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Physics 20 Energy Worksheets
Worksheet 1: Work = F x d
1) It is often possible to do work in pushing an object
without transferring any energy to the object being pushed.
What happens to the energy associated with the work done in
this case?
2) A 20.0 N object is lifted at a constant velocity from the
floor to a height of 1.50 m. How much work is done on the
object? (30.0 J)
11) A 1165 kg car travelling at 55 km/h is brought to a stop
while skidding 38 m. Calculate the work done on the car by
the frictional forces.
(-1.4 x 105 J)

12. How much work is done when an object is moved
3.8 m at 40° to a 6.2 N force and 35° to a 7.1 N force?
(40 J)
3) A 15.0 N object is moved horizontally 3.00 m across a
level floor using a horizontal force of
6.00 N. How much work is done on this object? (18.0 J)
4) A 2.20 N object is held 2.20 m above the floor for 10.0 s.
How much work is done on the object? (0)
5) A 10.0 kg object is accelerated horizontally from rest to a
velocity of 11.0 m/s in 5.00 s by a horizontal force. How
much work is done on this object assuming the object is on a
frictionless surface? (605 J)
6) A 90.0 N box is pulled 10.0 m along a level surface by a
rope. If the rope makes an angle of 20.0° with the surface,
and the force exerted through the rope is 75.0 N, how much
work is done on the box? (705 J)
7) A 60.0 kg student runs at a constant velocity up a flight of
stairs. If the vertical distance of the stairs is 3.2 m, what is
the work done against gravity? (1.9 x 103 J)
8) A 20.0 kg box is pulled horizontally 9.0 m along a level
frictionless surface at a constant velocity. How much work is
done on the box? (0)

13) A student exerts a horizontal force of 225 N to push a
heavy box along the school corridor at a constant speed of
2.00 m/s. How much work does she do in 15.0 s?
(6.75 x 103 J)
14) If a 50.0 kg box is pushed 10.0 m at a constant speed
along a horizontal surface by a force of 65.0 N acting at a
30.0° angle as shown in the diagram, how much work is done
on the box?
To find the work done, should you use the force of 65.0 N or
should you find the horizontal component of 65.0 N? Why?
(563 J)
15) Given the following force-displacement graph of an
object being pulled along a level surface, determine the work
done in moving
the object 16.0 m.
(56 J)
9) An 80.0 kg box is pushed at a constant velocity along a
frictionless incline as shown in the diagram.
How much work is done on the box in moving it from the
bottom to the top of the incline?
(5.5 x 103 J)
10) A 25.0 kg object is accelerated from rest through a
distance of 6.0 m in 4.0 s across a level floor. If the force due
to friction between the object and the floor is 3.8 N, what is
the work done in moving the object? (1.4 x 102 J)
16) Given the following force-displacement graph of an
object moving along a
horizontal surface,
determine the work
done in moving the
object
8.0 m. (-26 J)
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Physics 20 Energy Worksheets
Worksheet 2: Potential Energy
Worksheet 3: Kinetic Energy
1) In which of the following cases does potential energy
increase, and in which cases does potential energy decrease?
a) A positive charge is brought closer to a negatively
charged body.
b) The South pole of a magnet is moved away from the
South pole of a similar magnet.
c) A body is raised further above the surface of the earth.
d) A spring is stretched.
e) The North pole of a magnet is brought closer to the
South pole of a similar magnet.
f) A weight is place on top of a large spring.
g) A space capsule decreases the size of its orbit around
the earth.
h) A negatively charged body is moved in a circle around a
positively charged body.
1) A 3.0 kg object is traveling at a constant speed of 7.5 m/s.
What is the kinetic energy of this object? (84 J)
2) A 25.0 N object is held 2.10 m above the ground. What is
the potential energy of the object with respect to the ground?
(52.5 J)
3) An uncompressed spring is 20.0 cm in length. What is the
potential energy of this spring when an average force of 65.0
N compresses it to a length of 13.5 cm? (4.2 J)
4) A 2.75 kg box is at the top of a frictionless incline as
shown in the diagram.
