Chapter 4 – Newton’s Second Law of Motion
•
•
•
•
•
•
•
Force Causes Acceleration
Friction
Mass and Weight
Mass Resists Acceleration
Newton’s Second Law of Motion
When Acceleration is g – Free Fall
When Acceleration is Less Than g – Non-Free Fall
Physics 1100 –Spring 2012
Forces Cause Acceleration
Remember Newton’s First Law:
If the total “resultant” force acting on an object is zero, then the object will
either remain at rest or it would move along a line with a constant velocity.
Therefore:
If the force is non-zero, the speed or the direction (or both) will change –
this is acceleration
Physics 1100 –Spring 2012
Why Did This Discovery Take 2000 Years?
It appears as if a force is necessary to just keep an object in constant
motion
WHY?
Friction
•
•
•
the force produced when two objects “rub” against each other
independent of velocity of the object after it is in motion
– dynamic friction
– static friction is greater (don’t skid!)
friction always opposes the direction of motion
Physics 1100 –Spring 2012
Coefficient of Friction
Ffriction = Fnormal
Material on Material
s = static friction
k = kinetic friction
steel / steel
0.6
0.4
add grease to steel
0.1
0.05
metal / ice
0.022
0.02
brake lining / iron
0.4
0.3
tire / dry pavement
0.9
0.8
tire / wet pavement
0.8
0.7
Physics 1100 –Spring 2012
Some Questions
•
Does friction always exert a force that tends to bring things to a halt?
•
What does this say about the direction of the frictional force, relative to the
velocity vector?
•
What do you think would happen if we loaded lead bricks into the box?
Would it become harder to slide?
•
What are some ways to reduce frictional forces?
Physics 1100 –Spring 2012
Net Force
Physics 1100 –Spring 2012
Mass vs. Weight
Mass: The quantity of matter in an object. It is also the measure of the
inertia or sluggishness that an object exhibits in response to any effort made
to start it, stop it, or change its state
•
Mass is reluctance to accelerate (mass  inertia)
•
Weight is the force exerted by gravity on an object
– Go to the moon: Does your mass change?
Does your weight change?
•
Units of Mass and Weight
– 1 kilogram mass (1 kg), on earth weighs 2.2 lbs
– 1 newton of force = force necessary to accelerate 1 kg at 1 m/s2
– 1 kilogram weighs 9.8 newtons
Physics 1100 –Spring 2012
Forces Cause Acceleration
•
•
Acceleration is proportional to the applied force: The larger the force,
the more an object will accelerate, in the direction of the applied force.
Mass is inertia, i.e., reluctance to accelerate, so for the same force,
more massive objects experience smaller acceleration than less
massive ones.
Shorthand:
Force = mass  acceleration, or
F = ma
Newton’s 2nd Law
Newton’s Second Law
Physics 1100 –Spring 2012
Mass and Acceleration
Physics 1100 –Spring 2012
Falling Stuff
Physics 1100 –Spring 2012
Do Falling Objects Accelerate?
•
•
•
It sure seems like it!
– Starts from rest, goes faster and faster....
What about a feather, though?
– Air resistance, drag
– Terminal velocity
– What if we could get rid of the air?
What’s responsible for the downwards force?
– If it’s accelerating, then a force is acting:
F = ma
Physics 1100 –Spring 2012
Physics 1100 –Spring 2012
Acceleration Due to Gravity
•
•
At the earth’s surface, all objects experience the same acceleration from
gravity!
“g”= 9.8m/s2 = 32 ft/s2
If the acceleration due to gravity is indeed universal, then...
Since F = ma, the gravitational force must be
proportional to mass.
Physics 1100 –Spring 2012
Free Fall
Physics 1100 –Spring 2012
Golf Ball vs. Bowling Ball
•
•
•
•
Which one is more massive?
Which one experiences more gravitational force?
Which one is most reluctant to accelerate?
How do they respond to a gravitational force?
Physics 1100 –Spring 2012
Converting Mass to Weight
Weight W
•
Near the earth’s surface, the acceleration of an
object is g = 9.8 m/s2.
mass m
•
We DEFINE the weight of the object as the force
exerted on the object due to earth’s “gravitational
acceleration” g of the object
•
Newton’s Second Law: F = MA
W = mg where g = 9.8 m/s2 for earth
Physics 1100 –Spring 2012
Questions on Newton’s Second Law
1. If identical forces act on two objects, where object A is three
times as massive as object B, how do their accelerations
compare?
2. If I double the mass of an object, by what factor must I change
the applied force to maintain a certain acceleration?
