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Student Workbook
for
Physics
Quarter 2
(Work, Energy and Power)
Physics - Force Brush Up
Handout 5-0
to practice before beginning energy
Physics - Work and Energy
Handout 5-1
1. If friction is neglected for figure A, determine:
a) the value of F needed to cause an acceleration of 2.0 m/s2 to the right.
b) the work done by the force F as it moves 5.0-m to the right.
c) the work done by gravity as it moves 5.0-m to the right.
d) the work done by the normal force as it moves 5.0-m to the right.
f) the net work done on the box.
Figure A
10-kg
2. If the coefficient of friction for figure A is 0.22, determine:
a) the value of F needed to cause an acceleration of 2.0 m/s2 to the right.
b) the work done by the force F as it moves 5.0-m to the right.
c) the work done by gravity as it moves 5.0-m to the right.
d) the work done by the normal force as it moves 5.0-m to the right.
e) what type of friction is being considered and the work done by friction
as it moves 5.0-m to the right.
f) the net work done on the box.
Figure B
F
10-kg
3. If the coefficient of friction for figure B is 0.22, determine:
a) the value of F needed to cause an acceleration of 2.0 m/s2 to the right.
b) the work done by the force F as it moves 5.0-m to the right.
c) the work done by gravity as it moves 5.0-m to the right.
d) the work done by the normal force as it moves 5.0-m to the right.
e) what type of friction is being considered and the work done by friction
as it moves 5.0-m to the right.
f) the net work done on the box.
F
15°
10-kg
4. If the coefficient of friction for figure C is 0.22, determine:
a) the net work done on the box? The box moves 2.0m
b) the work done by gravity as it moves 2.0-m downhill.
c) the work done by the normal force as it moves 2.0-m downhill.
d) what type of friction is being considered and the work done by friction
as it moves 2.0-m downhill.
20º
5. A crane lifts a (1100-kg) car vertically at a constant speed. If the car is raised a total height of 4.0-m determine:
a) the value of the force needed to lift the car.
c) the work done by gravity.
b) the work done by this lifting force.
d) the net work done on the car.
Figure C
6. A crane lifts a (1100-kg) car vertically with an acceleration of 0.75 m/s2. If the car is raised a total height of 4.0-m during this acceleration
determine:
a) the value of the force needed to lift the car.
c) the work done by gravity.
b) the work done by this lifting force.
d) the net work done on the car.
7. An electron has a mass of 9.11 x 10 -31kg. A certain elephant weighs 6600-Lbs. If this elephant walked with a speed of 2.1 m/s would it be
possible for the electron to have the same kinetic energy? Support your answer.
HINT: the speed of light is 6.706 x 108 mph and there are 1609 meters in a mile.
8. What is the airspeed of an unladen swallow? What do you mean; an African or European Swallow?
If the average mass of a European Swallow is 20.3-grams and that of the Aftican Swallow is 141.75-grams determine the speed of each when
they have the same kinetic energy (1.228Joules).
9. Which has more potential energy: a 10-pound bowling ball that is 1-0 meter above the ground or a 2.7-gram ping pong ball that is 1000-m
above the ground?
10. How much energy is stored in a pinball machine spring (constant = 750 N/m) that is compressed 3.0-cm?
11. Mrs Klein (59-kg) climbs a ladder to the top of the roof (3.8-m) in 18-seconds. Mr. Bruening (115-kg) completes the same task in 22seconds and Mrs. Austin (55.5-kg) can do it in 15-seconds. Rank the teachers in order of the most powerful to the least.
12. A corvette can go from 0 – 60 mph in 4.3 seconds. If the mass of the car is 1443-kg how much work is required to complete this task
(assuming it is on a horizontal road)? B) What is the power (in HP) of the corvette?
13. How much work is required to lift a 10-kg object above your head (approximately 1.3-m)?
14. An 1100-kg car accelerates from rest to 90-km/h over a distance of 25.0-m. How much work is done?
applied through this distance?
B) What is the average force
15. A fighter jet (mass = 6020kg) is launched from an aircraft carrier with the aid of its own engines and a catapult. The thrust of the engines is
23000N. In being launched from rest is moved through a distance of 87-m and has a kinetic energy of 4.5 x 107 J at lift off.
a) what is the acceleration of the jet?
B) what is the work done by the engines?
C) what is the work done by the catapult?
Physics - Work and Energy
Handout 5-2
1. A stuntman stands atop of a high platform. At the top of the platform his potential
energy is 15,000J. If he jumps from the platform (vo = 0), determine his potential and
kinetic energies at the following locations: use the grid below to graph your answers
¼ the way down
½ the way down
¾ the way down
all the way down
Etotal PE
Etotal PE
Etotal PE
Etotal PE
KE
KE
KE
KE
2. For the situation described in problem 1, how fast is the 490 N man
traveling when he reaches the ground assuming there was no loss of mechanical energy?
