Review for Final Exam
1.
2.
Define the following:
a) kinematics
e) acceleration
b) dynamics
f) vector
c) mechanics
g) scalar
d) velocity
In terms of graphing distinguish between the following:
a) Average velocity and instantaneous velocity
The average velocity is equal to the slope of the straight line joining two points on a position-time graph. The
instantaneous velocity is the value approached by the average velocity as the time interval approaches zero. It
is obtained by finding the slope of the tangent at a moment in time on a position-time graph.
b)
Average acceleration and instantaneous acceleration
Average acceleration for an interval of time is equal to the slope of the line joining the two points on a
velocity-time graph. Instantaneous acceleration is the value approached by the average acceleration as the
time interval approaches zero. It is obtained by finding the slope of the tangent at a moment in time on a
velocity-time graph.
3.
Distinguish between position and displacement.
Position is the location of an object relative to the origin of the selected coordinate system. Displacement is the
change in position of an object.
4.
Identify the quantity that is changing every second when an object is accelerating.
When an object is accelerating, the velocity is changing every second. For example, if an object is accelerating
at 5 m/s2 , the velocity is changing, increasing by 5 m/s every second.
5.
What does a negative area calculation under a velocity-time graph mean?
A negative area under a velocity-time graph means the object is moving in the negative direction. For
example, if east is defined as the positive direction, the object would be moving west.
6.
(a) Define what is meant by a net or unbalanced force acting on an object.
A net or unbalanced force is the vector sum of all the forces acting on an object.
(b) Explain, with the aid of a free-body diagram, how an object can be experiencing no net force when it
has at least three forces acting on it.
The vector sum of the three forces is zero.
(c) Describe, with the aid of a free-body diagram, an object that is experiencing a net force. Identify in
which direction the object will move and with what type of motion. Relate the direction and type of
motion to the direction of the net force.
The vector sum of all forces acting on the object is greater than zero. Since a non-zero net force is acting on
the object, the object will be accelerating. Since the normal force and the gravitational force balance each
other, the applied force is the net force. The acceleration will be in the same direction as the net force.
7.
What is a normal force?
The normal force is a force that acts in a direction perpendicular to the common contact surface between two
objects.
8.
What is the difference between static and kinetic frictional force?
Static and kinetic frictional forces differ in that the static frictional force acts to keep an object at rest, and the
kinetic frictional force acts to slow down the motion of an object. The static frictional force is usually greater
than the kinetic frictional force.
9.
How would you describe a physicist’s concept of work to a non-physicist?
To a physicist, work is done on an object only when the object’s energy has been changed. This could be
positive work, which increases the object’s energy, or it could be negative work, which decreases the object’s
energy.
10. Describe a scenario where there is an applied force and motion and yet no work is done.
A scenario in which there is an applied force and motion, yet no work is done, would be if the applied force on
an object was perpendicular to the object’s displacement. An example would be a figure skater holding his
partner above his head while they glide forward over the ice. In this situation, he is pushing upward on his
partner to keep her from falling while they both move forward. No work is being done on her.
11. Describe the two general types of energy into which all forms of energy can be classified.
Two general types of energy into which all forms can be classified are kinetic energy and potential energy.
Kinetic energy is energy of motion, and only moving objects possess this type of energy. Potential energy is
energy that is stored within the object.
12. How much more kinetic energy would a baseball have if
a) its speed was doubled?
b) its mass was doubled?
Using the kinetic energy equation, Ek = ½ mv2
(a) if the baseball’s speed is doubled, its kinetic energy would quadruple
(b) if the baseball’s mass is doubled, its kinetic energy would double
13. Differentiate between potential energy and gravitational potential energy.
Potential energy is energy that is stored and can exist in many forms (e.g., elastic potential energy,
gravitational potential energy, and electric potential energy). Gravitational potential energy is energy that is
stored due to an object’s condition or position above some chosen reference point.
14. State whether each of the following is a scalar or vector quantity: (a) velocity, (b) mass, (c) distance, (d)
speed, (e) acceleration, (f) time interval, and (g) displacement.
Velocity, acceleration, and displacement are all vector quantities in that they have a direction associated with
them. Mass, distance, speed, and time interval are scalar quantities as they only require a magnitude and a
unit.
