fastest as 1 and the slowest as 5.
4. Identify when the toy car’s speed increased,
decreased, and remained constant. (Hint: How
does the slope of the line change between intervals?)
5. Infer how you might use a distance-time graph
to check that a car’s speedometer is working.
Safety Precautions
Procedure
1. Read the procedure and safety information, and
complete the lab form.
2. Make a data table to record the position and
speed of the toy car every 0.1 s.
3. Mark a starting line on the lab table or the surface recommended by your teacher.
4. Place a meterstick parallel to the path that the toy
car will take. Have one of the members of your
group get ready to operate the camera.
5. Place the toy car at the starting line.
?
Inquiry
0061_0063_C02L1_894583.indd 61
Lab
YOUR DATA
Compare your graph to those made by your
classmates. Discuss possible reasons why the
graphs might be different.
Chapter 2 • Lab
61
5/7/10 10:09 AM
LAB
The Momentum of Colliding Objects
SC.912.P.12.2: Analyze the motion of an object in terms of its position, velocity, and acceleration (with respect to a
frame of reference) as functions of time. MA.912.S.1.2: Determine appropriate and consistent standards of
measurement for the data to be collected in a survey or experiment. MA.912.S.3.2: Collect, organize, and analyze
data sets, determine the best format for the data and present visual summaries from the following: bar graphs, line
graphs, stem and leaf plots, circle graphs, histograms, box and whisker plots, scatter plots, cumulative frequency
(ogive) graphs.
Objectives
Safety Precautions
n Observe and calculate the momentum of
different balls.
n Compare the results of collisions involving
different amounts of momentum.
Background: In bowling, the ball’s momentum
is very important. The bowler must ensure that
the ball will travel toward the pins and not into
the gutter. The size of the momentum also matters. If the momentum is too small, the ball will
knock over very few pins.
Question: How do the mass and velocity of a
moving object affect its momentum?
Preparation
Materials
meterstick
softball
tennis ball
masking tape
trough
62
Chapter 2 • Motion
0061_0063_C02L1_894583.indd 62
stopwatch
racquetball
baseball
balance
Procedure
Make a Plan
1. Read the procedure and safety information, and
complete the lab form.
2. Copy the data table.
3. Use the balance to measure the mass of the
racquetball, tennis ball, and baseball. Record
these masses in your data table.
4. Measure a 2-m distance on the floor, and mark it
with two pieces of masking tape. Arrange the
trough so that it begins at one line of tape and
extends about a meter beyond the other line
of tape.
5. Place the softball in the trough over the piece of
tape. Starting from the other piece of tape, slowly
roll the racquetball along the trough toward the
softball.
?
Inquiry
Lab
5/7/10 10:09 AM
Data Table
Action
Time
Velocity
Mass
Momentum
Distance Softball Moved
Racquetball rolled slowly
Racquetball rolled quickly
Tennis ball rolled slowly
Tennis ball rolled quickly
Baseball rolled slowly
Baseball rolled quickly
6. Use a stopwatch to time how long it takes the
racquetball to roll the 2-m distance and hit the
softball. Record this time in your data table.
7. Measure and record the distance that the softball moved.
8. Repeat steps 5–7, rolling the racquetball quickly.
9. Repeat steps 5–7, rolling the tennis ball slowly
and then quickly.
10. Repeat steps 5–7, rolling the baseball slowly and
then quickly.
Concllud
de and
d Apply
Apply
Conclude
1. Infer from your graph how the distance that the
softball moves after each collision depends on
the momentum of the ball that hits it.
2. Describe How do an object’s velocity and mass
affect the amount of momentum that it has?
3. Explain why bowling balls have such a large
mass. What would happen if you tried to bowl
with a table tennis ball? Explain.
4. Infer When you bowl, should you roll the ball
gently? Explain.
Analyze Your Data
1. Calculate the momentum of the rolled ball for
each trial using the formula p = mv. Record
your calculations in the data table.
2. Graph the relationship between the momentum
of each ball and the distance that the softball
moved. The x-axis should be momentum
(kg·m/s), and the y-axis should be distance (m).
YOUR DATA
Make a Graph As a class, make a momentumdistance graph using data from everyone in
the class. Discuss how this graph is similar
to and different from the graphs made by
individual groups.
Chapter 2 • Lab
0061_0063_C02L1_894583.indd 63
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5/7/10 10:09 AM
No Driver?
No Worries!
SC.912.P.12.2: Analyze the motion of an object in terms of its position,
velocity, and acceleration (with respect to a frame of reference) as
functions of time. SC.912.N.4.1: Explain how scientific knowledge and
reasoning provide an empirically-based perspective to inform society’s
decision making.
he diesel-powered car nicknamed Stanley
faced a difficult mission—drive more than
200 km across the Mojave Desert in less
than ten hours, navigating narrow tunnels, dozens of sharp turns, and a winding mountain pass
with sheer drops on each side. The real challenge? Stanley, shown in Figure 1, was not
allowed to have a driver.
T
Grand challenge
This was the setting for the
2005 DARPA (Defense Advanced Research
Projects Agency) Grand Challenge, a competition
won by Stanley and the Stanford Racing Team.
The competition was part of an ongoing effort to
develop autonomous ground vehicles—vehicles
that drive and navigate without a remote control
or a human driver. Using autonomous vehicles in
combat situations keeps soldiers off the battlefield
and protects lives.
Physics at the wheel
How can a car drive
itself? To drive safely, it must interpret the environment, evaluate its position relative to the
destination, navigate obstacles, and control speed
and direction of motion. Light beams emitted by
lasers and radio waves given off by a radar unit
bounce off surrounding objects and geographical
features. Reflection times determine distances
between the car and these objects and help evaluate changes in position and terrain.
Additional position data is provided by the Global
Positioning System (GPS) and sensors that measure wheel rotation and direction of motion.
Stanley’s sophisticated computer integrates all
incoming data, compares it to a map of the route,
and makes necessary adjustments in steering,
throttling, and braking.
64
Figure 1 Stanley, an autonomous vehicle
designed by a team from Stanford University,
won the 2005 DARPA Grand Challenge.
Eliminating dangerous driving
Is this technology useful in the civilian world? Human drivers
face many distractions. Factors like cell phone use
and unexpected traffic situations contribute to
almost 40,000 deaths in U.S. traffic accidents each
year. But autonomous cars would not be distracted
and could make rapid course and speed adjustments and reduce accidents.
Participants in the 2007 DARPA Urban Challenge
proved that autonomous cars could function in a
city setting. This competition required complex
maneuvers like merging into traffic, parking,
negotiating stop signs, and rerouting around
unexpected roadblocks. Ultimately, cars like
Stanley could save lives on the battlefield and in
our communities.
WebQuest
Design an Advertisement
Brainstorm the potential benefits of using
automated cars in a city setting. Use your
ideas to design a poster to advertise an
automated car service. Share your poster
with the class.
Chapter 2 • Motion
0064_C02ITF_894583.indd 64
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2
THEME FOCUS Motion and Forces
The motion of an object can be described by the distance it travels, its displacement, speed, velocity,
momentum, and acceleration.
BIG Idea Motion occurs when an object changes its position.
Section
n 1 Describing Motion
displacement (p. 45)
motion (p. 44)
speed (p. 46)
MAIN Idea Position describes where an object is, and speed
describes how fast the object is moving.
• Motion occurs when an object changes its position relative to a
reference point.
• Displacement is the distance and direction of a change in position
from the starting point.
• Speed is the rate at which an object’s position changes.
• On a distance-time graph, time is the x-axis and distance is y-axis.
• The slope of a line plotted on a distance-time graph is the speed.
Section
n 2 Velocity and Momentum
momentum (p. 54)
velocity (p. 51)
MAIN Idea An object’s velocity describes the object’s speed and
direction of motion.
• The velocity of an object includes the object’s speed and its direction
of motion relative to a reference point.
• An object’s motion is always described relative to a reference point.
• The momentum of an object is the product of its mass and velocity:
p = mv.
Section
n 3 Acceleration
acceleration (p. 56)
centripetal acceleration (p. 59)
Review
0065_C02SG_894583.indd 65
Vocabulary eGames
MAIN Idea
Acceleration describes how the velocity of an object
is changing with time.
• Acceleration is the rate of change of velocity.
• The speed of an object increases if the acceleration is in the same
direction as the velocity.
• The speed of an object decreases if the acceleration and the velocity of
the object are in opposite directions.
• If an object is moving in a straight line, the size of the change in
velocity equals the final speed minus the initial speed.
• Acceleration toward the center of a curved or circular path is called
centripetal acceleration.
Chapter 2 • Study Guide
65
5/3/10 12:19 PM
2
SC.912.P.12.2, MA.912.S.1.2
Use Vocabulary
Compare and contrast the following pairs of terms.
31. speed—velocity
32. motion—displacement
33. velocity—momentum
34. acceleration—velocity
Check Concepts
35. Which of the following do you calculate
when you divide the total distance traveled
by the total travel time?
A) average speed
B) constant speed
C) variable speed
D) instantaneous speed
36. Which of the following is the SI unit of
acceleration?
A) s/km2
B) km/h
C) m/s2
D) cm/s
37. Which of the following is not used in calcu-
lating acceleration?
A) initial velocity
B) average speed
C) time interval
D) final velocity
38. A car, a bicycle, a mouse, and a bug have
the same velocity. Which has the greatest
momentum?
A) the car
B) the bicycle
C) the mouse
D) the bug
66
Chapter 2 • Motion
0066_0067_C02CR_894583.indd 66
39. In which of the following conditions does
the car not accelerate?
A) A car moves at 80 km/h on a flat, straight
highway.
B) The car slows from 80 km/h to 35 km/h.
C) The car turns a corner.
D) The car speeds up from 35 km/h to
80 km/h.
40. How is speed defined?
A) acceleration/time
B) change in velocity/time
C) distance/time
D) displacement/time
41. Which best describes why projectiles move
in a curved path?
A) They have constant horizontal velocity
and vertical acceleration.
B) They have horizontal acceleration and
constant vertical velocity.
C) They have horizontal momentum and
constant vertical velocity.
D) They have horizontal acceleration and
vertical momentum.
Interpret Graphics
Use the table below to answer question 42.
Distance-Time for Runners
Time (s)
1
2
3
4
Sally’s distance (m)
2
4
6
8
Alonzo’s distance (m)
1
2
2
4
42. Make a distance-time graph that shows the
motion of both runners. What is the average
speed of each runner? Which runner stops
briefly? Over what time interval do they
both have the same speed?