3. A 105-g hockey puck is sliding across the ice. A player exerts a constant horizontal force of
4.5N over a distance of 15-cm. How much work is done on the puck?
4. A 10-kg block is released from rest at the top of the incline shown in figure B. If the block
has a mass of 10.0-kg determine the:
Neglect friction
a) speed at the bottom of the incline.
b) acceleration of the block.
5. If friction is not neglected and the 10 kgblock is released
from rest at the top of the incline shown in figure B
determine:
h = 0.875m
a) work done by friction if the block is
moving with a speed of 3.5 m/s when it reaches the bottom.
b) the value of the frictional force.
c) the work done by gravity as it slides down the hill
d) the net work done
e) the acceleration of the block
1.75m
30°
6. A car accelerates from 8.0 m/s to 12.0 m/s in 4.5 seconds. What is the work done during this acceleration? You
may assume that the car travels horizontally. The car has a mass of 1050-kg
7. A shopper in a supermarket pushes a cart with a force of 35 N directed at an angle 25° downward with the
horizontal. What is the work done by this force as the cart moves 20.0m down the aisle?
b) If the coefficient of kinetic friction between the wheels and the floor is 0.15, what is the work done by the
frictional force? The cart has a mass of 4.5-kg
8. A 2.0-g bullet leaves the barrel of a gun with a speed of 300m/s. What is the work done in accelerating the bullet
? b) Find the average force exerted on the bullet by the expanding gases as the bullet moves the length of the 50.0cm
long barrel.
9. A weight lifter lifts a 350-N set of weights from the ground to a vertical distance of 2.00m. How much work does
the weight lifter do in lifting the weight? How much work does gravity do during this process?
10. A 1300-kg elevator is lifted upward by a cable. If the elevator accelerates upward at a rate of 0.65 m/s2
determine:
a) the magnitude of the lifting force.
b) the work done by this force as it moves 5.0m
Physics - Work and Energy
Handout 5-3
Work (W)  work is the (scalar) product of the parallel component of a force and the displacement through which that force is
applied.
Pay attention to:
1. Which force the problem is referring to.
2. The direction of the force…is it parallel to the distance?
3. The direction of the force…is it positive (with the direction) or negative (opposite the direction)?
30°
1. A 10-kg box is pushed to the right via a force, F, as
shown. There is friction between the box and the
floor; the kinetic coefficient is 0.37. If the box
moves 5.0-m at a constant speed determine:
a) the magnitude of the force, F.
d) the work done by gravity
b) the work done by the applied force, F.
e) the work done by the net force.
c) the work done by friction.
F) the work done by the normal force.
2. A 12-kg box is pushed UP an incline via the force, F, as shown.
the value of the force, F, is 100-N and the box accelerates uphill at 1.5 m/s2
Determine the work done by each of the following if the box moves 2m.
a) applied force.
b) normal force.
c) weight
d) frictional force.
e) the net force
f) what is the value of the coefficient of friction?
12-kg
20°
Energy  energy is the capacity to do work.
When an object has energy it can do work on itself or its surroundings. THEREFORE, work and energy are related!!!!
When work is done on an object, the energy of the object will change W = ΔE
When the energy of an object changes it is because work was done (by some force) W = ΔE
3. Two cars, A and B, are traveling with the same speed, 20 m/s. Each car then accelerates.
Car A (1200-kg) accelerates to 30 m/s and car B (1020 kg) accelerates to 35 m/s. Which car
did more work? How much more work?
4. A 55-kg person climbs the stairs (all 2109 of them) to the top of the Sears Tower in
Chicago. The total vertical accent of the climb is 443-m. Determine the work done:
a) by the person
b) by gravity
5. A 75-kg skier rides a 2830-m long chairlift to the top of a mountain. The lift makes an
angle of 14.6° with the horizontal. During the accent determine:
a) the change in the person’s potential energy
b) the work done by the lift
c) the work done by gravity.
This is
known as
the workenergy
theorem.
The ΔE can
include
all/any
form of
energy……
…we will
focus on
mechanical
energy
(potential
and
kinetic).
Conservation of Mechanical Energy  Energy is never created not destroyed; however, it CAN change from one form to another.
This includes ALL FORMS of energy.
For mechanical energy we will only consider potential, kinetic and work done by friction (i.e. heat produced)
6. A particle, starting from point A on a frictionless ramp, is released from rest. It is
Launched upward (due to a vertical turn in the track) to point C.
a) Determine the speed of the particle at point B.
C
b) Determine the height of point C.