What is the potential energy of the box with respect to the
bottom of the incline? (189 J)
5) The bob of a pendulum has a mass of 2.0 kg. This bob is
pulled sideways so that it is 0.75 m above the table top. What
is the potential energy of the bob with respect to the
equilibrium position? (4.9 J)
6) A 2.00 x 102 kg object is
pushed to me top of an incline as
shown in the diagram.
If the force applied along the
incline is 6.00 x 102 N, what is
the potential energy of the object when it is at the top of the
incline with respect to the bottom of the incline? (1.2 x 104 J)
2) The kinetic energy of a 20.0 N object is 5.00 x 10 2 J. What
is the speed of this object? (22.1 m/s)
3) A 10.0 N object is accelerated uniformly from rest at a rate
of 2.5 m/s2. What is the kinetic energy of this object after it
has accelerated a distance of 15.0 m? (38 J)
4) An 8.0 kg object is dropped from a height of
7.0 m. What is the kinetic energy of this object as it hits the
ground? (5.5 x 102 J)
5) A 10.0 N object has kinetic energy of 3.00 x 102 J. What is
the speed of the object? (24.3 m/s)
6) By what factor must the kinetic energy of an object be
increased to cause its speed to triple? (9 times)
Worksheet 4: Elastic (Spring) Potential
1) List three common devices that, like a stretched or
compressed spring, can store potential energy when
temporarily deformed.
2) An engineer is designing the suspension system for a car.
He decides that the coil spring used should compress 4.00 cm
when a force of 1000 N is applied
a) What is the spring constant of the spring
b) If the spring is compressed a distance of 14.0 cm, what
force was exerted on it? (2.50 x 104 N/m,
3.50 x 103 N)
3) The following data was generated from an experiment in
which a spring was stretched to different lengths by hanging
several masses on a spring:
x (m)
0.150
0.200
0.250
0.375
0.425
0.575
Force (N)
52.50
69.98
87.51
131.31
149.21
201.98
a) Use your graphing calculator to determine the best
approximation of the spring constant of the spring. (Plot
Force as the responding variable)
b) How much energy will be stored in the spring if it is
stretched to a length of 37.0 cm? (352 N/m, 24 J)
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Physics 20 Energy Worksheets
4) The following data was generated from an experiment in
which a spring was stretched by hanging several different
masses on a spring:
Mass (kg)
0
0.1000
0.2000
0.3000
0.4000
0.5000
Length of Spring (cm)
10.00
11.79
13.55
15.36
17.13
18.90
a) Use your graphing calculator to determine the best
approximation of the spring constant of the spring.
b) How much energy will be stored in the spring if it is
stretched to a length of 20.00 cm?
(55.1 N/m, 0.276J)
5) A 0.60 kg mass is vibrating at the end of a spring. If the
spring constant is 26 N/m, and the maximum displacement of
the mass is 0.15 m
a) How much energy is stored in the spring?
b) If the spring contracts to 0.03 m, what is the change in
elastic potential of the spring?
(2.93 x 10-1 J, -2.81 x 10-1 J)
6) The elastic constant for a spring is 750 N/m
a) How far must you stretch it from equilibrium in order to
store 45.0 J of elastic potential in it?
b) If you want to double the elastic potential of the spring,
how much farther would you need to stretch it?
(34.6 cm, 14.3 cm)
7) An object vibrates at the end of a horizontal spring
(k = 32 N/m) along a frictionless surface. If the object's
potential energy is 4.5 J, what is the displacement? (0.53 m)
Worksheet 5: Work-Energy Theorem
1) How much work is required to accelerate a 1.10 x 103 kg
car from rest to 5.00 km/h along a level frictionless surface?
(1.06 x 103J)
2) What was the average net force exerted on a 4.5 x 10 -3 kg
bullet by a gun while accelerating it from rest to a speed of
1.0 x 103 m/s through a displacement of 0.70 m?