Assessment
Online Test Practice
5/3/10 12:22 PM
2
43.
Copy and complete this
concept map on motion.
THEME FOCUS
Interactive Concept Map
Concepts in Motion
A pply Math
49. Calculate Speed A cyclist must travel
800 km. How many days will the trip take
if the cyclist travels 8 h/day at an average
speed of 16 km/h?
Motion
can be described by
50. Calculate Acceleration A satellite’s speed is
velocity
which is a
change in
position
which
includes
c.
d.
which equals
b.
which equals
change in
velocity
time
distance
time
Think Critically
44. Explain Why is knowing only a hurricane’s
speed not enough information to be able to
warn people to evacuate?
45. Evaluate Which of the following represents
the greatest speed: 20 m/s, 200 cm/s, or
0.2 km/s?
46. Recognize Acceleration can occur when a
car is moving at constant speed. What must
cause this acceleration?
47. BIG Idea Determine If you walked 20 m,
took a book from a table, and walked back
to your seat, what are the distance you
traveled and your displacement?
48. Explain When you are describing the rate
that a race car goes around a track, should
you use the term speed or velocity to describe
the motion?
Assessment
0066_0067_C02CR_894583.indd 67
Online Test Practice
5,000 m/s. After 1 min, it is 10,000 m/s.
What is the satellite’s acceleration?
51. Calculate Displacement A cyclist leaves
home and rides due east for a distance of
45 km. She returns home on the same
bike path. If the entire trip takes 4 h, what
is her average speed? What is her
displacement?
52. Calculate Velocity The return trip of the
cyclist in question 51 took 30 min longer
than her trip east, although her total time
was still 4 h. What was her velocity in each
direction?
Use the figure below to answer question 53.
Runners’ Motion
60
Distance (m)
a.
50
40
Runner #1
Runner #2
30
20
10
0
1
2
3
4
5
6
7
8
Time (s)
53. Interpret a Graph Use the graph to
determine which runner had the greater
speed.
54. Calculate Mass Find the mass of a car that
has a speed of 30 m/s and a momentum of
45,000 kg·m/s.
Chapter 2 • Review
67
5/3/10 12:22 PM
Standardized Test Practice
Multiple Choice
Record your answers on the answer sheet
provided by your teacher or on a sheet of paper.
1. If the speed of sound during a thunderstorm
is 330 m/s, how long does it take for the sound
SC.912.P.12.2
of thunder to travel 1485 m?
A. 45 s
C. 4900 s
B. 4.5 s
D. 0.22 s
Use the figure below to answer questions 2–4.
Speed Changing over Distance
30
5. A skier is going down a hill at a speed of
9 m/s. The hill gets steeper and her speed
increases to 18 m/s in 3 s. What is her
SC.912.P.12.2
acceleration?
2
2
A. 9 m/s
C. 27 m/s
2
B. 3 m/s
D. 6 m/s2
6. Which of the following best describes an
object with constant velocity?
A. It is changing direction.
B. Its acceleration is increasing.
C. Its acceleration is zero.
D. Its acceleration is negative.
SC.912.P.12.2
Speed (km/h)
25
Use the table below to answer questions 7–9.
20
Runner
15
Ling-Ling
LaToya
10
Bill
José
5
0
1
2
3
4
2. The graph shows how a cyclist’s speed
changed over a 0.25-h trip. What is the
SC.912.P.12.2
cyclist’s average speed?
A. 2 km/h
C. 20 km/h
B. 30 km/h
D. 8 km/h
3. Once the trip was started, how many times
SC.912.P.12.2
4. What was the fastest speed that the cyclist
traveled?
A. 20 km/h
B. 30 km/h
C. 12 km/h
D. 10 km/h
68
Standardized Test Practice
0068_0069_C02STP_894583.indd 68
Time (min)
10.5
8.9
42
38
32
30
5
Distance (km)
did the cyclist stop?
A. 0
C. 2
B. 4
D. 5
Distance
Covered (km)
12.5
7.8
SC.912.P.12.2
7. What is Ling-Ling’s average speed?
A. 0.3 km/min
C. 3.0 km/min
B. 530 km/min D. 3.4 km/min
SC.912.P.12.2
8. Which runner has the fastest average speed?
A. Ling-Ling
C. Bill
SC.912.P.12.2
B. LaToya
D. José
9. If all four runners have the same mass, who
has the smallest momentum?
A. Ling-Ling
C. Bill
B. LaToya
D. José
SC.912.P.12.2
10. The movement of the Australian plate pushes
Australia north at an average speed of about
17 cm per year. What will Australia’s
displacement be in meters in 1,000 years?
A. 170 m north C. 1,700 m north
B. 170 m south D. 1,700 m south SC.912.P.12.2
Assessment
Standardized Test Practice
5/3/10 12:18 PM
Short Response
Extended Response
Record your answers on the answer sheet
provided by your teacher or on a sheet of paper.
Record your answers on a sheet of paper.
14. Describe three ways that your velocity could
change as you jog along a park’s path.
Use the figure below to answer questions 11 and 12.
SC.912.P.12.2
Distance-Time Graph
2,400
15. Where would you place the location of a ref-
erence point in order to describe the motion
of a space probe traveling from Earth to
Jupiter? Explain your choice.
SC.912.P.12.2
2,200
2,000
1,800
Swimmer C
Distance (m)
1,600
16. Two cars approach each other. How does the
1,400
Swimmer B
speed of one car relative to the other compare with speed of each car relative to the
ground?
SC.912.P.12.2
1,200
1,000
800
Swimmer A
600
Use the figure below to answer question 17.
400
v = 13 m/s
200
0
10
20
30
Time (min)
11. The graph shows the motion of three swim-
mers during a 30-min workout. Which
swimmer had the highest average speed over
the 30-min time interval? Explain.
SC.912.P.12.2
17. Two balls are at the same height and released
12. Did all of the swimmers swim at a constant
speed? Explain how you know.
at the same time. One ball is dropped and
hits the ground 5 s later. The other initially
moves horizontally. When does the second
ball hit the ground? How far does it travel
SC.912.P.12.2
horizontally?
SC.912.P.12.2
13. If a car has a velocity of 40 km/h west and
then comes to a stop in 5 s, what is its accelSC.912.P.12.2
eration in m/s2?
NEED EXTRA HELP?
If You Missed
Question . . .
1
2
3
4
5
6
7
8
9
10
11
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17
Review Section . . .
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3
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Assessment
0068_0069_C02STP_894583.indd 69
Standardized Test Practice
Standardized Test Practice
69
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CHAPTER
3
Forces and Newton’s
Laws
Your one-stop online resource
connectED.mcgraw-hill.com
?
Video
WebQuest
Audio
Assessment
Review
Concepts in Motion
g
Inquiry
Multilingual eGlossary
Launch Lab
Force, Mass, and Acceleration
You have probably noticed that it is more difficult to lift a
bookbag containing three books than it is to lift a bookbag
containing one book. What effect does mass have on how
much force is needed to change an object’s motion?
For a lab worksheet, use your StudentWorks™ Plus Online.
?
Inquiry
Launch Lab
Make a three-tab book.
Label it as shown. Use it
to organize your notes on
Newton’s laws of motion.
1st law 2nd law 3rd law
of motion of motion of motion
Newton’s Laws
0070_0071_C03CO_894583.indd 70
5/3/10 11:49 AM
THEME FOCUS
Motion and Forces
Section 1 • Forces
Objects that interact exert forces on each other.
Section 2 • Newton’s Laws of
BIG Idea A force is a push or pull.
Motion
Section 3 • Using Newton’s Laws
Chapter 3 • Forces and Newton’s Laws
0070_0071_C03CO_894583.indd 71
71
5/3/10 11:50 AM
Section 1
SC.912.P.10.10: Compare the magnitude and range of the four fundamental forces (gravitational, electromagnetic,
weak nuclear, strong nuclear). SC.912.P.12.4: Describe how the gravitational force between two objects depends on
their masses and the distance between them. SC.912.N.1.6: Describe how scientific inferences are drawn from
scientific observations and provide examples from the content being studied. ALSO COVERS: MA.912.S.1.2.
Reading Preview
Forces
Essential Questions
MAIN Idea Unbalanced forces change motion.
◗ How are force and motion
Real-World Reading Link Have you ridden a bike down a steep hill?
You might have noticed that you went faster and faster or that you had to
brake very hard to stop the bike. In both cases, you and your bike were
accelerating. What caused that acceleration?
related?
◗ How is the net force on an object
determined?
◗ Why is there friction between
objects?
◗ What is the difference between
mass and weight?
Review Vocabulary
mass: amount of matter in an
object
New Vocabulary
force
net force
friction
gravity
field
weight
g
Multilingual eGlossary
What is force?
Catching a basketball and hitting a baseball with a bat are
examples of applying force to an object. A force is a push or a
pull. In both examples, the applied force changes the movement
of the ball. Sometimes, it is obvious that a force has been
applied. But other forces are not as noticeable. For instance, are
you conscious of the force that the floor exerts on your feet?
Can you feel the force of the atmosphere pushing against your
body or gravity pulling on your body? Think about all of the
forces that you exert in a day. Every push, pull, stretch, or bend
results in a force being applied to an object.
Changing motion What happens to the motion of an
object when you exert a force on it? A force can cause the
motion of an object to change. Think of kicking a soccer ball,
as shown in Figure 1. The player’s foot strikes the ball with a
force that causes the ball to stop and then move in the opposite
direction. If you have played billiards, you know that you can
force a ball at rest to roll into a pocket by striking it with
another ball. The force of the moving ball causes the ball at rest
to move in the direction of the force. In each case, the velocity
of the ball was changed by a force.
■ Figure 1 When the player kicks
the soccer ball, she is exerting a force
on the ball. This kick will cause the
ball’s motion to change.
72
Chapter 3 • Forces and Newton’s Laws
0072_0079_C03S1_894583.indd 72
5/7/10 9:59 AM
Net force When two or more forces act on an object at the
same time, the forces combine to form the net force. The net force
is the sum of all of the forces acting on an object. Forces have a
direction, so they follow the same addition rules as displacement,
as listed in Table 1. Forces are measured in the SI unit of newtons
(N). A force of about 3 N is needed to lift a full can of soda at a
constant speed.