A
1.5m
B
7. A rollercoaster is designed (without friction) as shown in the diagram below. If the speed at point A is
5.0 m/s, what is the speed at:
a) point B?
b) point C?
c) will the coaster reach point D?
D =15 m15m
A =10 m10m
C =8m 8m
B = 0m
8. If the speed of the rollercoaster (shown above) is 10.5m/s at point B, determine the work done by friction
(from A to B).
b) if the average angle of incline between points A and B is 40° and the mass of the car is 900-kg, determine
the force of friction.
c) Determine the coefficient of friction.
Power  Power is the (time) RATE at which work is done! Because work is a change in energy, power can also be thought of as t
he (time) RATE at which energy is transferred.
9. A motor drives a crane that can lift a 700-pound cow to a height of 2 meters. If this takes 12.0-seconds,
what is the power of the motor in a) watts? B) horsepower?
10. Electric energy units are often expressed in the form of kilowatt-hours.
a. Show that one kilowatt-hour (kWh) is equal to 3.6x106 J.
b. If the typical family of four in the United States uses electric energy at a rate of 500 W, how many
kWh would their electric bill be for one 30 day month?
c. At the cost of $0.12 per kWh, what would their monthly bill be?
Theory Practice
1. A slow moving car may have more kinetic energy than a fast moving car. How is this possible?
2. Determine if each of the following quantities can be positive or negative:
a) work
b) power
c) potential energy d) kinetic energy
3. Suppose (neglecting friction) that the kinetic energy of a system decreases. What happens to the
potential energy? Give an example of this occurring.
b) Suppose (neglecting friction) that the potential energy of a system decreases. What happens to
the kinetic energy? Give an example of this occurring.
4. A person is riding a Ferris Wheel. In one complete rotation of the wheel is the net work done by
gravity positive, negative or zero? WHY?
5. A mountain climber has the option of taking two paths up a very large mountain. Path A winds up
the side of the mountain while path B is almost a vertical accent. If both paths lead the same
location which path would require more work done by the climber?
Physics
Activity Sheet
Energy Investigation - pHet Simulation
A
Part 1 - Basic Ramp and No Friction
D
1) Sketch the graphs for the total, potential and kinetic energies when the skater
is at the following locations:
Position A
Position B
C
B
Position C
Position D
2) What do you notice about the relationship between the kinetic and potential energies?
3) What do you notice about the relationship between the kinetic, potential and total energies?
KE
total
PE
therm
KE
total
PE
therm
KE
total
PE
therm
KE
total
PE
Part 2 - Complex Ramp and Friction
1) WITH FRICTION SET TO "NONE"…Sketch the graphs for the total,
potential, kinetic, and thermal energies when the skater is at the following
locations:
A
C
B
2) WITH FRICTION SET TO APPROXIMATELY 1/4 THE MAXIMUM
D
VALUE… Sketch the graphs for the total, potential, kinetic, and thermal energies when the skater is at the
following locations:
therm
3) What do you notice about the relationship between the kinetic, potential, thermal and total energies?
Part 3 - Track Playground
Select the tab for "track playground" and design your own track. Establish your own settings for friction
and go! Be sure to turn on the bar graphs and monitor the changes and relationships between various forms
of energy.
Physics – Work and Energy Bar Graph Worksheet 5-4
For this worksheet you are to analyze different energy conversions/transformations through the use of bar graphs. Some of the
problems will have friction and on others friction will be ignored. The end goal of each problem is to complete the energy bar
graphs.
1. Diver Problem A stuntman (85 kg) stands atop of a high platform. At the top of the platform his potential energy is 15,000J. If he
jumps from the platform (vo = 0), complete the bar graphs for each of the following locations:
a) 0/4 way down
PE
b) ¼ way down
KE
PE
0/4 way down
KE
PE
1/4 way down
c) ½ way down
KE
PE
1/2 way down
KE
3/4 way down
d) ¾ way down
PE
KE
4/4 way down
e) 4/4 way down
PE
KE
f) h=? &
v=?
f) What is the height and velocity of the diver corresponding to part f) assuming the same scale for the first 5 diagrams?
h=
v=
2. Roller Coaster Problem The diagram below shows
a roller coaster on a frictionless track. The roller coaster
has a speed at 1 of 0 m/s. If ha = 100m, hb = 80m, and
hc = 50m, then complete the bar chart diagram for this
diagram?
If the roller coaster has a mass of 1700 kg, then
a) how much work was done to bring it to the top of hill 1?
b) if the motor available was 4.3 kW, how long would that take?
c) what is the speed at 4?