15. Distinguish between the average velocity and the instantaneous velocity.
16. (a) What does the slope of the tangent to the curve on a position-time graph represent?
This represents the instantaneous velocity at a point in time on the position-time curve.
(b) What does the slope of the tangent to the curve on a velocity-time graph represent?
This represents the instantaneous acceleration at a point in time on the velocity-time curve.
(c) What does the area under the curve on a velocity-time graph represent?
This represents the displacement of the object.
17. How are frequency and period related? What is a hertz?
Frequency and period are reciprocals. Hertz is the SI unit for frequency (s -1).
18. What determines the frequency of a wave?
The frequency of a wave is determined by the frequency of the vibrating source.
19. Explain what a wave is. How do transverse and longitudinal waves differ?
20. If the frequency of a wave travelling in a rope is doubled, what will happen to the speed of the wave? What
will happen to the wavelength of the wave?
Doubling the frequency of a wave in a rope halves the wavelength, but leaves the speed of the wave
unchanged.
21. A 1-cm high wave crest is travelling toward a 2-cm high wave crest in the same spring. What will be
produced when they meet? What kind of interference is this?
A 3 cm high super-crest will be formed. This is constructive interference.
22. A 1-cm high wave crest is travelling toward a 2-cm deep wave trough in the same medium. What will be
produced when they meet? What kind of interference is this?
A trough 1 cm deep will be formed. This is destructive interference.
23. What is a standing wave? What conditions are necessary to produce a standing wave? What are nodes?
How far apart are adjacent nodes?
A standing wave is a phenomenon in which the medium undergoes constructive interference between
stationary points of continual destructive interference. The pattern, consisting of super-crests and supertroughs (antinodes) between nodes, oscillates but does not travel. A standing wave is produced when two
waves with the same wavelength travel in opposite directions in the same medium. Nodes (in a linear standing
wave) are half a wavelength apart.
24. What happens to straight waves when they pass through an opening in a barrier? What do we call this
effect?
After passing through an opening in a barrier, straight waves (whose wavelength is large compared to the size
of the opening) spread. This process is called “diffraction.”
25. The amplitude of a sound wave represents what property of sound?
Amplitude is connected to the loudness of sound, which is related to energy.
26. Describe the motion of a molecule or particle as a sound wave passes.
As a sound wave passes, a molecule or a particle in front of it is pushed toward its adjacent molecules,
producing a small volume of higher pressure called “compression.” When the molecule is rebounded by
collision with other molecules, an expanded space is produced for molecules to spread out, resulting in a
volume of lower pressure called “rarefaction.”
27. Explain the meaning of the “quality” of sound.
The “quality” is an attribute in sound used to distinguish sounds having the same fundamental frequency but
a different set of overtones. The quality of sound enables you to identify sounds from two people, singing the
same note at the same loudness, or sounds from two musical instruments, playing notes with the same
loudness and pitch.
28. Describe two significant differences between sound and electromagnetic waves.
Sound waves require a medium through which to travel, whereas electromagnetic waves, unique among
waves, can travel in a vacuum. Sound waves are longitudinal waves (vibrations parallel to direction of wave
motion) while electromagnetic waves are transverse waves (vibrations perpendicular to direction of wave
motion).
29. A friend puts a battery and a siren from a toy into a Nerf ball. She connects the battery and tosses you the
ball with the siren wailing. Describe what you will hear and what she will hear as the ball moves through
the air.
Choose the letter of the best answer for each of the following questions.
30. An airplane is moving at constant velocity in a straight line flight. What is the net force acting on the plane.
a) zero According to Newton’s first law, the airplane continues its constant motion in a straight line when
there is no force acting on it.
31. A football is thrown by a quarterback to a receiver deep in the end zone. Neglecting friction the
acceleration of the football during the flight
Since the only force acting on the football is the force due to
c) is the same during its entire flight
gravity, the acceleration is the same during the entire flight.
32. A ball is thrown upward. After it is released, its acceleration
The acceleration of an object in free fall is always 9.81 m/s 2 [down].
e) remains constant
33. A ball of mass m1 is dropped from the roof of a 10-storey building. At the same instant, another ball of
mass m2 is dropped out of a ninth-storey window, 10 m below the roof. The distance between the balls
during the flight
Both objects accelerate at the same rate.
a) remains at 10 m throughout
34. You drop a 1.0 kg stone off the roof of a 10-storey building. Just as the stone passes the fifth-floor, your
friend drops a 1.0 kg ball out of a fifth-floor window. If air resistance is neglected, which of the following
statements is true? Explain your reasoning.
b) The stone hits the ground first and with a greater speed than the ball does.
