Chapter 1 – Graphs & Equations in 1-D
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Scalar and vector quantities
Distance vs displacement
Speed vs. velocity
D vs T graphs
V vs T graphs
Calculate Slope & Area under the
curve on various graphs
Acceleration due to gravity /
maximum height questions
Kinematics formulas
Chapter 2 – Vector Components & Motion
in 2-D
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Adding and subtracting vectors
Vector components (resolving
vectors)
Relative motion
Projectile motion
1.
A vacationer, on her newly purchased sailboat, moves at a constant
velocity of 9.0 m/s [south] for 35 min and then returns in the
opposite direction at a velocity of 4.0 m/s in 45 min. The average
velocity of the sailor for this trip is
a. 1.7 m/s [south]
b. 5.0 m/s [south]
c. 6.9 m/s [south]
d. 13 m/s [south]
2.
Below is a velocity-time graph for an in-line skater on the way to
school.
After 15.0 s of skating, the magnitude of the displacement of the
skater is
a. 1.2 x 102 m
b. 15 m
c. 8.0 m
d. 0 m
3.
A plane, initially at rest, accelerates down a runway, reaching a
velocity of 270 km/h [E] in 27.0 s. The acceleration of the plane
during take-off is
a. 1.00 m/s2 [E]
b. 2.00 m/s2 [E]
c. 2.78 m/s2 [E]
d. 3.60 m/s2 [E]
4.
A cyclist, with an initial velocity of 18.0 m/s [north], accelerates at
2.40 m/s2 [south] and comes to a complete stop. The distance
required for the cyclist to come to a complete stop is
a. 67.5 m [north]
b. 67.5 m [south]
c. 7.50 m [north]
d. 7.50 m [south]
5.
A piece of metal works itself loose from the top of a microwave
tower and falls directly to the ground in 2.32 s. The height of the
microwave tower is
a. 52.8 m
b. 26.4 m
c. 13.2 m
d. 9.81 m
6.
A cannon muzzle on a gunship, set at an angle of 40.0o above the
horizontal, fires a shell with a speed of 700 km/h. The maximum
range of the shell is
a. 1.83 km
b. 3.80 km
c. 4.53 km
d. 7.59 km
7.
A football is thrown at a velocity,
, of 60.0 km/h [E] to a
receiver whose position, relative to the thrower, is 40.0 m [E]. A
wind is blowing from the west at a speed of 30.0 km/h,
. The
resultant velocity,
a. 9.5 km/h
b. 30 km/h
c. 67 km/h
d. 90 km/h
8.
, of the football relative to the ground is
A soccer ball is kicked from the ground with a speed of 12.0 m/s at
an angle of 40.0o. It returns to the ground in a time of 1.57 s. At
the instant of being kicked, the horizontal and vertical components
of the velocity of the soccer ball are, respectively,
a. 7.71 m/s, and 9.19 m/s
b. 9.19 m/s, and 7.71 m/s
c. 15.7 m/s, and 18.7 m/s
d. 18.7 m/s, and 15.7 m/s
9.
A ball is thrown into the air at an angle of 60.0o and lands on the
ground 40.0 m away in 2.80 s. The maximum height reached by
the ball in its flight is
a. 1.36 m
b. 2.52 m
c. 10.4 m
d. 31.2 m
Numeric Response
1. The total displacement of the object after 18.0 s is ________ m [W].
(Record your two-digit answer on the answer sheet.)
10. Using the graph above, the velocity of the car when 10.0 s have
elapsed is
a. 20.0 m/s
b. 2.00 m/s
c. 20.0 m/s [east]
d. 2.00 m/s [east]
2. A speedboat accelerates uniformly from rest at 3.0 m/s 2. The distance the
speedboat will travel between 4.0 s and 6.0 s is ______ m. (Record your
two-digit answer on the answer sheet.)