(3.2 x 103 N).
3) A student throws a 1.0 kg rock vertically into the air with
an average force of 18 N. If this force was exerted through a
displacement of 0.30 m, what was the speed of the rock as it
left the student's hand? (2.2 m/s)
4) A spring exerts an average horizontal force of 23.0 N on a
0.12 kg pebble while acting through a displacement of 5.0 x
10-2 m. What is the speed of the pebble as it leaves the
spring? (4.4 m/s)
5) A force of friction of 3.2 N acts on a 1.1 kg puck while it
is sliding along a horizontal surface. If the initial velocity of
the puck was 7.5 m/s, how far will the puck travel before
coming to rest? (9.7 m)
6) A 0.65 kg puck is sliding along a horizontal surface at a
speed of 2.0 m/s. If the puck comes to a stop in 5.5 m, what is
the force of friction acting along the surface? (0.24 N)
7) A student throws a 1.1 kg rock vertically into the air while
accelerating it through a displacement of 0.36 m. If the rock
leaves the student's hand at a speed of 4.2 m/s, what was the
average force exerted by the student on the rock while
accelerating it? (38 N)
8) An object vibrates at the end of a horizontal spring
(k = 28 N/m). If the object's displacement is 0.18 m, what is
its potential energy? (0.45 J)
8) A 15 kg box is pulled along a horizontal frictionless
surface by a horizontal force of 35 N. If the box accelerates
uniformly from rest, how fast is it travelling after 3.5 m?
(4.0 m/s)
9) A 0.46 kg object vibrates at the end of a horizontal spring
(k = 12 N/m). If the object's kinetic energy is 7.3 J, what is its
speed? (5.6 m/s)
9) How much energy is needed to accelerate a 1.1 x 103 kg
object along a horizontal frictionless surface from 15 km/h to
25 km/h in 5.0 s? (1.7 x 104 J)
10) How much work was done on a spring (k = 76.0 N/m) in
stretching it 3.50 cm? (0.0466 J)
Worksheet 6: Conservation of Energy
11) A force of 8.2 x 101 N is required to hold a Hooke's Law
rubber band with a stretch of 2.7 cm. What is the potential
energy stored in the band? (1.1 J)
12) A 75 g object vibrates at the end of a frictionless spring
(k = 5.0 N/m). If the maximum displacement of the object is
0.080 m, what is the maximum acceleration? (5.3 m/s2)
1) A heavy object is dropped. If this object reaches the floor
at a speed of 3.2 m/s, from what height was it dropped?
(0.52 m)
2) A heavy object is dropped from a vertical height of 8.0 m
above the ground. What is the speed of this object as it hits
the ground? (13 m/s)
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Physics 20 Energy Worksheets
3) A heavy object is dropped from the top of a building. If
this object hits the ground with a speed of 37.0 m/s, how tall
was the building? (69.8 m)
10) A system containing a frictionless pulley is described in
the diagram. If this system is released, at what speed does the
12.0 kg object hit the floor? (3.1 m/s)
4) A 4.0 N box slides along a frictionless surface, while
travelling at a speed of 2.1 m/s. This object hits an ideal
spring as shown in the diagram compressing it 2.3 x 10-2 m.
What is the spring constant of the spring? (3.4 x 103 N/m)
11) A heavy box slides down a frictionless incline as shown
in the diagram.
5) A heavy object is thrown vertically down from the top of a
1.3 x 102 m building at a speed of 11.0 m/s. What is the
velocity as it hits the ground? (52 m/s)
6) A 0.20 kg mass vibrates at the end of a horizontal spring
(k = 15 N/m) along a frictionless surface. What is the
maximum displacement of the mass if it reaches a maximum
speed of 0.12 m/s? (1.4 x 10-2 m)
7) A 0.40 kg mass vibrates at the end of a horizontal spring
along a frictionless surface reaching a maximum speed of
0.50 m/s. If the maximum displacement of the mass is
0.11 m, what is the spring constant? (8.3 N/m)
If the box starts from rest at the top of the incline, what is its
speed at the bottom? (10.8 m/s)
12) A roller coaster car starts from rest at point A.