While passing the fifth floor, the stone is already travelling much faster than the ball.
35. If action and reaction forces are always equal and opposite then why do objects more at all?
b) the forces act on different objects While passing the fifth floor, the stone is already travelling much
faster than the ball.
36. A hockey puck and a curling stone are at rest on a sheet of ice. If you apply equal impulses to each of them
with a hockey stick.
e) they will have the same momentum but different velocities
The mass of a hockey puck is different from the mass of a curling stone.
37. Displacement between two points is always
c) less than or equal to distance
38. A negative acceleration means that
c) the acceleration vector is pointing in a negative direction
39. An object is slowing down when
b) the signs of the velocity and acceleration are opposite
40. If an object is in uniform motion
c) its acceleration is zero
41. On a position versus time graph, a straight horizontal line corresponds to motion at
a) zero speed
For each of these questions, list the given information, state the formula you are using, round your answer to the
correct number of significant digits, indicate the units of the answer, and write your answer in scientific
notation, if appropriate.
42. A delivery truck travels 15 km north, then 13 km east and finally heads south for 18 km. Determine the
truck’s displacement. {13 km[E13°S]}
43. A car is travelling 5.0 x 101 km/h [N]. It turns a corner and heads down a side street at 4.0 x 101 km/h [E].
Determine the car’s change in velocity. {64 km/h[E51°S]}
44. A car travels directly north. The car is on a highway for 2.4 h travelling with a velocity of 85 km/h. It
slows to 25 km/h for 45 min while going through a town. It reaches the highway north of town and travels
another 1.6 h at 95 km/h.
a) How far did the car travel? {3.7 x 102 km}
b) What was the car’s average velocity for the entire trip? {79 km/h}
45. A child on a sled starts from rest and accelerates down a snowy hill at 0.65 m/s2. How long does it take the
child to reach the bottom of the hill if it is 17 m away? {7.2 s}
46. How far does a car travel while it is accelerating from 22 m/s [W] to 28 m/s [W] at a rate of 3.0 m/s2?
{5.0 x 101 m}
47. How long does it take a race car, accelerating from a velocity of 6.0 m/s at 4.0 m/s2 to travel a distance of
216 m? {9.0 s}
48. Jerry watches a stick float downstream in a river and notes that it moves 12 m [E] in 2.0 x 101 s. His friend
Bill is starting on the south side of the river and is going to swim across. In still water Bill knows that he
can swim a speed of 1.7 m/s. What is Bill’s velocity relative to the shore? If the river is 1.5 km wide, how
long will it take Bill to cross the river? How far downstream will he land?
{1.8 m/s[N19°E]; 8.8 x 10 2 s; 5.3 x10 2 m}
49. A passenger climbs aboard a northbound bus and walks toward the back at a rate of 1.8 m/s. The bus starts
off up the street at 9.2 m/s. What velocity will the passenger appear to be walking relative to
a) a person standing on the sidewalk. {7.4 m/s[N]}
b) a person who is walking 2.1 m/s south along the sidewalk. {9.5 m/s[N]}
c) a person who is walking 2.1 m/s north along the sidewalk. {5.3 m/s[N]}
50. A sailboat is using its motor to travel with a velocity of 42 km/h [E40.0oS] when a wind from the north
starts blowing at 5.0 km/h. What will be the velocity of the sailboat relative to the shore?