Unbalanced forces Look at Figure 2A. The students are each
Table 1
Rules for
Adding Forces
1. Add forces in the same direction.
2. Subtract forces in opposite
directions.
3. Forces not in the same direction
or in opposite directions cannot
be directly added together.
pushing on the box in the same direction. These forces are
combined, or added together, because they are exerted on the
box in the same direction. The students in Figure 2B are pushing in opposite directions. Here, the direction of the net force
is the same as the direction of the larger force. In other words,
the student who pushes harder causes the box to move in the
direction of that push. The net force will be the difference
between the two forces because they are in opposite directions.
In Figure 2A and Figure 2B, the net force had a value that was
not zero and the box moved. The forces that the students
applied are considered unbalanced forces.
?
Inquiry
Video Lab
Balanced forces Now suppose that the students were pushing
with the same size force but in opposite directions, as shown in
Figure 2C. The net force on the box is zero because the two
forces cancel each other. Forces on an object that are equal in
size and opposite in direction are called balanced forces.
Unbalanced forces cause changes in motion. Balanced forces do
not cause a change in motion.
+
=
Net Force =
[A] These students are pushing
on the box in the same direction.
These forces are unbalanced. The
net force is the sum of the two
forces, and the box will move in the
direction that the students push.
+
=
Net Force =
[B] These students are pushing on the
box with unequal forces in opposite directions. These forces are unbalanced.
The net force is the difference of the two
forces, and the box will move in the direction of the larger force.
■
Figure 2 Forces can be balanced or
unbalanced.
Identify another example of
unbalanced forces and another
example of balanced forces.
+
= 0
Net Force = 0
[C] These students are pushing on the
box with equal forces but in opposite directions. These forces are balanced. The net
force is zero and the box does not move.
Section 1 • Forces
0072_0079_C03S1_894583.indd 73
73
5/7/10 9:59 AM
Friction
Suppose you give a skateboard a push with your hand. After
you let go, the skateboard slows down and eventually stops.
Because the skateboard’s motion is changing as it slows down,
there must be a force acting on it. The force that slows the
skateboard is called friction. Friction is the force that opposes
the sliding motion of two surfaces that are touching each other.
What causes friction? Would you believe that the surface of a highly polished piece of metal is rough? Surfaces that
appear smooth actually have many bumps and dips. These
bumps and dips can be seen when the surface is examined
under a microscope, as shown in Figure 3. If two surfaces are
in contact, welding or sticking occurs where the bumps touch
each other. These microwelds are the source of friction. To
move one surface over the other, a force must be applied to
break the microwelds.
Reading Check Describe the source of friction.
■
Figure 3 The surface of this tea-
pot looks and feels smooth, but it is
rough at the microscopic level.
The amount of friction between two surfaces depends on the
kinds of surfaces and the force pressing the surfaces together.
Rougher surfaces have more bumps and can form more microwelds, increasing the amount of friction. In addition, a larger
force pushing the two surfaces together will cause more of the
bumps to come into contact, as shown in Figure 4. The microwelds will be stronger, and a greater force must be applied to
the object to break the microwelds.
Static friction Suppose you have a cardboard box filled
with books, such as the one in Figure 5, and want to move that
box. The box is resting on what seems to be a smooth floor, but
when you push on the box, it does not budge. The box experiences no change in motion, so the net force on the box is zero.
The force of friction cancels your push.
More
force
Force
■ Figure 4 Friction is caused by
microwelds that form between two
surfaces. Microwelds are stronger
when the two surfaces are pushed
together with a larger force.
Explain how the area of contact
Surfaces
Microwelds form where
bumps come into contact.
Same two
surfaces
More force presses the
bumps closer together.
between the surfaces changes when
they are pushed together.
74
Chapter 3 • Forces and Newton’s Laws
0072_0079_C03S1_894583.indd 74
5/7/10 9:59 AM
Applied force
Applied force
Static friction
Sliding friction
Static friction balances the applied force. The box remains at
rest and does not accelerate.
Sliding friction and the applied force are unbalanced. The box
accelerates to the right.
This type of friction is called static friction. Static friction
prevents two surfaces from sliding past each other and is due to
the microwelds that have formed between the bottom of the
box and the floor. Your push is not large enough to break the
microwelds, and the box does not move, as shown in Figure 5.
Sliding friction If you and a friend push together, as
shown on the right in Figure 5, the box moves. Together, you
and your friend have exerted enough force to break the
microwelds between the floor and the bottom of the box. But if
you stop pushing, the box quickly comes to a stop. To keep the
box moving, you must continually apply a force. This is because
sliding friction opposes the motion of the box as the box slides
across the floor. Sliding friction opposes the motion of two surfaces sliding past each other and is caused by microwelds constantly breaking and forming as the objects slide past each
other. The force of sliding friction is usually smaller than the
force of static friction.
Rolling friction You may think of friction as a disadvantage. But wheels, like the ones shown in Figure 6, would not
work without friction. As a wheel rolls, static friction acts over
the area where the wheel and surface are in contact. This special case of static friction is sometimes called rolling friction.
You may have seen a car that was stuck in snow, ice, or mud.
The driver steps on the gas, but the wheels just spin without the
car moving. The force used to rotate the tires is larger than the
force of static friction between the wheels and the ground, so
the tires slide instead of gripping the ground. Spreading sand
or gravel on the surface increases the friction until the wheels
stop slipping and begin rolling. When referring to tires on
vehicles, people often use the term traction instead of friction.
■ Figure 5 Friction opposes the
sliding motion of two surfaces that are
touching each other.
Describe the net force on each box.
VOCABULARY
WORD ORIGIN
Friction
from the Latin fricare meaning
“to rub”
Oil can be used to reduce friction.
■ Figure 6 Rolling friction
between the in-line skate’s wheels
and the pavement keeps the
wheels from slipping.
Rolling
friction
Wheel
rotation
Section 1 • Forces
0072_0079_C03S1_894583.indd 75
75
5/7/10 9:59 AM
Gravity
?
Inquiry
MiniLab
Compare Friction and
Gravity
Procedure
1. Read the procedure and safety
information, and complete the
lab form.
2. Place an ice cube, a rock, an
eraser, a wood block, and a
square of aluminum foil at
one end of a metal or plastic
tray.
3. Slowly lift the end of the tray
with the items.
4. Have a partner use a metric
ruler to measure the height of
the raised end of the tray at
which each object begins to
slide. Record the measurements.
Analysis
1. Create a table and include the
height at which each object
began to slide.
2. Infer Which item experienced
the greatest frictional force?
How do you know?
3. Identify the force that caused
the objects to slide.
At this moment, you are exerting an attractive force on
everything around you—your desk, your classmates, and even
the planet Jupiter, millions of kilometers away. This attractive
force acts on all objects with mass and is called gravity. Gravity
is an attractive force between any two objects that depends on
the masses of the objects and the distance between them.
Gravity is one of the four basic forces. These forces are called
the fundamental forces. The other basic forces are the electromagnetic force, the strong nuclear force, and the weak nuclear
force. Gravity acts on all objects with mass, and the electromagnetic force acts on all charged particles. Both gravity and
the electromagnetic force have an infinite range. The nuclear
forces only affect particles in the nuclei of atoms.
The law of universal gravitation In the 1660s, British
scientist Isaac Newton used data on the motions of the planets
to find the relationship between the gravitational force between
two objects, the objects’ masses, and the distance between
them. This relationship is called the law of universal gravitation
and can be written as the following equation.
mm
d
1 2
F = G_
2
In this equation, G is the universal gravitational constant,
and d is the distance between the centers of the two masses, m 1
and m 2. The law of universal gravitation states that the gravitational force increases as the mass of either object increases and
as the objects move closer, as shown in Figure 7. The force of
gravity between any two objects can be calculated if their
masses and the distance between them are known.
SC.912.P.12.4: Describe how the gravitational
force between two objects depends on their masses
and the distance between them.
■ Figure 7 The law of universal
gravitation states that the gravitational force between two objects depends
on their masses and the distance
between them.
76
If the mass of either of the objects
increases, the gravitational force
between them increases.
If the objects are closer together, the
gravitational force between them
increases.
Chapter 3 • Forces and Newton’s Laws
0072_0079_C03S1_894583.indd 76
5/7/10 10:00 AM
Gravity and you The law of universal gravitation explains why
you feel Earth’s gravity but not the Sun’s gravity or this book’s
gravity. While the Sun has much more mass than Earth, the
Sun is too far away to exert a noticeable gravitational attraction
on you. And while this book is close, it does not have enough
mass to exert an attraction that you can feel. Only Earth is both
close enough and has a large enough mass that you can feel its
gravitational attraction.
Review
Additional Practice Problems
The range of gravity According to the law of universal gravi-
tation, the gravitational force between two masses decreases
rapidly as the distance between the masses increases. For
example, if the distance between two objects increases from
1 m to 2 m, the gravitational force between them becomes onefourth as large. If the distance increases from 1 m to 10 m, the
gravitational force between the objects is one-hundredth as
large. However, no matter how far apart two objects are, the
gravitational force between them never completely goes to
zero. Because the gravitational force between two objects never
disappears, gravity is called a long-range force.
Reading Check Explain why gravity is called a long-range force.
The gravitational field Because contact between objects is not
required, gravity is sometimes discussed as a field. A field is a
region of space that has a physical quantity (such as a force) at
every point. All objects are surrounded by a gravitational field.
Figure 8 shows that Earth’s gravitational field is strongest near
Earth and becomes weaker as the distance from Earth increases.
The strength of the gravitational field, represented by the letter g,
is measured in newtons per kilogram (N/kg).
_
g = 9.8 N
kg
_
g = 0.98 N
kg
_
g = 4.9 N
kg
_
g = 7.4 N
kg
_
g = 2.5 N
kg
■
Figure 8 Earth’s gravitational field
exists at all points in space. It is strongest
near the surface and decreases in
strength as one moves away from Earth.
Section 1 • Forces
0072_0079_C03S1_894583.indd 77
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5/7/10 10:00 AM
Weight The gravitational force exerted on an object is the
object’s weight. The universal law of gravitation can be used to
calculate weight, but scientists use a simplified version of this
equation that combines m 1, d 2, and G into a single number
called the gravitational strength, g.