8) A heavy box slides down a frictionless incline as shown in
the diagram.
What is the speed of this car at point C, if the track is
frictionless? (13 m/s)
If the box starts from rest at the top of the incline, what is its
speed at the bottom? (8.9 m/s)
9) A pendulum is dropped from the position as shown in the
diagram 0.25 m above the equilibrium position.
What is the speed of the pendulum bob as it passes through
the equilibrium position? (2.2 m/s)
13) A 2.5 kg object is dropped from a height of 10.0 m above
the ground. Calculate the speed of the object as it hits the
ground. (14 m/s)
14) A student is running at a speed of 3.5 m/s and grabs a
long rope that is hanging vertically from a tree.
How high can the student swing? (0.62 m)
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Physics 20 Energy Worksheets
15) A pendulum is 1.20 m long. What is the speed of the
pendulum bob when it passes through its equilibrium position
if it is pulled aside until it makes a 25.0° angle to the
vertical? (1.49 m/s)
3) A constant force of 85 N accelerates a 12 kg box from a
speed of 2.0 m/s to a speed of 8.0 m/s as it travels 15 m along
a horizontal surface. What is the coefficient of friction
between the two surfaces? (0.52)
4) A 1.50 x 102 N force is pulling a 50.0 kg box along a
horizontal surface. The force acts at an angle of 25.0° as
shown in the diagram.
16) A 45 kg student runs with a speed of 2.0 m/s off a
horizontal ledge that is 5.0 m above a swimming pool.
Calculate the speed of the student when she hits the water.
(10 m/s)
17) A 1.0 kg box slides without friction around the loop-theloop apparatus as shown in the diagram.
If the object starts from rest at point A, and the radius of the
loop is 0.75 m, what is the speed of the box at point B?
(6.3 m/s)
Worksheet 7: Energy Questions with Friction
1) A 12 kg box initially at rest slides from the top of an
incline as described in the diagram.
If the force of friction along the incline is 5.0 N, what is the
speed of the object as it reaches the bottom of the incline?
(1.0 x 101 m/s)
2) A 45.0 kg box initially at rest slides from the top of an
incline as described in the diagram.
(*note that FN is not mg in this problem)
If this force acts through a displacement of 12.0 m, and the
coefficient of friction is 0.250, what is the speed of the box,
assuming it started from rest? (3.74m/s)
5) Calculate the mechanical
energy converted to thermal
energy when a 8.0 kg box is
pushed 5.0 m along a 30.0°
incline at constant velocity by an average force of 75 N
parallel to the incline. (1.8 x 102J)
6) A 45.0 kg box is pulled across a horizontal surface by a
constant horizontal force of 192 N. If the box starts from rest,
and the coefficient of friction is 0.35, what is the final speed
of the box when it has travelled 8.0 m? (3.7 m/s)
7) A 2.5 kg box slides from rest
0.850 m down a 30.0° incline as
shown in the diagram.
If the force of friction acting along the incline is 3.2 N, what
is the speed of the box when it reaches the bottom of the
incline? (2.5 m/s)
8) An 18.0 N box slides from rest
0.750 m down a 30.0° incline as
shown in the diagram. If the box
reaches the bottom of the incline
with a speed of 1.30 m/s, what was
the force of friction along the incline? (6.93 N)
9) A 115 N box slides 50.0 m along a
40.0° incline as shown in the diagram.
If the force of friction along the incline is
35.0 N, what is the change in the box's
gravitational potential energy? (3.70 x 103J)
If the box reaches the bottom of the incline at a speed of 5.0
m/s, what is the force of friction on the box along the incline?
(1.3 x 102 N)
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Physics 20 Energy Worksheets
10) A 75.0 kg box, starting from rest, slides down the incline
described in the diagram.