{45 km/h[E45oS]}
51. A pitcher throws a baseball with a velocity of 26 m/s [S]. It strikes a player’s bat and the velocity changes
to 3.0 x 101 m/s [N]. If the player’s bat was in contact with the ball for 3.0 x 10-3 s, determine the
acceleration of the ball. {1.9 x 104 m/s2[N]}
52. A girl is taking her dog for a walk. They walk 5.0 km [N] and then turn around and walk 12 km [S].
a) What is the total distance that they travelled? {17 km}
b) What is their displacement? {7 km[S]}
c) What displacement would they have to walk to get back to their starting point? {7 km[N[}
53. A cyclist is travelling with an average velocity of 5.9 m/s [W]. What will be his displacement after 1.2 h?
{25 km[W]}
54. A canoeist paddles 1.6 km downstream and then turns around and paddles back upstream for 1.2 km. The
entire trip takes 45 minutes.
a) What is the displacement of the canoeist? {+0.4 km}
b) Calculate the average velocity of the canoeist. {0.53 km/h[downstream]}
55. The closest star to our solar system is Alpha Centauri, which is 4.12 x 1016 m away. How long would it
take light from Alpha Centauri to reach our solar system if the speed of light is 3.00 x 108 m/s? Provide an
answer in both seconds and in years. {1.37 x 108 s or 4.35 years}
56. A car is travelling at 14 m/s when the traffic light ahead turns read. The car brakes and comes to a stop in
5.0 s. Calculate the acceleration of the car. {-2.8 m/s2}
57. A bowling ball is rolling with an average velocity of 2.7 m/s[E]. If it started at a position 0.45 s from the
foul line, where was the ball after 7.5 s? {21 m[E]}
58. Jocelyn drove north at 45 km/h for 20 min then turned west and drove at 54 km/h for 27 min. Finally she
drove south at 18 km/h for 6.4 min.
a) the distance that Jocelyn drove {41 km}
b) her displacement {28 km[W28oN]}
c) her average speed {46 km/h}
d) her average velocity {31 km/h[W28oN]}
59. A pilot wants to fly due north. However, a strong wind is blowing from the west. Therefore the pilot
maintains a heading of a few degrees west of north so that her final ground speed will be in a direction due
north. Is the airplane accelerating in this situation? Why or why not?
60. At the very end of the race, a runner accelerates at 0.3 m/s2 for 12 s to attain a speed of 6.4 m/s. Determine
the initial velocity of the runner. {3 m/s}
61. The acceleration due to gravity on the moon is 1.6 m/s2 [down]. If a baseball was thrown with an initial
velocity of 4.5 m/s [up], what would its velocity be after 4.0 s? {-1.9 m/s}
62. A cyclist is travelling at 5.6 m/s when she starts to accelerate at 0.60 m/s2 for a time interval of 4.0 s.
a) How far did she travel during this time interval? {27.2 s}
b) How long did it take the truck driver to change his speed? {8.1 m/s}
63. A skydiver falling toward the ground accelerates at 3.2 m/s2. Calculate his displacement if after 8.0 s he
attained a velocity of 28 m/s [down]. {-1.1 x 102 m}
64. A car is travelling on the highway at a constant speed of 24 m/s. The driver misses the posted speed limit
sign for a small town she is passing through. The police car accelerates from rest at 2.1 m/s2. From the time
that the speeder passes the police car:
a) How long will it take the police car to catch up to the speeder? {23 s}
b) What distance will the cars travel in that time? {5.50 x 102 m}
65. A person walks 3.0 km [S] and then 2.0 km [W], to go to the movie theatre.
a) Draw a vector diagram to illustrate the displacement.
b) What is the total displacement? {3.6 km[S34oW]}
66. A person in a canoe paddles 5.6 km [N] across a calm lake in a time of 1.0 h. He then turns west and
paddles 3.4 km in 30.0 minutes.
a) Calculate the displacement of the canoeist from his starting point. {6.6 km[N31oW]}
b) Calculate the change in velocity. {4.4 km[N31oW]}
67. A physics teacher is on the west side of a river and wants to swim across and end up at a point directly
across from his starting point. He notices that there is a current in the river and that a leaf floating by him
travels 4.2 m [S] in 5.0 s. He is able to swim 1.9 m/s in calm water.
a) What direction will he have to swim in order to arrive at a point directly across from his position?