11. Two friends decide to have a friendly race on their bikes. The girl
travels at a speed of 6.0 m/s while her boyfriend speeds off in the
same direction at a speed of 6.5 m/s. If they both start from the
same starting point, how much farther will the boyfriend have
travelled in 15 s?
a. 0.50 m
b. 6.0 m
c. 6.5 m
d. 7.5 m
1. A kicked soccer ball travels 20 m [E], careens off another player, and
travels 10 m [60o S of E]. What is the net displacement of the ball? [
12. Which of the following is false regarding an object that is
accelerating?
a. An object that is accelerating has motion that is constant.
b. An object that is accelerating has motion that is
decreasing.
c. An object that is accelerating has motion that is increasing.
d. An object that is accelerating has motion that is changing
direction.
Long Answer
2. A coin is dropped from a hot-air balloon. The distance the coin will fall
during the third second is ______ m. (Record your three-digit answer on the
answer sheet.)
3. A getaway car from a bank robbery travels 22 km at 15 o E of S and
then changes course and travels 9 km at 37o W of N. If the entire trip took
200 minutes, what is the resultant velocity of the getaway car?
Forces Can Change Velocity!
- What are forces?... units, definition, laws!
-Newton’s 1st law (Inertia) , 2nd law (F=ma) and 3rd law
(Action/Reaction).
-Friction- static and kinetic, “mu” value!
-Inclined Planes, elevator problems & pulleys!
-Free Body Diagrams
diagrams
Gravitational Forces!
-weight vs. mass
-action at a distance (gravity as a field)
-Gravitational Field Strength (acceleration of gravity)
-Newton’s Law of Gravitation Fg = Gm1m2/r2
-using proportions to solve for unknowns using Newton’s Gravitation
formula
-true weight vs. apparent weight on elevators
- free fall and weightlessness
Q: Two cats are on a roof. Which slides off first?
A: The one with the smaller mew (Greek letter mu
- μ).
Multiple Choice
____
Identify the choice that best completes the statement or answers the
question.
4.
The four vectors in the
diagram represent forces of
equal magnitude acting on a
ball. Which of the following
vectors best represents the
net force acting on the ball?
1. Which of the descriptions below are for situations involving dynamics?
I
A soccer player exerts a force of 100 N on the ball to kick it
toward the goal.
II
The maximum speed a cheetah can reach on Earth is about
113 km/h.
III
The force of gravity on a person on the moon is less than on
Earth.
IV
The acceleration of a ball drop toward Earth is 9.81 m/s2.
a
.
Choose your answer from the following.
a. I and II only
c. I and IV only
b. III and IV only
d. I and III only
b
.
c
.
d
.
2. What are the base units of the SI unit of force, the newton (N)?
a. kg·m/s
c. kg·m/s2
b. kg·m2/s
d. kg·m2/s2
____
3.
5.
While moving horizontally
forward at constant
velocity on a snowmobile,
the rider throws a ball
straight up so that it
reaches a height of 5 m.
Ignoring air resistance,
where will the ball land?
In a tractor pull, four
tractors are connected
by strong chains to a
heavy load. Tractors A
and B pull with forces
of 4000 N [E] and
3000 N [E],
respectively. Tractors
C and D pull with
forces of 3500 N [W]
and 2500 N [W],
respectively. The force
of friction exerted by
the ground on the load
is 750.0 N. What is
the net force on the
load?
a. 2250 N [E]
b. 1750 N [E]
a. back in the rider’s hand
b. in front of the rider’s hand
c. 1000 N [E]
d. 250 N [E]
6.
c. behind the rider’s hand
d. behind the snowmobile
____
The tension,
, in a string
attached to the object shown is
equal to the force of gravity,
, acting on the object. Which
of the following motions is/are
possible?
I
II
III
force gives a mass, m2, an acceleration
=
, then
a. 4:1
The object is moving upward at constant velocity.
The object is moving downward at constant velocity.
The object is stationary.
____
Choose your answer from the following.
a. I only
c. III only
b. II only
d. I, II, and III
7. A dynamics cart, initially at rest, is pulled with a constant net force.
Which velocity-time graph best represents the motion of the cart?
a.
8. A net force gives a mass, m1, an acceleration of
c.
d.
. If the magnitude of
is equal to _____
b. 2:1
c. 1:2
d. 1:4
c. 3.3 m/s2
d. 6.7 m/s2
9.