4. A 4.00 x 103 kg object is lifted from the earth's
surface to an altitude of 3.2 x 105 m.
If the force due to friction along the incline is 17.9 N,
a) How much thermal energy was produced? HINT: When
work is done to overcome friction, what happens to some
of the mechanical energy? (1.4 x 102 J)
b) What is the velocity of the box at the bottom? (9.7 m/s)
11) A 45.0 kg student starts from rest and slides 28.0 m down
a water slide. What is the speed of the student at the bottom if
the force of friction along the slide is 55.0 N and the vertical
drop is 5.00 m? (5.45 m/s)
Worksheet 8: Absolute Potential Energy
How much work does this require? (1.2 x 1010 J)
Use the following information for the problems below
mass of earth = 5.98 x 1024 kg
mass of the sun = 1.99 x 1030 kg
mass of the moon = 7.35 x 1022 kg
radius of the earth = 6.37 x 106 m
radius of the sun = 6.96 x 108 m
radius of the moon = 1.74 x 106 m
distance earth to moon = 3.84 x 108 m
distance earth to sun = 1.496 x 1011 m

1. What is the absolute potential energy of the moon with
respect to the earth? (-7.63 x 1028 J)

2. What is the absolute potential energy of the sun with
respect to the earth? (-5.31 x 1033 J)

3. Answer the following questions concerning absolute
potential energy .
a) What is the change in the absolute potential energy of a
1500 kg rocket as it rises from the earth’s surface to a position
150 km above the earth's surface? ( 2.16 x 109 J)
b) What value do you get if you use the formula
Ep = mgh? (2.21 x 109 J)
c) Which of these values is more 'correct'. Explain
your choice.
d) The rocket drops from its position in a) down
to a height of 25 km above the earth. By how much
has its potential energy changed. (-1.79 x 109 J)
5. A 50 kg object is 100 km above the earth's surface
and moves to a position 50 km above the earth's surface.
How much does its potential energy change? (-2.4 x 107 J)
6. A spacecraft of mass 470 kg rests on the surface of
an asteroid of radius 1 400 m and mass 2.0 × 1012 kg.
How much energy must be expended so that the
spacecraft may rise to a height of 2 800 m above the
surface of the asteroid? (30 J)
7. A 1 250 kg rocket rests on the surface of the Earth.
To what maximum distance from the Earth's center
would the rocket be lifted if 2.5 x 1010 J of work were
done on it? (9.36 x 106 m)
8. What minimum energy is required to take a stationary
3.5 × 103 kg satellite from the surface of the Earth and put
it into a circular orbit with a radius of 6.88 × 106 m and an
orbital speed of 7.61 × 103 m/s? (Ignore Earth's rotation.)
(1.2 x 1011 J)
9. Show that the velocity of escape from a parking orbit
500 km above the earth is about 3.88 x 104 km/h.
10. Calculate the velocity of escape
from an orbit 500 km above Jupiter.
(6.01 x 104 m/s
11. Calculate the velocity of escape from an orbit
500 km above Mars. (4.70 x 103 m/s)
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Physics 20 Energy Worksheets
12. If a satellite is in geostationary orbit around the
Earth, what is its escape velocity? (4.35 x 103 m/s)
13. A 1 500 kg satellite travels around the earth in a stable orbit
with a radius of 1. 3 x107 m
a) What is the speed of the satellite in this orbit? (5.5 x 10 3 m/s)
b) What is the value of the escape velocity from this orbit?
(7.83 x 103m/s)
Worksheet 9: Power
1) What is the power output of a machine which applies a force
of 2.50 x 104 N for 12.0 s in pulling a block through 60.0 m?
(1.25 x 102 kW)
2) How much work can a 2.00 HP motor do in 2.00 h?
(1.07 x 107J)
3) A shot-putter accelerates a 7.30 kg shot from rest to 15.0 m/s.