{E26oN}
b) Calculate his velocity relative to the shore. {1.7 m/s[E]}
c) If the lake is 4.8 km wide, how long will it take him to cross? {47 min}
68. A jogger runs 15 km [N35oE], and then runs 7.5 km [N25oW]. It takes a total of 2.0 hours to run.
a) Determine the displacement of the jogger. {20 km[N16oE]}
b) Calculate the jogger’s average velocity. {9.9 km/h[N16oE]}
69. An object weighs 78.3 N on the Moon. How much does it weigh on
a) Earth {468 N}
b) Mars {178 N}
c) Jupiter {1.24 x 103 N}
70. You are moving a 95 kg wood crate across a wood floor.
a) What is the magnitude of the force with which you must push to start the crate moving? {3.7 x 102 N}
b) After it starts moving, how hard must you push to keep it moving at a constant velocity? {1.9 x 102 N}
71. A hockey stick exerts a force of 575 N [E] on a 0.125 kg hockey puck. What is the acceleration of the
puck? {4.63 x 103 m/s2}
72. An applied force with a magnitude of 335 N is required to push a chair across a living room with an
acceleration of 0.722 m/s2. If the coefficient of kinetic friction between the chair and the floor is 0.330,
what is the mass of the chair? {84.6 kg}
73. Three children pull a sled loaded with logs by tying ropes to the sled. Angie pulls with a force of 7.3 N
[E25.0oN], Sean pulls with a force of 9.2 N [E], and Sid pulls with a force of 8.8 N [E20.6oS]. The friction
between the sled and the snow is negligible. If the mass of the load is 192 kg, what is the velocity of the
sled after 3.50 s? Use scale diagrams in your solution. {0.44 m/s[E]}
74. A toboggan is being pulled with an applied force that is at an angle of 30o to the horizontal.
a) Draw a free-body diagram to illustrate all the forces acting on the toboggan.
b) Predict the motion of the toboggan if the horizontal component is greater than the frictional force.
{The toboggan will accelerate in the horizontal direction.}
c) Predict the motion of the toboggan if the horizontal component of the applied force is equal to the
frictional force. {The toboggan will move at a constant velocity in the horizontal direction.}
d) Predict the motion of the toboggan if the horizontal component of the applied force is less than the
frictional force. {It would slow down and stop.}
75. A parachutist jumps from a plane and falls faster and faster through the air. At one point in time her
acceleration is 8.0 m/s2 [down]. If she has a mass of 65 kg, calculate the force of air resistance that is
acting opposite to her motion. {1.2 x 102 N[up]}
76. Two objects, m1 and m2, are accelerated independently by forces of equal magnitude. Object m1 accelerates
at 10.0 m/s2 and m2 at 20.0 m/s2. What is the ratio of
a) their inertial masses? {2:1}
b) their gravitational masses? {2:1}
77. A 1500 kg car stands at rest on a hill that has an incline of 15o. If the brakes are suddenly released, describe
the dynamics of the car’s motion by calculating the following:
a) the car’s weight, {1.5 x 104 N}
b) the component of the weight parallel to the incline, {3.8 x 103 N}
c) the car’s acceleration, {2.5 m/s2[down the incline]}
d) the velocity acquired after travelling 100.0 m (in m/s and km/h), {23 m/s, 81 km/h} and
e) the time for the car to travel 100.0 m. {8.9 s}
78. How much force is needed to push a 75.0 kg trunk at constant velocity across a floor, if the coefficient of
friction between the floor and the crate is 0.27? {2.0 x 102 N}
79. A car can accelerate from rest to 1.00 x 102 km/h in 6.0 s. If its mass is 1.5 x 103 kg, what is the magnitude
and direction of the applied force? {6.9 x 103 N}
80. A 1572 kg car is pulling a 982 kg trailer. If the car and trailer are accelerating at 1.07 m/s2 west, what force
is the road exerting on the wheels of the car? What force does the trailer hitch exert on the trailer?
{1.54 x 104 N; 1.05 x 103 N}
81. A 1400 kg car travels north at 25 m/s. What is its momentum? {3.5 x 104 kgm/s[N]}
82. What impulse is needed to stop the following?
a) 150 g baseball travelling at 44 m/s {-6.6 kgm/s}
b) 5.0 kg bowling ball travelling at 8.0 m/s {-4.0 x 101 kgm/s}
c) 1200 kg car rolling forward at 2.5 m/s {3.0 x 103 kgm/s[backward]}
83. A 0.80 kg ball travelling at 12 m/s [N] strikes a wall and rebounds at 9.5 m/s [S]. The impact lasts 0.065 s.
a) What is the initial momentum of the ball? {9.6 kgm/s[N]}
b) What was the change of momentum of the ball? {17 kgm/s[S]}
c) What was the impulse on the wall? {17 kgm/s[N]}
d) What was the average force acting on the wall? {2.6 x 102 N[N]}
e) What was the average force acting on the ball? {2.6 x 102 N[S]}
84. A tennis player smashes a serve so that the racquet is in contact with the ball for 0.055 s, giving it an
impulse of 2.5 N  s.