3. If one force pulls an object to the East, while a second force of
equal magnitude pulls it to the West, what is the object’s
acceleration?
Physics 1100 –Spring 2012
Quantitative exercises, real numbers
If you see an object with a mass of 1 kg increase its speed by
1m/s in each second:
Is it accelerating?
How much is it accelerating?
What force is acting on it?
Physics 1100 –Spring 2012
Quantitative exercises, real numbers
If you see an object with a mass of 1 kg increase its speed by
1m/s in each second, what force is acting on it?
Is it accelerating?
Yes!
How much is it accelerating?
Velocity changing by 1m/s per sec is acceleration of 1 m/s/s =1 m/s 2
What force is acting on it?
F = mass  acceleration = 1 kg  1 m/s2 = 1 kg m/s2 = 1 Newton
Physics 1100 –Spring 2012
Summary
•
•
•
•
•
•
Velocity refers to both speed and direction
Acceleration means a change in velocity
Mass is a property of objects that represents their reluctance to accelerate
If an object is accelerating, it’s being acted on by an unbalanced force, and
F = ma
Gravity causes all objects to suffer the same acceleration, regardless of
their mass or composition
Gravitational acceleration only affects the vertical component of motion –
think in terms of components
Physics 1100 –Spring 2012
“Free” Fall
•
•
Terminal velocity reached when Fdrag = Fgrav (= mg)
For 75 kg person subtending 0.5 m2,
vterm  50 m/s, or 110 m.p.h.
which is reached in about 5 seconds, over 125 m of fall
•
Free fall only lasts a few seconds, even for skydivers
Physics 1100 –Spring 2012
Air Resistance and Terminal Velocity
Physics 1100 –Spring 2012
Class Problems
Which encounters the greater force of air resistance—a
falling elephant or a falling feather?
a) Elephant
b) feather
Physics 1100 –Spring 2012
1. Compared to a 1-kg block of solid iron, a 2-kg block of solid
iron has twice as much
a) volume.
b) mass.
c) inertia.
d) all of these
e) none of these
2. A ride on a roller-coaster car containing 6 passengers takes 3
minutes. Neglecting friction, a similar ride with 12 passengers
aboard would take
a) 6 minutes. b) 3 minutes. c) 18 minutes. d) 1.5 minutes.
Physics 1100 –Spring 2012
3. A rock weighs 30 N on Earth. A second rock weighs 30 N on the
moon. Which of the two rocks has the greater mass?
A) the one on Earth
B) the one on the moon
C) They have the same mass.
D) not enough information to say
4. A 10-kg brick and a 1-kg book are dropped in a vacuum. The
force of gravity on the 10-kg brick is
A) 10 times as much
B) zero.
C) the same as the force on the 1-kg book.
D) one-tenth as much.
Physics 1100 –Spring 2012
5. An apple weighs 1 N. When held at rest above your head, the net
force on the apple is
A) 9.8 N.
B) 0.1 N.
C) 0 N.
D) 1 N.
E) none of these
6. The maximum acceleration of a car while towing a second car
twice its mass, compared to its acceleration with no car in tow,
is
A) one half.
B) the same.
C) one third.
D) one fourth.
E) none of these
Physics 1100 –Spring 2012
7. Your car is coasting on level ground at 60 km/h and you apply the
brakes until the car slows to 40 km/h. If you suddenly release the
brakes now, the car tends to
A) decrease in speed if no other forces act.
B) continue moving at 40 km/h.
C) momentarily regain its higher initial speed.
8. Hang from a pair of gym rings and the upward support forces of
the rings will always
A) add up to equal your weight.
B) each be equal to your weight.
C) each be half your weight.
Physics 1100 –Spring 2012
9. A tow truck exerts a force of 3000 N on a car, accelerating it at 2
meters per second per second. What is the mass of the car?
A) 3000 kg
B) 500 kg
C) 1000 kg
D) 1500 kg
E) none of these
10. The force required to maintain an object at a constant velocity in
free space is equal to
A) the mass of the object.
B) the force required to stop it.
C) zero.
D) the weight of the object.
E) none of these
Physics 1100 –Spring 2012
11. Two objects of the same size, but unequal weights are dropped from a
tall tower. Taking air resistance into consideration, the object to hit the
ground first will be the
A) heavier object. B) lighter object.
C) Both hit at the same time. D) not enough information
12. A sack of potatoes weighing 200 N falls from an airplane. As the
velocity of fall increases, air resistance also increases. When air
resistance equals 200 N, the sack's acceleration in meters per second
per second is
A) 0.
B) 9.8.
C) 4.9.
D) infinite.
E) none of these
Physics 1100 –Spring 2012