A light string with a mass at
each end is hung over a
frictionless light pulley, as
shown. The pulley and
masses are suspended from
a newton spring scale. The
acceleration due to gravity
at this location is 10 m/s2
[down]. What is the
magnitude of the
acceleration of the masses?
a. 1.0 m/s2
b.
. The same net
b. 2.0 m/s2
10.
A 2.0-kg puck at rest on a horizontal frictionless
platform is pushed north with a constant net force for 1.5 s and then
released. When released, the velocity of the puck is 3.0 m/s
[forward]. What is the displacement of the puck starting from rest
in 2.25 s?
a. 4.5 m [north]
c. 9.0 m [north]
b. 5.1 m [north]
d. 10 m [north]
____
A First Nations hunter is
using a snowmobile to drag
a 20.0-kg sled up a wet,
snowy hill that forms an
angle of 25.0 with the
horizontal, as shown. The
coefficient of kinetic friction
for the sled on wet snow is
0.140. Calculate the force
the snowmobile must exert
to accelerate the sled at
2.00 m/s2 [uphill].
a. 24.9 N [uphill]
b. 82.8 N [uphill]
b.
14.
The derived unit for the universal gravitational constant, G, is
a. N·kg/m
N·m/kg
b.
c. N·m2/kg2
d. N·kg2/m2
c. 148 N [uphill]
d. 196 N [uphill]
12. What happens to the magnitude of the gravitational field strength if
the distance from a planet doubles and the test mass quadruples? The
gravitational field strength
a. doubles
c. halves
b. remains the same
d. quarters
13. For a test mass, which of the following graphs best represents the
gravitational field strength, g, versus the distance from Earth’s centre,
r?
a.
d.
c.
15.
A spaceship moves so that the distance from the centre of
Earth triples.
The force of gravity on the spaceship
a. becomes three times smaller
b. becomes three times larger
c. becomes nine times smaller
d. becomes nine times larger
16.
An 80.0-kg astronaut is standing on a scale in a rocket.
Which pair of free-body diagrams, drawn to scale, show the
astronaut in a weightless condition and then in free fall in the
presence of a gravitational field?
is the force of gravity and
is the normal force.
I
I
II
I
I
a. I weightless; I free fall
b. I weightless; II free fall
c. I weightless; III free fall
d. II weightless; III free fall
Numeric Response
17. Use the following information to answer the next question.
Written A planet in a newly discovered planetary system has a mass of 4.65 x
1028 kg and a radius of 3.24 x 108 m. If a 2.00 kg rock was
dropped from rest and allowed to fall 6.00 m to the planet’s surface,
how long would it take the rock to reach the planet’s surface? (0.637
s)
[3 marks]
2. Use the following information to answer the next question.
The magnitude of the net force acting on the object illustrated above
is _____ N. (Record your three-digit answer on the answer sheet.)
(63.6 N)
18. Use the following information to answer the next question.
Forces and Fields Definitions
1 Three-dimensional region of influence
2 Region of influence surrounding any object with mass
3 Attractive force between two objects due to their mass
4 Gravitational force exerted on an object by a celestial body
Match each of the definitions listed above with the appropriate term
given below.
Field
___ (Record in the first column.)
Weight
___ (Record in the second column.)
Gravitational field
___ (Record in the third column.)
Gravitational force
___ (Record in the fourth column.)
The gravitational force exerted on Earth by the Moon is 1.9 X 1020 N
[toward the Moon’s centre]. The gravitational force exerted on Earth
by the Sun is 5.5 X 1022 N [toward the Sun’s centre]. Calculate the
magnitude of the net gravitational force exerted on Earth by the
Moon and the Sun. (5.48 X 1022 N)
3. Use the following information to answer the next question.
(Record all four digits of your answer on the answer sheet.)