Weight of
Common
Table 2
Objects on
Earth
Object
Weight
Cell phone
Backpack full of
books
Jumbo jet
Weight Equation
1N
weight (N) = mass (kg) × gravitational strength (N/kg)
F g = mg
100 N
3.4 million N
We use Fg for weight because weight is the force due to gravity. Weight has units of newtons (N) because it is a force. The g
in the subscript stands for gravity. The gravitational strength, g,
has the units N/kg. Recall that 1 N = 1 kg ∙ m/s2. So, g can also
be written with units of m/s2.
Weight and mass Weight and mass are not the same. Weight
is a force, and mass is a measure of the amount of matter an
object contains. But, according to the weight equation, weight
and mass are related. Weight increases as mass increases.
SC.912.P.12.4: Describe how the gravitational
force between two objects depends on their masses
and the distance between them. MA.912.S.1.2:
Determine appropriate and consistent standards of
measurement for the data to be collected in a
survey or experiment.
Weight on Earth We often need to know an object’s weight on
Earth. Near Earth’s surface, m 1, from the law of universal gravitation, is Earth’s mass and d is Earth’s radius. As a result,
g = 9.8 N/kg. Table 2 lists the weights of some objects on Earth.
EXAMPLE Problem 1
Solve for Weight An elephant has a mass of 5,000 kg. What is the elephant’s weight?
Identify the Unknown:
weight: F g
List the Knowns:
mass: m = 5,000 kg
gravitational strength: g = 9.8 N/kg
Set Up the Problem:
F g = mg
Solve the Problem:
F g = (5,000 kg)(9.8 N/kg) = 49,000 N
Check the Answer:
The gravitational strength is about 10 N/kg, so we
would expect the elephant’s weight to be about
50,000 kg. Our answer (F g = 49,000 N) makes sense.
PRACTICE Problems
Find Additional Practice Problems in the back of your book.
1. A squirrel has a mass of 0.5 kg. What is its weight?
2. A boy weighs 400 N. What is his mass?
Review
Additional Practice Problems
3. Challenge An astronaut has a mass of 100 kg and has a weight of 370 N on
Mars. What is the gravitational strength on Mars?
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Weight away from Earth An object’s weight usually refers to
the gravitational force between the object and Earth. But the
weight of an object can change, depending on the gravitational
force on the object. For example, the gravitational strength on
the Moon is 1.6 N/kg, about one-sixth as large as Earth’s gravitational strength. As a result, a person, such as the astronaut in
Figure 9, would weigh only about one-sixth as much on the
Moon as on Earth.
Finding other planets Earth’s motion around the Sun
is affected by the gravitational pulls of the other planets in the
solar system. In the same way, the motion of every planet in
the solar system is affected by the gravitational pulls of all of
the other planets.
In the 1840s, the most distant planet known was Uranus.
The motion of Uranus calculated from the law of universal
gravitation disagreed slightly with its observed motion. Some
astronomers suggested that there must be an undiscovered
planet affecting the motion of Uranus. Using the law of universal gravitation and the laws of motion, two astronomers
independently calculated the orbit of this planet. As a result of
these calculations, the planet Neptune was found in 1846.
Section 1
Review
Section Summary
◗ A force is a push or a pull on an object.
◗ The net force on an object is the combina-
tion of all of the forces acting on the
object.
◗ Unbalanced forces cause the motion of
objects to change.
◗ Friction is the force that opposes the slid-
ing motion of two surfaces that are in
contact.
◗ Gravity is an attractive force between all
objects that have mass.
■ Figure 9 Although the astronaut has the same mass on the
Moon, he weighs less than he does
on Earth. He can take longer steps
and jump higher than on Earth.
SC.912.P.12.4, MA.912.S.1.2
4.
Describe two forces that would change the motion of a
bicycle traveling along a road.
MAIN Idea
5. Explain Can there be forces acting on an object if the object is at
rest? Must there be an unbalanced force acting on a moving
object? Explain your answers.
6. Explain Why does coating surfaces with oil reduce friction
between the surfaces?
7. Distinguish between the mass of an object and the object’s weight.
8. Think Critically Suppose Earth’s mass increased but Earth’s diameter did not change. How would the gravitational strength near
Earth’s surface change?
Apply Math
9. Calculate Weight On Earth, what is the weight of a large-screen TV
that has a mass of 75 kg?
10. Calculate Net Force Two students push on a box in the same direction, and one student pushes in the opposite direction. What is the
net force on the box if each student pushes with a force of 50 N?
Assessment
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Online Quiz
Section 1 • Forces
79
5/7/10 10:00 AM
Section 2
SC.912.P.12.3: Interpret and apply Newton’s three laws of motion. ALSO COVERS: MA.912.S.1.2
Reading Preview
Newton’s Laws of Motion
Essential Questions
MAIN Idea Newton’s laws of motion relate the change in an
◗ What is inertia and how is it
related to Newton’s first law of
motion?
◗ How can an object’s acceleration
be calculated using Newton’s
second law of motion?
◗ According to Newton’s third law
of motion, how are the forces
between interacting objects
related?
Review Vocabulary
acceleration: rate of change of
velocity
New Vocabulary
Newton’s first law of motion
inertia
Newton’s second law of motion
Newton’s third law of motion
g
Multilingual eGlossary
Video
BrainPOP
■ Figure 10 You might have seen
the law of inertia without even
knowing it. For example, as the car hits
the block and stops, the red block
continues to move forward.
Describe another example of inertia.
80
object’s motion with the forces acting on it.
Real-World Reading Link Suppose you try to push a wagon and a car
with the same amount of force. How will their motions be different?
Newton’s laws of motion describe how the wagon and the car will move.
Isaac Newton and the Laws of Motion
In 1665, Cambridge University in Britain closed for
18 months because of the bubonic plague. Isaac Newton, a
23-year-old student, used this time to develop the law of universal gravitation, calculus, and three laws describing how
forces affect the motion of objects. Newton’s laws of motion
apply to the motion of everyday objects, such as cars and bicycles, as well as the motion of planets and stars.
Newton’s First Law of Motion
Recall that forces change an object’s motion. Newton’s first
law explains the relationship between force and change in
motion. Newton’s first law of motion states that an object
moves at a constant velocity unless an unbalanced force acts on
it. This means that a moving object will continue to move in a
straight line at a constant speed unless an unbalanced force acts
on it. If an object is at rest, its velocity is zero and it stays at rest
unless an unbalanced force acts on it.
Inertia Newton’s first law is sometimes called the law of
inertia. Inertia (ih NUR shuh) is the tendency of an object to
resist any change in its motion. Figure 10 shows a toy car hitting a block and stopping. The block on top of the car is not
attached to the car and keeps traveling. The block’s forward
motion demonstrates the property of inertia.
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Inertia and mass Does a bowling ball have the same inertia as
a table-tennis ball? Why is there a difference? You could not
change the motion of a bowling ball much by swatting it with a
table-tennis paddle. But you could easily change the motion of
the table-tennis ball. A greater force would be needed to change
the motion of the bowling ball because it has greater inertia.
Recall that mass is the amount of matter in an object. An
object’s inertia is related to its mass. The greater an object’s
mass is, the greater its inertia is. A bowling ball has more mass
than a table-tennis ball has, so the bowling ball has a greater
inertia.
You will sometimes hear people say that when an object
begins to move, inertia is overcome. This is not true. The object
still has mass when it is moving, so it still has inertia. As long
as the mass is the same, the object has the same inertia.
Newton’s Second Law of Motion
Newton’s first law of motion states that the motion of an
object changes only if an unbalanced force acts on the object.
Newton’s second law of motion describes how the forces
exerted on an object, its mass, and its acceleration are related.
Force and acceleration How are throwing a ball as hard
as you can and tossing it gently different? When you throw
hard, you exert a greater force on the ball. The ball has a greater
velocity when it leaves your hand. The hard-thrown ball has a
greater change in velocity, and the change occurs over a shorter
period of time. Recall that acceleration equals the change in
velocity divided by the time it takes for the change to occur. So,
a hard-thrown ball is accelerated more than a gently thrown
ball, as shown in Figure 11.
?
Inquiry
MiniLab
Observe Inertia
Procedure
1. Read the procedure and safety
information, and complete the
lab form.
2. Create an inclined plane
between 25° and 50° using a
board and textbooks. Place a
stop block (brick or other
heavy object) at the end of the
plane.
3. Place a small object in a cart
and allow both to roll down the
plane. Record the results.
4. Secure the object in the cart
with rubber bands (safety
belts). Allow both to roll down
the plane again. Record the
results.
Analysis
1. Identify the forces acting on
the object in the cart in both
runs.
2. Explain why it is important to
wear safety belts in a car.
SC.912.P.12.3: Interpret and apply Newton’s three
laws of motion.
360 m/s2
120 m/s2
50 N
17 N
?
Inquiry
Virtual Lab
■ Figure 11 According to Newton’s
second law of motion, the harder you
throw a baseball, the greater its
acceleration will be.
Section 2 • Newton’s Laws of Motion
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■
Figure 12 If the pitchers apply the
same force, the baseball will experience a greater acceleration because it
has less mass than the softball.
170 m/s2
240 m/s2
0.20 kg
0.14 kg
34 N
34 N
Mass and acceleration If you throw a softball and a
baseball as hard as you can, as shown in Figure 12, why do they
not have the same speed? The difference is due to their masses.
A softball has a mass of about 0.20 kg, but a baseball’s mass is
about 0.14 kg. The softball has less velocity after it leaves your
hand than the baseball does, even though you exerted the same
force. The softball has a smaller final speed because it experienced a smaller acceleration. The acceleration of an object
depends on its mass as well as the force exerted on it. Force,
mass, and acceleration are related.
Reading Check Identify You apply a force of 2 N to a toy car and to a
real car. Which car has the greater acceleration?
FOLDABLES
Incorporate information
from this section into
your Foldable.
Relating force, mass, and acceleration Newton’s
second law of motion states an object’s acceleration is in the
same direction as the net force on the object and is equal to the
net force exerted on it divided by its mass. Newton’s second law
can be written as the following equation.
The Second Law of Motion Equation
net force (in newtons)
mass (in kilograms)
acceleration (in meters/second2) = __
F
net
a=_
m
In the above equation, acceleration has units of meters per
second squared (m/s2) and mass has units of kilograms (kg).
Recall that the net force is the sum of all of the forces on an
object. Remember that the SI unit for force is a newton (N) and
that 1 N = 1 kg∙m/s2. Just like velocity and acceleration, force
has a size and a direction.