If this motion takes 0.500 s, what average power was developed?
( 1.64 x 103 W )

4) A truck gained a kinetic energy of 4.2 x 10 4 J in 14.0 s. What
was its minimum power output? (3.0 kW)
5) What power is exerted by a weight lifter, who clean and jerks
350 kg from the floor to a height of 2.14 m in 1.5 s? How many
horsepower has the weight lifter produced?
( 4.9 x 103 W or 6.6 HP)
6) The battery of your calculator can provide energy at the rate of
0.0290 J/s for 275 h. If this energy could be used to accelerate a
0.145 kg baseball from rest, what speed would the ball reach?
(629 m/s)

7) A winch of power output 5.0 kW can raise a crate with a steady
maximum speed of 10.0 m/s. What is the mass of the crate?
(51 kg)
8) A 70.0 kg hiker climbs to the top of a 4.20 x 103 m high
mountain. The climb is made in 4.00 h starting at an
elevation of 3.20 x 103 m.
a) How much work is done against gravity?
b) What is the average power output?
(6.87 x 105 J) (47.7 W)
9) The maximum output power of an electric motor is 400.00 W.
It is used to operate a conveyer belt carrying sand. The belt is
12.0 m long and the sand is lifted 4.00 m by the belt. What mass
of sand can be allowed to flow onto the conveyer belt every
minute so that the motor will not be over - loaded. Ignore any
friction of the conveyer belt. (612 kg)
11) What is the shortest amount of time it could possibly
Take an average horse, who can develop 1.000 HP, to
pull a 350.0 kg weight up a frictionless incline plane if
the rise of the plane is 3.00 m? (13.8 s.)
Worksheet 10: Efficiency
1) A machine lifts a 3.00 kg mass a distance of 3.00 m while
operating at a power consumption of 3.50 W for 40.00 s.
Calculate the machine's efficiency. (63.1 %)
2) A 1500 kg, 145 HP car, achieves a speed of 100 km/h
in 7.00 s. What is the efficiency of the car? (76.4%)
3) An electric power saw operates at a power
consumption of 0.77 kW for 3.6 h per day, 5 days per
week. In the process, it produces 1.1 x 10 7 J of heat
energy. Calculate the saw's mechanical efficiency. (78%)
4) A car in a long distance rally requires an average force of
5.15 x 103 N while travelling at 100 km/h and that the
gasoline used over a 50.0 h period contains 1.3 x 1011 J of
chemical energy, what's its efficiency of the car engine?
(19.8 %)
5) A 100 kg runner burns 750 cal (1 cal = 4.19 x 103 J) while
running a 10.0 km race in 40.0 min on a surface with a
frictional coefficient of 0.250. What is the efficiency of the
jogger. (22.0 %)
6) Bill replaced a 60 W filament bulb with an energy efficient
alternative rated at 11 W. Both bulbs give out 9.0 W of light.
Find their efficiencies. (15 %, 82%)
7) A 0.0300 kg toy car
is pushed back against
a spring-based
launcher as shown in
Diagram 1.
Diagram 2 shows a graph of the force required to compress
the spring 0.090 m
a) What is the work
done in compressing
the spring?
b) Assuming no losses
due to heat, what
maximum speed is
reached by the toy car
when it is released?
c) If in fact, the
maximum kinetic
energy of the car is 0.78 J, what is the efficiency of the
spring-based launcher? (0.87 J, 7.6 m/s, 90%)
10) An electric motor raises a 1.5 x 10 2 kg block at a
steady speed of 2.0 m/s. Find the minimum power
output of the motor. (2.9 x 103 W)

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Physics 20 Energy Worksheets
8) An electric motor pumps water from the bottom of a 55.0
m well to a household reservoir where it enters the reservoir
at 3.50 m/s. If the pump is 65% efficient and needs to pump
1.50 L/s, what is the minimal electrical power the pump must
have. (1 L = 1 kg for water, 1.26 x 10 3 W)
5. A ball is oscillating on a spring with a maximal displacement
of 15 cm and a frequency of 13 Hz.