Using the distances
above and the masses of the planets listed on your data sheet,
calculate the magnitude of the net gravitational force exerted on
Earth by the Moon and the Su. (3.5 X 1022 N)
Chapter 5 – Circular Motion
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Speed and velocity in circular
motion
Centripetal force (horizontal &
vertical situations)
centripetal acceleration
period & frequency
Kepler’s 3 Laws
Satellites & celestial bodies in
circular motion
Chapter 6 – Energy & Work
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Work
Potential, Kinetic and Mechanical
Energy
Work – Energy Theorem
Conservation of Energy
Power
Pendulum
1.
The hard disk drive in a computer spins at a rate of 7.20 x 103
rpm. If the disk has a radius of 8.26 cm, what is the tangential
speed of the outer edge of the disk?
a. 62.3 m/s
b. 19.8 m/s
c. 3.74 x 103 m/s
d. 6.23 x 103 m/s
6.
The moon Ariel orbits Uranus with an average radius of 1.91 x 108
m once every 2.18 x 105 s. If Uranus's moon Titania orbits with a
radius of 4.36 x 108 m, what would you expect its period to be?
a. 7.52 x 105 s
b. 4.98 x 105 s
c. 3.78 x 105 s
d. 3.92 x 105 s
2.
The carriages on a Ferris wheel travel at a speed of 1.86 m/s. If
the wheel has a radius of 6.25 m, what is its period of rotation?
a. 3.48 s
b. 10.6 s
c. 18.7 s
d. 21.1 s
7.
A force of 56.0 N does work over a displacement of 24.5 m. If the
angle between the force and the displacement is 35.0o, what is the
work done by this force?
a. 1.37 x 103 J
b. 1.12 x103 J
c. 9.61x 102 J
d. 7.87 x 102 J
3.
A car is travelling around a horizontal circular track that has a
radius of 85.0 m. If the speed of the car is constant at 24.0 m/s,
what is the magnitude of its acceleration?
a. 0
b. 2.42 m/s2
c. 9.81 m/s2
d. 6.78 m/s2
8.
If a force of 256 N is applied to a spring, the spring is stretched a
distance of 9.50 cm from its equilibrium position. What is the elastic
constant of this spring?
a. 2.69 x 103 N/m
b. 2.43 x 103 N/m
c. 26.9 N/m
d. 24.3 N/m
9.
A car with a mass of 1.60 x103 kg has 4.61 x 105 J of kinetic
energy. What is the speed of the car?
a. 12.0 m/s
b. 17.0 m/s
c. 24.0 m/s
d. 34.0 m/s
4.
5.
A 0.350 kg ball on a 1.75 m string is swung in a vertical circle. At
the instant the ball moves through the top of the circle, it has a
speed of 6.00 m/s. What is the tension in the string?
a. 7.20 N
b. 3.77 N
c. 10.6 N
d. 0 N
Which of the following are predicted by Kepler's laws for the
motion of planets orbiting the Sun?
I. Planets move in elliptical orbits about the Sun.
II. Planets move such that in equal periods of time a line
from the Sun to the planet sweeps out equal areas.
III. The speed of a planet is greatest when it is farthest from
the Sun.
a.
b.
c.
d.
I and II
II and III
I and III
I, II, and III
10. A force of 785 N [W] is applied to a cart with a mass of 68.0 kg.
The cart is rolling with an initial velocity of 12.9 m/s [W]. The force
acts over a displacement of 17.5 m [W], causing the cart to
accelerate to a velocity of 24.7 m/s [W]. What is the work done
by the force on the cart?
a. 1.37 x 104 J
b. 1.03 x 104 J
c. 1.51 x 104 J
d. 4.75 x103 J
11. A spring is compressed a distance of 15.0 cm as it slows a 7.50 kg
mass to a stop. If the elastic constant of the spring is 3.20 x 104
N/m, what was the initial speed of the block?
a. 8.94 m/s
b. 17.9 m/s
c. 9.80 m/s
d. 25.3 m/s
Long Answer / Numeric Response
The diagram shows a skateboarder starting to roll down a hill. Assume that
the skateboard rolls with negligible friction.