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Calculating net force Newton’s second law can also be used to
calculate the net force if mass and acceleration are known. To
do this, the equation for Newton’s second law must be solved
for the net force, F net. To solve for the net force, multiply both
sides of the above equation by the mass.
VOCABULARY
ACADEMIC VOCABULARY
Period
a length of time
Each class period is 45 minutes.
F
net
m×a=m×_
m
The mass, m, on the right side cancels.
Fnet = ma
For example, when a tennis player hits a ball, the racket and
the ball might be in contact for only a few thousandths of a
second. Because the ball’s velocity changes over such a short
period of time, the ball’s acceleration could be as high as
5,000 m/s2. The ball’s mass is 0.06 kg, so the size of the net force
exerted on the ball would be 300 N.
Fnet = ma = (0.06 kg)(5,000 m/s2) = 300 kg ∙ m/s2 = 300 N
SC.912.P.12.3: Interpret and apply Newton’s three laws of motion. MA.912.S.1.2: Determine
appropriate and consistent standards of measurement for the data to be collected in a survey or
experiment.
EXAMPLE Problem 2
Solve for Acceleration You push a wagon that has a mass of 12 kg. If the net
force on the wagon is 6 N south, what is the wagon’s acceleration?
Identify the Unknown:
acceleration: a
List the Knowns:
mass: m = 12 kg
net force: F net = 6 N south
F
Set Up the Problem:
net
a=_
m
Solve the Problem:
N south = 0.5 m/s2 south
a = 6_
Check the Answer:
PRACTICE Problems
12 kg
The value of the net force (6) is less than the value of
the wagon’s mass (12), so we would expect the
acceleration’s value to be less than one. Our answer
(0.5 m/s2) makes sense.
Find Additional Practice Problems in the back of your book.
11. If a helicopter’s mass is 4,500 kg and the net force on it is 18,000 N upward,
what is its acceleration?
Review
Additional Practice Problems
12. What is the net force on a dragster with a mass of 900 kg if its acceleration
is 32.0 m/s2 west?
13. A car pulled by a tow truck has an acceleration of 2.0 m/s2 east. What is
the mass of the car if the net force on the car is 3,000 N east?
14. Challenge What is the net force on a sky diver falling with a constant
velocity of 10 m/s downward?
Section 2 • Newton’s Laws of Motion
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Newton’s Third Law of Motion
What happens when you push against a wall? If the wall is
sturdy, nothing happens. But if you pushed against a wall while
wearing roller skates, you would go rolling backward. This is a
demonstration of Newton’s third law of motion. Newton’s
third law of motion states that when one object exerts a force
on a second object, the second object exerts a force on the first
that is equal in strength and opposite in direction.
Sometimes, Newton’s third law is written as “to every action
force there is an equal and opposite reaction force.” However,
one force is not causing the second force. They occur at the
same time. It does not matter which object is labeled Object 1
and which is labeled Object 2. Think about a boat tied to a dock
with a taut rope. You could say that the action force is the boat
pulling on the rope and the reaction force is the rope pulling on
the boat. But it would be just as correct to say that the action
force is the rope pulling on the boat and the reaction force is
the boat pulling on the rope.
■ Figure 13 The student pushes on
the box, and the box pushes on the
student. To understand the motion of
each object, the other forces on that
object must be examined.
Net force = 0 N
Force from box,
30 N
Static friction,
30 N
Forces on the Student
84
Forces on different objects do not cancel If these
two forces are equal in size and opposite in direction, you
might wonder how some things ever happen. For example, if
the box in Figure 13 pushes on the student when the student
pushes on the box, why does the box move? According to the
third law of motion, action and reaction forces act on different
objects. Recall that the net force is the sum of the forces on a
single object. The left picture in Figure 13 shows the forces on
the student. The net force is zero and the student remains at
rest. The right picture shows that there is a net force of 20 N to
the right on the box and the box accelerates to the right.
Reading Check Explain why the action and reaction forces do
not cancel.
Net force = 20 N
Applied force,
30 N
Sliding friction,
10 N
Forces on the Box
Chapter 3 • Forces and Newton’s Laws
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Forces are interactions Newton’s third law
states a very important fact: forces are interactions
between objects. For example, it makes no sense to
say, “The box has a force of 30 N.” Is this force acting on the box? Is the box pushing on something?
What is causing this force? It makes sense, however, to say, “The student applied a force of 30 N
to the box.”
Furthermore, both objects experience a force
from the interaction. Look at the skaters in
Figure 14. The male skater is pulling upward on
the female skater, while the female skater is pulling downward on the male skater. The two forces
are equal in size but opposite in direction. Both
skaters feel a pull of the same size.
Even if the two objects have different masses,
they will feel the same size force. For example, if a
bug flies into the windshield of a truck, the bug
and the truck exert forces on each other. According to Newton’s third law, the bug and the truck
experience the same size force even though their
masses and accelerations are different.
Section 2
Review
Section Summary
◗ Newton’s first law of motion states that
the motion of an object at rest or moving
with constant velocity will not change
unless an unbalanced force acts on
the object.
◗ Inertia is the tendency of an object to resist
a change in motion.
◗ Newton’s second law of motion states that
the acceleration of an object depends on
its mass and the net force exerted on it.
■
Figure 14 The skaters exert forces on each other.
According to Newton’s third law of motion, the two
forces are equal in size but opposite in direction. Both
skaters feel the same amount of force.
SC.912.P.12.3, MA.912.S.1.2
15.
MAIN Idea Describe Use Newton’s laws of motion to describe
what happens when you kick a soccer ball.
16. Explain why Newton’s first law of motion is sometimes called the
law of inertia.
17. Determine whether the inertia of an object changes as the object’s
velocity changes.
18. Explain why an object with a smaller mass has a larger acceleration
than an object with a larger mass if the same force acts on each.
19. Think Critically You push a book across a table. The book moves at
a constant speed, but you do not move. Identify all of the forces
on you. Then, identify all of the forces on the book.
◗ According to Newton’s third law of motion,
when an object exerts a force on a second
object, the second object exerts a force on
the first object.
Apply Math
20. Calculate Acceleration A student pushes on a 5-kg box with a force
of 20 N forward. The force of sliding friction is 10 N backward.
What is the acceleration of the box?
21. Calculate Mass You push yourself on a skateboard with a force of
30 N east and accelerate at 0.5 m/s2 east. Find the mass of the
skateboard if your mass is 58 kg.
Assessment
0080_0085_C03S2_894583.indd 85
Online Quiz
Section 2 • Newton’s Laws of Motion
85
5/7/10 10:13 AM
Section 3
SC.912.P.12.3: Interpret and apply Newton’s three laws of motion. ALSO COVERS: SC.912.N.1.3,
MA.912.S.3.2, LA.910.2.2.3
Reading Preview
Using Newton’s Laws
Essential Questions
MAIN Idea Newton’s laws can be used to explain everyday
◗ How does Newton’s first law
explain what happens in a car
crash?
◗ How does Newton’s second law
explain the effects of air
resistance?
◗ When is momentum conserved?
Review Vocabulary
momentum: property of a
moving object that equals its mass
times its velocity
New Vocabulary
air resistance
terminal velocity
free fall
centripetal force
law of conservation of momentum
g
Multilingual eGlossary
Figure 15 The crash dummies have
inertia and resist changes in motion.
■
events, such as falling and collisions.
Real-World Reading Link Have you ever stepped off a skateboard and
seen the skateboard moved backward? You may have wondered why this
happened. Newton’s laws of motion explain this occurrence.
What happens in a crash?
Newton’s first law of motion can explain what happens in a
car crash. When a car traveling about 50 km/h collides head-on
with something solid, the car crumples, slows down, and stops
within approximately 0.1 s. According to Newton’s first law, the
passengers will continue to travel at the same velocity that the
car was moving unless a force acts on them.
This means that within 0.02 s after the car stops, any
unbelted passengers will slam into the windshield, dashboard,
steering wheel, or the backs of the front seats, as shown on the
left in Figure 15. These unbelted passengers are traveling at the
car’s original speed of 50 km/h (about 30 miles per hour).
Safety belts Passengers wearing safety belts, also shown in
Figure 15, will be slowed down by the force of the safety belt.
This prevents the person from being thrown out of the seat.
Car-safety experts say that about half of the people who die in
car crashes would survive if they wore safety belts. Thousands
of others would suffer fewer serious injuries.
Even in a low-speed crash, inertia causes the unrestrained
dummies to slam into the windshield or seat in front of them.
86
This crash dummy was restrained safely with a safety belt
and cushioned with an air bag in this low-speed crash.
Chapter 3 • Forces and Newton’s Laws
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The force needed to slow a person’s speed from 50 km/h to 0
in 0.1 s is equal to 14 times the force of gravity on the person.
Therefore, safety belts are designed to loosen a little as they
restrain the passengers. The loosening increases the time it
takes to slow the person down, meaning a smaller acceleration
and a smaller force is exerted on the passenger.
Air bags Air bags also reduce injuries in car crashes by providing a cushion that reduces the acceleration of the passengers
and prevents them from hitting the dashboard. When impact
occurs, a chemical reaction occurs in the air bag that produces
nitrogen gas. The air bag expands rapidly and then deflates just
as quickly as the nitrogen gas escapes out of tiny holes in the
bag. The entire process is completed in about 0.04 s.
VOCABULARY
SCIENCE USAGE V. COMMON USAGE
Gravity
Science usage
an attractive force between any two
objects that depends on the masses of
the objects and the distance between
them
Gravity is the force that keeps Earth
orbiting around the Sun.
Common usage
seriousness
If you understood the gravity of the situation, you would not find it funny.
Newton’s Second Law and Gravitational
Acceleration
Recall that the gravitational force exerted on an object is
equal to the object’s mass times the strength of gravity
(Fg = mg). If gravity is the only force acting on an object
(Fnet = Fg), then Newton’s second law states that the object’s
acceleration is the force of gravity divided by the object’s mass.
Notice that the mass cancels and the object’s acceleration due
to gravity is equal to the strength of gravity.
F
Fg
Concepts in Motion
Animation
■
Figure 16 In a vacuum, there is
no air resistance. As a result, the
feather and the billiard ball fall with
the same acceleration in a vacuum.
mg
net
_ _
a=_
m = m= m =g
When discussing the acceleration due to gravity, g is written
with the units m/s2. On Earth, any falling object with only
gravity acting on it will accelerate at 9.8 m/s2 toward Earth.