a) What is the period of this motion? (0.077 s)
b) What is the mass of the ball if the spring constant is
3.33 x 104 N/m (5.0 kg)
9) The most efficient solar cells devised have an efficiency
of 40.8%. If A 3.00 m2 cell can produced a photocurrent of
1.50 A @ 120 V, what solar energy must be falling on the
cell each second? (441 J/s)
6. Ignoring the damping introduced by the shock absorbers,
explain how the number of passengers in a car affects the
vibration frequency of the car's suspension system.
(as mass increases f decreases)
Worksheet 11: Simple Harmonic Motion
7. A spring stretches by 0.018 m when a 2.8 kg object is
suspended from its end. How much mass should be
attached to this spring so that its frequency of vibration
is f = 3.0 Hz? (4.3 kg)
1. A.......B.......C......D......E
An object moves with a simple harmonic motion between the
points marked A and E.
a) What is its equilibrium position.
b) At what point or points does it have a maximum speed?
c) At what point or points does it have maximum acceleration?
d) When the object moves from B toward A, is the direction of
the acceleration positive (to the right) or negative (to the left)?
e) At point E, is the force acting on the object positive, negative,
or zero?
f) If the distance between each two letters above is 1 cm, what is
the amplitude of the vibration?
g) What is the displacement at point D?
h) If the object moves from A to E in 1 s, what is the period of
vibration?
i) What is the frequency of the vibration?

a) C b) C c) A, E d) positive e) negative f) 2 cm g) 1 cm h)
2 s i) 0.5 Hz
2. A meter stick is held vertically behind an object on a spring.
The object vibrates from the 20. cm mark on the
stick to the 32 cm mark. Find :
(a) the equilibrium position
(b) the amplitude
(c) the displacement when the object is at the 20 cm mark, the
24 cm mark, the 26 cm mark, and the 30 cm mark.
(a) 26 cm b) 6 cm c) +6 cm, +2 cm, 0 cm, -4 cm)
3 The figures shows the shadow of an object
in circular motion as the shadow moves in
simple harmonic motion. Where on the
shadow's path is:
a) the velocity equal to zero
b) the acceleration equal to zero?
4. A 2.0 N force was used to hold a 300 g object attached to a
spring 10 cm from equilibrium. The object is then pulled down,
released and allowed to vibrate.
a) What is the spring constant? (20 N/m)
b) What is the frequency and period of the object? (1.3 Hz)
8. A 1.1 kg object is suspended from a vertical spring
whose spring constant is 120 N/m.
a) Find the amount by which the spring is stretched from
its unstrained length. (9.0 x 10-2 m)
b) The object is pulled straight down by an additional
distance of 0.20 m and released from rest. Find the speed
with which the object passes through its original position
on the way up. (2.1 m/s)
9. If you double the amplitude of a simple harmonic
motion, how does this change the frequency, maximum
velocity, maximum acceleration and the total mechanical
energy of the medium particles?
(f = same, vmax doubles amax doubles, Emech four times )
10. What should be the length of
a pendulum for which
the period is to be 1.00 s in a
place where g = 9.81 m/s?
(0.25 m)

11. A pendulum makes 200 complete swings in 2 min
30 sec. Find the period and frequency. (T = 0.8)
T = 0.8 s f = 1 Hz)
12. A pendulum with a length of 200 cm vibrates with
a period of 2.82 s. What is the value of the acceleration
of gravity in that location? (9.93 m/s2)

13. A pendulum has a length of 150 cm and a bob of 100 g
and vibrates with a period of T = 2.44 s.
a) What is the value of the acceleration of gravity in that
location? (9.95 m/s2)
b) The pendulum is displaced to the side through an angle of
10.0o. What is the restoring force on the bob? (0.170 N)
c) What is the velocity of the bob as it moves through the
equilibrium point of its vibration? (0.673 m/s) 
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