12. A crane lifts a pallet of lumber with a mass of 435 kg from the 4th
to the 23rd floor of a building. If each floor has a height of 3.20 m,
what is the work done against the force of gravity?
a. 2.73 x 105 J
b. 2.59 x 105 J
c. 2.46 x 105 J
d. 2.64 x 104 J
13. The Moon orbits Earth once every 27.32 days. What would be the
orbital period of a satellite that orbits Earth with a radius
that
of the Moon's orbit?
a. 164 h
b. 81.9 h
c. 40.9 h
d. 1.28 h
14. A 30.0 N centripetal force acts on a mass causing it to move in a
circle with a radius of 0.750 m and a period of 1.50 s. If the radius
of the circular motion is to be increased to 1.00 m and the period
to be decreased to 1.00 s, what centripetal force would be
required?
a. 10.0 N
b. 90.0 N
c. 20.0 N
d. 3.33 N
15. Venus, with a mass of 4.87 x 1024 kg, is held in orbit by the Sun's
force of gravity. If the Venus orbits the Sun at a radius of 1.08 x
1011 m with a period of 1.94 x 107 s, what is the force of gravity
that the Sun exerts on Venus?
a. 1.70 x 1029 N
b. 5.52 x 1022 N
c. 8.78 x 1021 N
d. 1.39 x 1021 N
1.
A skateboarder and his skateboard have a combined mass of 76.4
kg. The skateboarder passes a point P that is 3.90 m above bottom
of the hill with a speed of 1.25 m/s. When he passes point Q that is
1.30 m above the bottom of the hill, the skateboarder has a speed
of ______ m/s. (Record your three-digit answer on the answer
sheet.) (7.97)
2.
A 5.20 kg pail of water is swung in a vertical circle with a radius of
2.40 m. If the water in the pail is to stay at the bottom of the pail
then the slowest speed that the pail could have at the top of the
circle is _________ m/s. (Record your three-digit answer on the
answer sheet.) (4.85)
3.
If a satellite orbits Earth at an average height of 560 km, then the
period of its orbit is a.bc x 10d s. The values of a, b, c, and d,
respectively, are ______, ______, ______, and ______. (Record all
four digits of your answer on the answer sheet.) (5743)
Simple Harmonic Motion (Oscillatory Motion)
-Oscillatory Motion of Springs and Pendulums
-Period and Frequency
-Hookes Law (F=-kx) and the spring constant
-Horizontal and Vertical Springs/Elastics
-How Position, Acceleration, Velocity and Time affects spring systems.
-Natural, Forced and Mechanical Resonance- examples, why, how to fix it etc.
Mechanical Waves
-mechanical waves- transverse and longitudinal
-amplitude, crest, trough, wavelength, frequency
-universal wave equation
-reflection
-constructive and destructive interference
-resonance and harmonics, closed and open ended instruments
Unit 4 Review Package
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Block on a Spring
A block on a horizontal frictionless surface attached to a spring. Diagram is
not to scale.
1. Which of the following conditions are necessary for oscillatory motion?
I. The motion must be repeated.
II. The frequency must be constant.
III. The period must be less than one hour.
a. I only
b. I and II only
c. II and III only
d. I, II, and III
2. The restoring force exerted by a spring is
constant of this spring is
a. 1.38 cm [N]
b. 2.42 cm [N]
N [N]. If the spring
N/m, what is the position of the spring?
c. 1.38 cm [S]
d. 2.24 cm [S]
3. A harmonic oscillator consists of a 6.75-kg mass attached to a spring with a
spring constant of
N/m. If the mass, which oscillates on a
horizontal frictionless surface, reaches a maximum speed of 5.90 m/s, what
is the amplitude of the oscillation?
a. 0.226 m
c. 0.292 m
b. 0.259 m
d. 0.315 m
4. What is the length of a pendulum on Earth that has a period of 1.00 s?
a. 49.8 cm
c. 12.8 cm
b. 24.8 cm
d. 6.17 cm
5. Refer to the diagram Block on a Spring to answer this question.
A block on a horizontal frictionless surface is attached to a spring, as shown
in the diagram. When the block is released, it oscillates back and forth
between the positions indicated by the vectors
. Which points (I, II, and
III) best indicate where the acceleration of the block will be zero?
a. I and III
c. II only
b. I and II
d. I, II, and III
6. Which of the following factors affect the period of a pendulum?
I. the length of the string supporting the bob
II. the mass of the bob
III. the acceleration due to gravity in the region of the pendulum
a. I and II
b. II and III
c. I and III
d. I, II, and III
7. Which of the following is an example of mechanical resonance?
a. A bell ringer pulls on a bell rope to keep the bell ringing.
b. A mass suspended on a spring is pulled down and released.
c. A tree branch oscillates in the wind.
d. A pendulum gradually loses amplitude.