Air resistance The gravitational force causes objects to fall
toward Earth. However, objects falling in the air experience air
resistance. Air resistance is a friction-like force that opposes
the motion of objects that move through the air. Air resistance
acts in the direction opposite to the motion of an object moving through air. If the object is falling downward, air resistance
exerts an upward force on the object.
The amount of air resistance on an object depends on the
size, shape, and speed of the object, as well as the properties of
the air. Air resistance, not the object’s mass, is the reason feathers, leaves, and pieces of paper fall more slowly than pennies,
acorns, and billiard ball. If there were no air resistance, then all
objects, including the feather and the billiard ball, would fall
with the same acceleration, as shown in Figure 16.
Reading Check Explain why some objects fall faster than others.
Section 3 • Using Newton’s Laws
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Size and shape The more spread out an object is,
the more air resistance it will experience. Picture
dropping two plastic bags, as shown in Figure 17.
One is crumpled into a ball and the other is spread
out. When the bags are dropped, the crumpled
bag falls faster than the spread-out bag. The
downward force of gravity on both bags is the
same, but the upward force of air resistance on the
crumpled bag is less. As a result, the net downward force on the crumpled bag is greater.
Force of
gravity
Net
force
Force of
gravity
Force of air resistance
Net
force
Force of air
resistance
■
Figure 17 An object’s surface size and shape
determine how fast it will fall. Because of its greater surface area, the bag on the left has more air
resistance acting on it as it falls.
Concepts in Motion
Animation
■
Figure 18 As the sky diver’s speed increases, so
does the force of air resistance acting on her. At some
point, the force of the air resistance equals the force
due to gravity and the sky diver falls at a constant
speed called terminal velocity.
Fair = 0 N
Fnet = 750 N
resistance also increases as the object’s speed
increases. As an object falls, gravity causes it to
accelerate downward. But, as an object falls faster,
the upward force of air resistance increases. So,
the net force on the object decreases as it falls, as
shown with the sky diver in Figure 18.
Eventually, the upward air resistance force
becomes large enough to balance the downward
force of gravity and the net force on the object is
zero. Then the acceleration of the object is zero,
and the object falls with a constant speed called
the terminal velocity. Terminal velocity is the
maximum speed an object will reach when falling
through a substance, such as air.
A falling object’s terminal velocity depends on
its size, shape, and mass. For example, the air
resistance on an open parachute is much larger
than the air resistance on the sky diver alone.
With the parachute open, the sky diver’s terminal
velocity is small enough that she can land safely.
Fair = 375 N
Fnet = 375 N
Fg = 750 N
Sky diver begins to fall.
(v is zero)
88
Speed and terminal velocity The amount of air
Fair = 750 N
F net = 0 N
Fg = 750 N
Sky diver accelerates downward.
(v is increasing)
Fg = 750 N
Sky diver falls at terminal velocity.
(v is constant)
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Free fall Suppose an object were falling and there were no air
resistance. Gravity would be the only force acting on the object.
If gravity is the only force acting on an object, the object is said
to be in free fall. For example, the feather and the billiard ball
falling in a vacuum, previously shown in Figure 16, are in free
fall. Another example is an object in orbit. Earth, for example,
is in free fall around the Sun. If Earth did not have a velocity
perpendicular to the gravitational force, it would fall into the
Sun. Similarly, satellites are in free fall around Earth.
Weightlessness You might have seen pictures of astronauts
and equipment floating inside an orbiting spacecraft. They are
said to be experiencing weightlessness. But, according the law
of universal gravitation, the strength of Earth’s gravitational
field at a typical orbiting altitude is about 90 percent of its
strength at Earth’s surface. So, an 80-kg astronaut would weigh
about 700 N in orbit and would not be weightless.
What does it mean to say that something is weightless?
Think about how you measure your weight. When you stand on
a scale, as shown on the left of Figure 19, you are at rest. The net
force on you is zero, according to Newton’s second law of
motion. The scale exerts an upward force that balances your
weight. The dial on a scale shows the size of the upward force,
which is the same size as your weight.
Now suppose you stand on a scale in an elevator that is in
free fall, as on the right in Figure 19. You would no longer push
down on the scale at all. The scale dial would read zero, even
though the force of gravity has not changed. An orbiting spacecraft is in free fall, and objects in it seem to float because they
are all falling around Earth at the same rate.
When the elevator is stationary, the scale shows
the girl’s weight.
Review
Additional Practice Problems
Concepts in Motion
Animation
■
Figure 19 The reading on the
scale depends on the upward force the
scale exerts on the girl. If both the girl
and the scale are in free fall, the girl
experiences the sensation of weightlessness, even though the force of
gravity has not changed.
If the elevator were in free fall, the scale would
show
a zero weight.
M627-10C-MSS02-A
Section 3 • Using Newton’s Laws
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■ Figure 20 The riders on this
amusement park ride are traveling in a
circle because of the centripetal force
acting on them.
Identify the force that acts as the
centripetal force.
Centripetal Forces
Orbiting objects, such as space shuttles, are traveling in
nearly circular paths. According to Newton’s first law, this
change in motion is caused by a net force acting on the object.
Newton’s second law states that because the object’s acceleration is toward the center of the curved path, the net force is also
toward the center. A centripetal force is a force exerted toward
the center of a curved path.
Anything that moves in a circle is doing so because a centripetal force is accelerating it toward the center. Many different
forces can act as a centripetal force. Gravity is the centripetal
force that keeps planets orbiting the Sun. On the amusement
park ride in Figure 20, the push of the walls of the ride on the
people is the centripetal force.
When a car rounds a level curve on a highway, friction
between the tires and the road acts as the centripetal force. If
the road is slippery and the frictional force is small, it might
not be large enough to keep the car moving around the curve.
Then the car will slide in a straight line, as shown in Figure 21.
Force due
to friction
■ Figure 21 If the inward frictional
force is too small, the car will continue
in a straight line and not make it
around the curve.
90
Path car would
take if there
were no friction
Chapter 3 • Forces and Newton’s Laws
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5/7/10 10:17 AM
p = 1 kg ∙ m/s
p = 3 kg ∙ m/s
Total momentum = 3 kg ∙ m/s right
p = 4 kg ∙ m/s
Total momentum = 3 kg ∙ m/s right
■
Force and Momentum
Recall that acceleration is the difference between the initial
and final velocities, divided by the time. Therefore, we can
write Newton’s second law in the following way.
(v – v )
Figure 22 When two objects collide and there are no external forces
acting on the objects, momentum is
conserved.
?
Inquiry
Virtual Lab
(mv – mv )
f
i
f
i
=_
F = ma = m × _
t
t
Recall that an object’s momentum equals its mass multiplied
by its velocity. In the equation above, mvf is the final momentum
and mvi is the initial momentum. The equation states that the net
force exerted on an object equals the change in its momentum
divided by the time over which the change occurs. In fact, this is
how Newton originally wrote the second law of motion.
Conservation of momentum Newton’s second and
third laws of motion can be used to describe what happens
when objects collide. For example, consider the collision of the
balls in Figure 22. We will assume that friction is too small to
cause a noticeable change in the balls’ motion. In this ideal case,
there are no external forces, but the balls exert forces on each
other during the collision. According to Newton’s third law, the
forces are equal in size and opposite in direction. Therefore, the
momentum lost by the first ball is gained by the second ball and
the total momentum of the two balls is the same before and after
the collision. This is the law of conservation of momentum—if
no external forces act on a group of objects, their total momentum does not change.
Review
Additional Practice Problems
■
Figure 23 Momentum is conserved
in collisions with more than two
objects if there are no external forces
acting on the objects. The momentum
of the cue ball just before the collision
is equal to the total of the momentums of the billiard balls (including the
cue ball) just after the collision.
Collisions with multiple objects When a cue ball hits the
group of motionless balls, as shown in Figure 23, the cue ball
slows down and the rest of the balls begin to move. The
momentum that the group of balls gained is equal to the
momentum that the cue ball lost. Momentum is conserved.
Section 3 • Using Newton’s Laws
0086_0092_C03S3_894583.indd 91
91
5/7/10 10:17 AM
Momentum of rocket
Force of rocket on gas
Force of gas on rocket
Momentum of
expelled gases
■
Figure 24 If more gas is ejected
from the rocket engine or expelled
at a greater velocity, the engine will
exert a larger force on the rocket.
Section 3
Rocket propulsion Suppose you are standing on skates
holding a softball. You exert a force on the softball when you
throw it. According to Newton’s third law, the softball exerts a
force on you. This force pushes you backward in the direction
opposite the softball’s motion. Rockets use the same principle
to move, even in the vacuum of outer space. In the rocket
engine, burning fuel produces hot gases. The rocket engine
exerts a force on these gases and causes them to escape out the
back of the rocket. By Newton’s third law, the gases exert a
force on the rocket and push it forward. Figure 24 shows one of
the Apollo rockets that traveled to the Moon. Notice that the
force of the rocket on the gases is equal in size to the force of
the gases on the rocket.
Momentum is conserved when a rocket ejects the hot gas. If
the rocket is initially at rest, then the total momentum of the
rocket and the fuel is zero. After the fuel is burned and the hot
gas is expelled, the gas travels backward with a momentum of
m gasv gas and the rocket travels forward with a momentum of
m rocketv rocket. These momentums are equal in size, but opposite
in direction. By controlling how much gas is ejected and the
gas’s velocity, the rocket’s motion can be controlled.
Review
Section Summary
◗ In a car crash, an unrestrained passenger
will continue moving at the velocity of the
car before the crash.
◗ Air resistance is a force that opposes an
object’s motion through the air.
◗ If gravity is the only force acting on an
object, then the object is in free fall.
◗ Objects appear to be weightless in free fall.
◗ The force that causes an object to move in
a circular path is called the centripetal
force.
◗ The law of conservation of momentum
states that if objects exert forces only on
each other, their total momentum is
conserved.
SC.912.P.12.3
22.
MAIN Idea Describe Use Newton’s laws to describe how inertia,
gravity, and air resistance affect sky divers as they fall, open their
parachutes, and reach terminal velocity.
23. Discuss the advantages of wearing a safety belt when riding in
a vehicle.
24. Explain why planets orbit the Sun instead of traveling off into space.
25. Describe what happens to the momentum of two billiard balls
that collide.