a) What average force was applied during this time? {45 N}
Assume that the vertical motion of the ball can be ignored. If the ball’s mass is 0.060 kg, what will be
the ball’s horizontal velocity? {42 m/s}
85. A car travels at a constant velocity of 27.0 m/s for 1.00 x 102 m.
a)
Name all of the forces that act on the car. {The forces on the car are the thrust pushes the car forward,
b)
the drag is the total of all of the frictional forces pushing backward on the car, the weight is the force of
gravity downward on the car, and the normal force or reaction force from the ground pushing upward
on the car.}
b)
Which, if any, of these forces are doing work on the car? How much work are these forces doing?
{The thrust does positive work on the car, since it is pointed in the same direction as the car’s
displacement, and the drag does negative work on the car since its direction is opposite to the direction
of the car’s displacement. The amount of work done by each of these forces is equal, since the car is
travelling at a constant velocity. The weight and normal force do no work on the car, since they are
perpendicular to the direction of the car’s displacement.}
86. In order to start her computer, a student pushes in the button to turn on the monitor. This action requires
her to do 0.20 J of work. Find the average force that must be applied if she pushes the button a total
distance of 0.450 cm. {44 N}
87. A young girl pushes her toy box at a constant velocity with a force of 50.0 N. Calculate the work done by
the girl if she moves the box 7.00 m. {3.5 x 102 J}
88. A horse pulls a wagon that was initially at rest. The horse exerts a horizontal force of 525 N, moving the
wagon 18.3 m. The applied force then changes to 345 N and acts for an additional distance of 13.8 m.
Calculate the total work done by the horse on the wagon during the trip. {1.44 x 104 J}
89. A man drags a small boat 6.00 m across the dock with a rope attached to the boat. Find the amount of work
done if the man exerts a 112.0 N force on the rope at an angle of 23o with the horizontal. {6.2 x 102 J}
90. A 65.0 kg rock is moved 12.0 m across a frozen lake. If it is accelerated at a constant rate of 0.561 m/s2
and the force of friction is ignored, calculate the work done. {438 J}
91. A 68 kg in-line skater starts from rest and accelerates at 0.21 m/s2 for 15 s. Find her final velocity and total
kinetic energy after the 15 s of travel. {3.15 m/s; 3.4 x 102 J}
92. A 0.80 kg block of wood has an initial velocity of 0.25 m/s as it begins to slide across a table. The block
comes to rest over a distance of 0.72 m.
a) What is the average frictional force on the block? {-3.5 x 10-2 J}
b) How much work is done on the block by friction? {-2.5 x 10-2 J}
c) How much work is done on the table by the block? {2.5 x 10-2 J}
93. A 1.5 kg book falls 1.12 m from a table to the floor.
a) How much work did the gravitational force do on it? {-16 J}
b) How much gravitational potential energy did it lose? {16 J}
94. A 175 kg cart is pushed along level ground for 18 m, with a force of 425 N, and then released.
a) How much work did the applied force do on the cart? {7.7 x 103 J}
b) If a frictional force of 53 N was acting on the cart while it was being pushed, how much work did the
frictional force do on the cart? {-9.5 x 102 J}
c) Determine how fast the cart was travelling when it was released. {8.7 m/s}
d) Determine how far the cart will travel after it is released. {1.3 x 102 m}
95. A man is pushing a 75 kg crate at constant velocity a distance of 12 m across a warehouse. He is pushing
with a force of 225 N at an angle of 15o down from the horizontal. The coefficient of friction between the
crate and the floor is 0.24. How much work does the man do on the crate? {2.6 x 103 J}
96. If 25 N are required to compress a spring 5.5 cm, what is the spring constant of the spring? {4.6 x 102 N/m}
97. a) What is the change in elastic potential energy of a spring that has a spring constant of 120 N/m if it is
compressed by 8.0 cm? {3.8 x 10-1 J}
b) What force is required to compress the spring by 8.0 cm? {9.6 N}
98. A dart gun has a spring with a constant of 74 N/m. An 18 g dart is loaded into the gun, compressing the
spring from a resting length of 10.0 cm to a compressed length of 3.5 cm. If the spring transfers 75% of its
energy to the dart after the gun is fired, how fast is the dart travelling when it leaves the gun? {3.6 m/s}