Wave Phase Points
8. When a transverse wave moves through a medium, the medium
a. moves back and forth across the direction of motion of the wave but
generally stays in the same place.
b. moves back and forth parallel to the direction of the wave’s motion but
generally stays in the same place.
c. moves back and forth across the direction of motion of the wave as it
travels in the direction of wave motion.
d. moves back and forth parallel to the motion of the wave as it travels in
the direction of wave motion.
9. Which of the following statements applies/apply to the reflected pulse that
is created when a pulse travelling along an ideal spring reflects from a
fixed point at the end of the spring?
I. The pulse is inverted.
II. The amplitude of the reflected pulse is less than the amplitude of the
incident pulse.
a. I only
b. II only
c. both I and II
d. neither I nor II
10. Refer to the diagram Wave Phase Points to answer this question.
Listed below are four pairs of points from the wave train in the diagram. For
which of these pairs of points is the distance between them equal to one
wavelength?
I. C and G
II. A and J
III B and K
IV. D and M
a. I, II, and III
b. II, III, and IV
c. I, III, and IV
d. I, II, and IV
11. Refer to the diagram Wave Phase Points to answer this question.
Listed below are four pairs of points from the wave train diagram. Which of
the pairs of points are in phase?
I. A and J
II. G and N
III. E and N
IV. C and L
a. I, II, and III
b. I, II, and IV
c. I, III, and IV
d. II, III, and IV
12. Refer to the diagram Wave Phase Points to answer this question.
For which pair of points on the diagram is the vertical distance between their
positions equal to the amplitude of the wave?
a. B and F
c. C and L
b. H and E
d. H and P
13. When a longitudinal wave moves through a medium, the medium
a. moves back and forth across the direction of motion of the wave but
generally stays in the same place.
b. moves back and forth parallel to the direction of the wave’s motion but
generally stays in the same place.
c. moves back and forth across the direction of motion of the wave as it
travels in the direction of wave motion.
d. moves back and forth parallel to the motion of the wave as it travels in
the direction of wave motion.
b. B and D
and E
d. E only
16. A wave in a spring, stretched to a length of 5.30 m, travels at a speed of
3.40 m/s. What is the lowest resonant frequency for this spring?
a. 0.160 Hz
c. 0.642 Hz
b. 0.321 Hz
d. 1.14 Hz
Numeric Response
17. If a 4.85-kg pendulum bob is pulled sideways so that the string makes an
angle of 14.9o with the vertical, then the magnitude of the restoring force
acting on the mass is ______ N. (Record your three-digit answer on the
answer sheet.) (12.2 N)
18. A spring is stretched to a length of 5.40 m. You generate a standing wave
using a frequency of
. If there are 5 antinodes and 6 nodes along
the spring, then the speed of the wave in the spring is ______ m/s. (Record
your three-digit answer on the answer sheet.) (10.3 m/s)
A Standing Wave Pattern in a Spring
Written Response:
1.
Oscillations in many devices such as musical instruments are
desirable. However, many oscillations, such as those caused by winds or
earthquakes, can be very destructive.
(a) Define what is meant by resonant frequency, forced frequency, and
mechanical resonance. Give an example of each.
(b) Give an example of a structure or machine in which mechanical
resonance may be used to advantage. Describe how mechanical
resonance is used in this device.
(c) Give an example or situation in which oscillations are undesirable.
Describe what scientists and engineers can do to eliminate or reduce
the effects of unwanted oscillations.
15. Refer to the diagram A
Standing Wave Pattern
in a Spring to answer this
question.
The labelled points that
are located at nodal
points are
a. A and C
c.
A, C,