26. Explain how a rocket can move through outer space where there is
no matter for it to push on.
27. Think Critically Suppose you are standing on a scale in an elevator
that is accelerating upward. Will the scale read your weight as
larger or smaller than the weight it reads when you are stationary? Explain.
Apply Math
28. Calculate Momentum A fuel-filled rocket is at rest. It burns its fuel
and expels hot gas. The gas has a momentum of 1,500 kg · m/s
backward. What is the momentum of the rocket?
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0086_0092_C03S3_894583.indd 92
Assessment
Online Quiz
5/7/10 10:18 AM
LAB
The Effects of Air Resistance
SC.912.P.12.3: Interpret and apply Newton’s three laws of motion. LA.910.2.2.3: The student will organize
information to show understanding or relationships among facts, ideas, and events (e.g., representing key points
within text through charting, mapping, paraphrasing, summarizing, comparing, contrasting, or outlining).
Objectives
Effects of Air Resistance
n Measure the effect of air resistance on sheets
of paper with different shapes.
n Design a shape that maximizes air resistance.
Use a piece of paper to create your design.
Background: If you dropped a bowling ball and a
feather from the same height on the Moon, they
would both hit the surface at the same time. The
objects are attracted to the Moon with the same
force, but there is no atmosphere and no air resistance. But on Earth, a bowling ball and a feather will
not hit the ground at the same time. Even though all
objects on Earth are attracted with the same force,
air resistance affects the feather more than it affects
the bowling ball.
Question: How does air resistance affect the
acceleration of falling objects?
Preparation
Materials
paper (4 sheets of equal size)
scissors
meterstick
stopwatch
masking tape
Safety Precautions
Paper Type
Time
Flat paper
Loosely crumpled paper
Tightly crumpled paper
Your paper design
4. Have one group member drop the flat sheet of
paper from the 2.5-m mark. Use the stopwatch to
time how long it takes for the paper to reach the
ground. Record the time in your data table.
5. Crumple a sheet of paper into a loose ball, and
repeat step 4.
6. Crumple a sheet of paper into a tight ball, and
repeat step 4.
7. Shape a piece of paper so that it will fall slowly.
You may cut, tear, or fold your paper into any
design that you choose. Repeat step 4.
Conclude and Apply
1. Compare the falling times of the different sheets
of paper.
2. Explain why the different-shaped papers fell at
different accelerations.
3. Explain how your design caused the force of air
resistance on the paper to be greater or smaller
than the air resistance on the other paper shapes.
Procedure
1. Read the procedure and safety information, and
complete the lab form.
2. Copy the data table, or create it on a computer.
3. Measure a height of 2.5 m on the wall, and mark
the height with a piece of masking tape.
?
Inquiry
0093_0095_C03L1_894583.indd 93
Lab
YOUR DATA
Compare your paper design with the
designs created by your classmates. As a class,
compile a list of characteristics that increase
air resistance.
Chapter 3 • Lab
93
5/3/10 12:06 PM
LAB
DESIGN YOUR OWN
Motion from Different Forces
SC.912.P.12.3: Interpret and apply Newton’s three laws of motion. MA.912.S.3.2: Collect, organize, and analyze
data sets, determine the best format for the data and present visual summaries from the following: bar graphs, line
graphs, stem and leaf plots, circle graphs, histograms, box and whisker plots, scatter plots, and cumulative frequency
(ogive) graphs.
Goals
Make a Plan
n Identify several forces that you can use to
propel a small toy car across the floor.
1. Read the procedure and safety information, and
complete the lab form.
2. As a group, agree upon a hypothesis and decide
how you will test it. Identify which results could
confirm the hypothesis you have written.
3. Identify the steps that you will need to test your
hypothesis. Be sure to include a control run. Be
specific. Describe exactly what you will do in
each step. Include your materials.
4. Prepare a data table to record your observations.
5. Read the entire experiment to make sure all steps
are in logical order and will lead to a useful
conclusion.
6. Identify all constants, variables, and controls of
the experiment. Make sure your plan tests only
one variable at a time. Keep in mind that you will
need to measure the toy car’s position at multiple
points in time. These points are needed to graph
your results. You should have several data points
taken after you stop applying the force and before
the car starts to slow down. It might be useful to
have several students taking measurements,
making each responsible for one or two points.
n Demonstrate the motion of the toy car using
each of the forces.
n Graph the position versus time for each force.
n Compare the motion of the toy car resulting
from each force.
Background: Think about a small ball. How
many ways could you exert a force on the ball to
make it move? You could throw it, kick it, roll it
down a ramp, blow it with a large fan, and so on.
Question: Do you think the distance and speed of
the ball’s motion would be the same for all of these
forces? Do you think the acceleration of the ball
would be the same for all of these types of forces?
Preparation
Possible Materials
small toy cars
ramps or boards of different lengths
springs or rubber bands
string
stopwatch
meterstick or tape measure
graph paper
Safety Precautions
Form
Make aa Hypothesis
Plan
Based on your reading and observations, state a
hypothesis about how the type of force applied will
affect the acceleration, speed, and distance of a toy
car.
94
Chapter 3 • Forces and Newton’s Laws
0093_0095_C03L1_894583.indd 94
?
Inquiry
Lab
5/13/10 9:47 AM
Analyze
A
nally
zeYour
Your
Plan
Data
TFollow
Test
the
Model
Conclude and Apply
Ap
pply
y
1. Make sure your teacher approves your plan
before you begin.
2. Carry out the experiment as planned.
3. While doing the experiment, record your
observations in your data table.
1. Evaluate Did the average speed of the toy car
vary depending on the force applied to it?
2. Determine For any particular force, did the
speed of the toy car change over time? If so, how
did the speed change? Describe how you can use
your graphs to answer these questions.
3. Draw Conclusions Did your results support
your hypothesis? Why or why not?
4. Design Whether or not a hypothesis is supported, experimental results often lead to new
hypotheses and experiments. Based on what you
have learned from this lab, state a new problem,
your hypothesis, and describe how you would
test it.
Analyze Your Data
1. Graph the position of the car versus time for
each type of force that you applied.
2. Analyze How can you use the graphs to compare the speeds of the toy car?
3. Calculate the average speed of the toy car over
the same time interval for each type of force that
you applied.
4. Analyze How do the calculated average speeds
compare?
5. Identify some ways that you might improve your
experiment.
YOUR DATA
Compare your data with those of other students. Discuss how the forces that you applied
might be different from those others applied.
How were your results affected?
Chapter 3 • Lab
0093_0095_C03L1_894583.indd 95
95
5/3/10 12:07 PM
Extreme Altitudes
SC.912.P.12.3: Interpret and apply Newton’s three laws of motion.
SC.912.N.1.3: Recognize that the strength or usefulness of a scientific
claim is evaluated through scientific argumentation, which depends on critical
and logical thinking, and the active consideration of alternative scientific
explanations to explain the data present.
n July of 1969, Apollo 11 rocketed toward an
historic meeting with the Moon. The editors at
The New York Times were in a distinctly
uncomfortable position. Forty-nine years before,
the newspaper published an editorial that ridiculed the scientist who suggested that rockets
could travel in space. Three days before astronauts first walked on the Moon, editors wrote,
“The Times regrets the error.”
I
Rocket man
Robert Goddard, shown in Figure 1,
was passionate about rocketry. In 1919, Goddard
wrote a report to the Smithsonian Institution entitled, “A Method of Reaching Extreme Altitudes.”
Near the end of the paper, Goddard proposed that
a large rocket propelled by powerful fuel could
reach the Moon. Goddard was unprepared for the
scornful reaction.
Public scorn, private determination
An
editorial in The New York Times ridiculed Goddard
and accused him of lacking “the knowledge ladled
out daily in high schools.” According to the writer,
even students knew that a rocket could not function
in space because there was nothing for the fuel
exhaust to push against as it exited the rocket to
create forward motion.
Goddard continued his experiments, despite the
public humiliation. On March 16, 1926, his 3-m
rocket, Nell, soared into the sky at 28 m/s. Nell
reached a height of 12.5 m, becoming the first
liquid-fueled rocket. This launch began the age of
modern rocketry that led to space exploration
and landing on the Moon.
Figure 1 Robert Goddard works on a rocket in 1940.
Faulty physics
Why was the editorial incorrect?
Consider Newton’s third law of motion: For every
action, there is an equal and opposite reaction. The
writer believed that because the exhaust would
have nothing to push against in space, there could
be no opposing force pushing the rocket forward.
However, he failed to consider what happens inside
the rocket. As rocket fuel is burned, a gas is generated. The gas expands rapidly, pushing against
everything around it, and escapes through a nozzle
at the bottom of the rocket. The escaping exhaust
exerts a force on the rocket, causing the rocket to
move in the opposite direction.
Goddard’s legacy Modern liquid-fueled rockets
are based on Goddard’s designs. He developed
systems to maintain control of rockets, tested
parachute systems to recover spent rockets, put
meteorological instruments on rockets to acquire
high-altitude weather data, and proposed the idea
of multi-stage rockets. Many believe that Goddard’s
legacy lies in those first footprints left on the Moon.
WebQuest
Research Robert Goddard said, “Every vision is a joke until the first man
accomplishes it; once realized, it becomes commonplace.” Research a modern technology whose inventors
might have been ridiculed had they proposed the idea in 1920. Use your findings to write a brief report.
96
Chapter 3 • Forces and Newton’s Laws
0096_C03HF_894583.indd 96
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3
THEME FOCUS Motion and Forces
There are many ways objects interact and exert forces on one another. Friction and air resistance are
forces that oppose motion. Gravity is the attractive force between all objects due to mass.
BIG Idea A force is a push or pull.
Section
n 1 Forces
MAIN Idea
field (p. 77)
force (p. 72)
friction (p. 74)
gravity (p. 76)
net force (p. 73)
weight (p. 78)
•
•
•
•
•
Unbalanced forces change motion.
A force is a push or a pull on an object.
The net force on an object is the combination of all the forces acting
on the object.
Unbalanced forces cause the motion of objects to change.
Friction is the force that opposes the sliding motion of two surfaces
that are in contact.
Gravity is an attractive force between all objects that have mass.
Section
n 2 Newton’s Laws of Motion
inertia (p. 80)
Newton’s first law of motion (p. 80)
Newton’s second law of motion (p. 82)
Newton’s third law of motion (p. 84)
MAIN Idea Newton’s laws of motion relate the change in an
object’s motion with the forces acting on it.