99. Calculate the power developed by a runner able to do 7.0 x 102 J of work in 2.0 s. {3.5 x 102 W}
100. Calculate the amount of energy required to operate each of the following devices for 30 min.
a) 150 W light bulb {2.7 x 105 J}
b) 900 W hair dryer {2 x 106 J}
c) 2000 W portable heater {4 x 106 J}
d) 2.5 x 106 W electric motor {4.5 x 109 J}
101. A 12 kg sled is pulled by a 15 N force at an angle of 35o to the horizontal along a frictionless surface.
a) Sketch the situation.
b) Calculate the acceleration of the sled. {1.0 m/s2}
c) Calculate the distance travelled by the sled in 3.0 s if it started from rest. {4.5 m}
d) Calculate the work done on the sled in 3.0 s. {55 J}
e) Calculate the power generated in pulling the sled. {18 W}
102. A farmer is contemplating using a small water fall on his property for hydroelectric power generation. He
collects data, and finds that 3000 kg of water fall 15.0 m every minute. Assuming the highest possible
efficiency that he is able to achieve in transforming the water’s gravitational potential energy to electric
energy is 74%, what continuous power in Watts could he generate? {5.44 x 103 W}
103. A pendulum takes 1.0 s to swing from the rest line to its highest point. What is the frequency of the
pendulum? {The period of the pendulum is 4.0 s. Frequency is the reciprocal of the period, so the
frequency will be 0.25 Hz.}
104. By what factor will the wavelength change if the period of a wave is doubled? {If the period of a wave is
doubled, the wavelength must double, because the velocity remains the same.}
105. A wave with an amplitude of 50.0 cm travels down a 8.0 m spring in 4.5 s. The person who creates the
wave moves her hand through 4 cycles in 1 second. What is the wavelength? {0.44 m}
106. Water waves in a ripple tank are 2.6 cm long. The straight wave generator used to produce the waves sends
out 60 wave crests in 42 s.
a) Determine the frequency of the wave. {1.4 Hz}
b) Determine the speed of the wave. {3.7 m/s}
107. A tsunami travelled 3700 km in 5.2 h. If its frequency was 2.9 x 10 -4 Hz, what was its wavelength?
{6.8 x 102 m}
108. A storm produces waves of length 3.5 m in the centre of a bay. The waves travel a distance of 0.50 km in
2.00 min.
a) What is the frequency of the waves? {1.2 Hz}
b) What is the period of the waves? {0.84 s}
109. An electronic fish-finder uses sound pulses to locate schools of fish by echolocation. What would be the
time delay between the emission of a sound pulse and the reception of the echo if a school of fish was
located at a depth of 35 m in a lake? Assume that the temperature of the water is 20oC. {4.7 x 10-2 s}
110. a) How long does it take for sound to travel 2.0 km in air at a temperature of 22oC? {5.8 s}
b) The speed of light is 3.0 x 108 m/s. How long does it take for light to travel 2.0 km? {6.7 x 10-7 s }
c) The rumble of thunder is heard 8.0 s after a flash of lightning hits a church steeple. The temperature is
22 oC. How far away is the church? {2.6 km}
111. Light travels from air into a material at an angle of incidence of 59o. If the angle of refraction is 41o, what
is the index of refraction of the material? Identify the material by referring to Table 9.2, Index of
Refraction of Various Substances on page 397. {1.31}
112. A beam of light travels from air into a zircon crystal at an angle of incidence of 72.0o. What is the angle of
refraction in the zircon? {32.7°}
113. What is the angle of incidence of light travelling from air into ethyl alcohol when the angle of refraction is
35o? {51.4°}
114. A beam of light passes from air into ethyl alcohol at an angle of incidence of 60.0o. What is the angle of
refraction? {39.5°}
115. A beam of light passes from ethyl alcohol into air. The angle of refraction is 44.5o. Determine the angle of
incidence. {31.0°}