• Newton’s first law of motion states that the motion of an object at rest
or moving with constant velocity will not change unless an
unbalanced force acts on the object.
• Inertia is the tendency of an object to resist a change in motion.
• Newton’s second law of motion states that the acceleration of an object
depends on its mass and the net force exerted on it.
• According to Newton’s third law of motion, when an object exerts a
force on a second object, the second object exerts a force on the first
object.
Section
n 3 Using Newton’s Laws
air resistance (p. 87)
centripetal force (p. 90)
free fall (p. 89)
law of conservation of momentum
(p. 91)
terminal velocity (p. 88)
Review
0097_C03SG_894583.indd 97
Vocabulary eGames
MAIN Idea
Newton’s laws can be used to explain everyday
events, such as falling and collisions.
• In a car crash, an unrestrained passenger will continue moving at the
velocity of the car before the crash.
• Air resistance is a force that opposes an object’s motion through
the air.
• If gravity is the only force acting on an object, then the object is in
free fall.
• Objects appear to be weightless in free fall.
• The force that causes an object to move in a circular path is called the
centripetal force.
• The law of conservation of momentum states that if objects exert
forces only on each other, their total momentum is conserved.
Chapter 3 • Study Guide
97
5/3/10 12:11 PM
3
SC.912.P.12.2, SC.912.P.12.3, SC.912.P.12.4, MA.912.S.1.2
Use Vocabulary
Complete each statement with the correct term
from the Study Guide.
29. _________ opposes the sliding motion of
two surfaces that are in contact.
30. The _________ of an object is different on
every planet in the solar system.
37. Which body exerts the strongest gravita-
tional force on you?
A) the Moon
C) the Sun
B) Earth
D) this book
38. Which term describes the tendency of an
object to resist a change in motion?
A) balanced force
C) net force
B) inertia
D) acceleration
Use the figure below to answer question 39.
31. When an object moves in a circular path,
Speed of a Car
the net force is called a(n) _________.
that depends on their masses and the
distance between them is _________.
Speed (m/s)
32. The attractive force between two objects
d
30
c
20
10
e
b
a
33. _________ relates the net force exerted on
an object to its mass and acceleration.
0
10
20
30
40
Time (s)
Check Concepts
34. What is the gravitational force exerted on
an object called?
A) centripetal force C) momentum
B) friction
D) weight
35. Which explains why astronauts seem
weightless in orbit?
A) Earth’s gravity is much less in orbit.
B) The spacecraft is in free fall.
C) The gravity of Earth and the Sun cancel.
D) The centripetal force on the shuttle
balances Earth’s gravity.
36. Which term best describes the forces on an
object with a net force of zero?
A) balanced forces
B) unbalanced forces
C) inertia
D) acceleration
98
Chapter 3 • Forces and Newton’s Laws
0098_0099_C03CR_894583.indd 98
39. The graph shows the speed of a car moving
in a straight line. Over which segments are
the forces on the car balanced?
A) A and C
C) C and E
B) B and D
D) A, C, and E
40. Which of the following is true about an
object in free fall?
A) Its acceleration depends on its mass.
B) It has no inertia.
C) It pulls on Earth, and Earth pulls on it.
D) Its momentum is constant.
41. An object always accelerates in the same
direction as which of the following?
A) net force
C) static friction
B) air resistance
D) gravity
42. BIG Idea Which of the following is not a
force?
A) weight
B) friction
C) momentum
D) air resistance
Assessment
Online Test Practice
5/7/10 10:26 AM
3
48. Explain whether there can be forces acting
Interpret Graphics
on a car that is moving in a straight line
with constant speed.
43. Copy and complete the following concept
map on forces.
49. Explain You pull open a door. If the force
Concepts in Motion
Forces
Gravity
depends on
c.
d.
the door exerts on you is equal to the force
you exert on the door, why do you not move?
Interactive Concept Map
50.
Describe the action and reac-
tion force pairs involved when an object
falls toward Earth. Ignore the effects of air
resistance.
a.
b.
depends on
depends on
force
between
surfaces
THEME FOCUS
surface
area
e.
51. Explain why a passenger who is not wearing
a safety belt will likely hit the windshield in
a head-on collision.
52. Determine the direction of the net force on a
car if it is slowing down. Explain.
Use the table below to answer questions 44–46.
Time of Fall for Dropped Objects
Object
Mass (g)
Time of Fall (s)
A
5.0
2.0
B
5.0
1.0
C
30.0
0.5
D
35.0
1.5
44. If the objects in the data table above all fell
the same distance, which object fell with the
greatest average speed?
A pply Math
53. Calculate Mass Find your mass if a scale on
Earth reads 650 N when you stand on it.
54. Calculate Gravitational Strength You weigh
yourself at the top of a high mountain and the
scale reads 728 N. If your mass is 75 kg, what
is the gravitational strength at your location?
Use the figure below to answer question 55.
Before Collision
6 kg·m/s
45. Which object was aggeted the most by air
resistance?
46. Explain why the four objects do not fall
with the same speed.
Metal
ball
After Collision
2 kg·m/s
Wooden
ball
Metal
ball
p=?
Wooden
ball
55. Calculate Momentum What is the momen-
tum of the wooden ball after the collision?
Think Critically
47. Predict Suppose you are standing on a
bathroom scale next to a sink. How does the
reading on the scale change if you push
down on the sink? Explain your prediction.
Assessment
0098_0099_C03CR_894583.indd 99
Online Test Practice
56. Calculate Sliding Friction A box being
pushed with a force of 85 N right slides
along the floor with a constant speed. What
is the force of sliding friction on the box?
Chapter 3 • Review
99
5/7/10 10:26 AM
Standardized Test Practice
Multiple Choice
Record your answers on the answer sheet
provided by your teacher or on a sheet of paper.
5. Which of the following would cause the grav-
itational force between object A and object B
SC.912.P.12.4
to increase?
A. Increase the mass of object A.
B. Increase the distance between them.
C. Decrease the mass of object A.
D. Decrease the mass of both objects.
1. The net force on an object moving with
constant speed in circular motion is in which
SC.912.P.12.3
direction?
A. downward
B. opposite to the object’s motion
C. toward the center of the circle
D. in the direction of the object’s velocity
Use the figure below to answer questions 2–4.
Object Falling with Air Resistance
25
6. Which of the following is a force?
A. friction
B. acceleration
C. inertia
D. velocity
Use the figure below to answer question 7.
Speed of Sliding Book
1.5
15
Speed (m/s)
Speed (m/s)
20
10
5
0
SC.912.P.12.3
0
1
2
3
4
5
Time (s)
1.0
0.5
0
0.5
1.0
1.5
2.0
2.5
Time (s)
2. According to the trend in these data, which of
the following values is most likely the speed
SC.912.P.12.3
of the object after falling for 6 s?
A. 26.7 m/s
C. 20.1 m/s
B. 15.1 m/s
D. 0 m/s
3. Over which of the following time intervals is
the acceleration of the object the greatest?
SC.912.P.12.3
A. 0 s to 1 s
B. 1 s to 2 s
C. 2 s to 3 s
D. 4 s to 5 s
4. Over which of the following time intervals is
the net force on the object the smallest?
SC.912.P.12.3
A. 0 s to 1 s
C. 2 s to 3 s
B. 1 s to 2 s
D. 4 s to 5 s
100
Standardized Test Practice
0100_0101_C03STP_894583.indd 100
7. The graph above shows how the speed of a
book changes as it slides across a table in a
straight line. Over what time interval is the
net force on the book in the opposite direcSC.912.P.12.3
tion of the book’s motion?
A. 0 s to 0.5 s
B. 0.5 s to 2.4 s
C. 0 s to 2.4 s
D. 2 s to 2.4 s
8. How does the gravitational force change as
two objects move farther apart?
A. It increases.
B. It decreases.
C. It remains constant.
D. It is zero.
Assessment
SC.912.P.12.4
Standardized Test Practice
5/3/10 12:09 PM
Short Response
Extended Response
Record your answers on the answer sheet
provided by your teacher or on a sheet of paper.
Record your answers on a sheet of paper.
13. Give an example of a force applied to an object
9. You are pushing a 30-kg wooden crate across
the floor. The force of sliding friction on the
crate is 90 N. How much force must you
exert on the crate to keep it moving with a
SC.912.P.12.3
constant velocity?
10. A sky diver with a mass of 60 kg jumps from
an airplane. Five seconds after jumping, the
force of air resistance on the sky diver is
300 N. What is the sky diver’s acceleration
five seconds after jumping?
SC.912.P.12.3
that does not change the object’s velocity.
Why does the object’s velocity not change?
SC.912.P.12.3
14. A tennis ball is rolling east. You apply a force
to it in the north direction. How will your
push affect the direction of the ball? Explain.
SC.912.P.12.3
15. Two balls are dropped from an airplane.
Both balls are the same size, but one has a
mass ten times greater than the other. The
force of air resistance on each ball depends
on the ball’s speed. Explain whether both
balls will reach the same terminal velocity.
11. A pickup truck is carrying a load of gravel.
SC.912.P.12.3
The driver hits a bump and gravel falls out,
so that the mass of the truck is one half as
large after hitting the bump. If the net force
on the truck does not change, how does the
truck’s acceleration change?
SC.912.P.12.3
Use the table below to answer question 12.
16. When the space shuttle is launched from
Earth, the rocket engines burn fuel and
apply a constant force on the shuttle until
they burn out. Explain why the shuttle’s
acceleration increases while the rocket
SC.912.P.12.3
engines are burning fuel.
17. An object in motion slows down and comes
Car Mass (kg) Stopping Distance (m)
A
B
1,000
1,250
80
100
C
D
1,500
2,000
120
160
to a stop. Use Newton’s first law of motion to
explain why this happens.
SC.912.P.12.3
18. In an airplane flying at a constant speed, the
force pushing the airplane forward is exerted
by the engine and is equal to the opposite
force of air resistance. Describe how these
forces compare when the plane speeds up
and slows down. In which direction is the
net force on the airplane in each case?
12. What is the relationship between a car’s
mass and its stopping distance? How can
SC.912.P.12.3
you explain this relationship?
SC.912.P.12.3
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Assessment
0100_0101_C03STP_894583.indd 101
Standardized Test Practice
Standardized Test Practice
101
5/3/10 12:09 PM