PE
KE
1
PE
KE
2
PE
KE
3
PE
KE
4
3. Sliding Hockey Puck A hockey puck (5 g) slides horizontally without friction across the ice from position A to position
E. Draw the energy bar graphs for each position in graph 1. Ignore W NC (friction) for graph 1
A
Sliding Hockey Puck Graph 1
PE
KE
W nc
PE
A
B
KE
C
W nc
PE
B
KE
E
D
W nc
PE
KE
C
W nc
PE
KE
D
W nc
E
Sliding Hockey Puck Graph 2 – Draw the graphs for the same situation as before but with a kinetic coefficient of friction on the
puck of uk = 0.06. You can assume the puck would come to a stop at position E.
PE
KE
W nc
PE
A
KE
W nc
PE
B
KE
W nc
PE
KE
C
W nc
PE
KE
D
W nc
E
4. Pendulum w/ friction & resistance A pendulum swings starting from position 1 and goes to 3 and back
to 1 again. For this problem we will consider the effects of friction and air resistance all as W nc.
Examine the first few graphs below to and use that data to complete the remaining graphs and answer
the questions.
1, 2, and 3 are the first swing (starting at 1 ending at 3). 3, 2’, and 1’ are the second swing. 1’, 2’’ and
3’’ are the third swing.
How many total swings will the pendulum have before it stops? (Hint: more than this graph will show.)
PE
KE
1
W nc
PE
KE
2
W nc
PE
KE
3
W nc
PE
KE
2'
W nc
PE
KE
1'
W nc
PE
KE
2''
W nc
PE
KE
3''
W nc
Physics - Work and Energy
Handout 5-5
A. Consider a football kicked from level ground. The ball reaches the maximum height at B and returns to the ground at C.
Assume position A is immediately after the football is kicked and position C is immediately before the football hits the ground.
1. At which point(s) does the ball have maximum gravitational potential energy?
a. At A and C
b. At A only
c. At C only
d. At B only
e. The gravitational potential energy is constant over the entire trajectory.
2. At which point(s) does the ball have maximum kinetic energy?
a. At A and C
b. At A only
c. At C only
d. At B only
e. The kinetic energy is constant over the entire trajectory.
3. At which point(s) does the ball have minimum gravitational potential
energy?
a. At A and C
b. At A only
c. At C only
d. At B only
e. The gravitational potential energy is constant over the entire trajectory.
4. At which point(s) does the ball have minimum kinetic energy?
a. At A and C
b. At A only
c. At C only
d. At B only
e. The kinetic energy is constant over the entire trajectory.
5. At which point(s) does the ball have zero kinetic energy?
a. At A and C
b. At A only
c. At C only
d. At B only
e. At none of these
6. At which point(s) does the ball have maximum total mechanical energy?
a. At A and C
b. At A only
c. At C only
d. At B only
e. The mechanical energy is constant over the entire trajectory.
B. Each of the following graphs (1-4) represents a velocity vs time relationship for a particle moving along a straight line. Sketch
the corresponding graphs for kinetic energy vs time below each numbered graph.
Physics - Work and Energy
Springs
1.
Handout 5-6
p. 172 (Q1-3)
2. A spring with a force constant of 5.2N/m has a relaxed length of 2.45m. When a
mass is attached to the end of the spring and slowed to come to rest, the4 vertical
length of the spring is 3.57m. Calculate the elastic potential energy stored in the
spring.
3. The staples inside a stapler are kept in place by a spring with a relaxed length of
0.115 m. If the spring constant is 51.0N/m, how much elastic potential energy is
stored in the spring when its length is 0.150m?
4. A 40.0kg child is in a swing that is attached to ropes 2.00m long. Find the
gravitational potential energy associated with the child relative to the child’s lowest
position under the following conditions.
a. when the ropes are horizontal’
b. when the ropes make a 30 degree angle with the vertical
c. at the bottom of the circular arc
5. A 0.250kg block on a vertical spring with a spring constant of 5000N/m is pushed
downward, compressing the spring 0.100m. When released the block leaves the
spring and travels upward vertically. How high does it rise above the point of
release. (p.187 Q42)
Physics - Work and Energy
Handout 5-7
1.) A mass, M, is hung from a spring and reaches equilibrium at position B. The mass is then raised to
position A and released. The mass oscillates between positions A and C. (a) At which position (A, B, or
C) is mass M located when the kinetic energy of the system is at a maximum? Explain it. (b) At which
position is mass M located when the gravitational potential energy of the system is at a maximum?
Explain it. (c) At which position is mass M located when the elastic potential energy of the system is at a
maximum? Explain it.
2.) A rollercoaster cart leaves point A at a speed of 4 m/s, passes through point B on the ground, and
reaches point C at a speed of 6 m/s. The total mass of the cart assembly and the passengers are 300 kg,
(a) What is the speed of the cart at point B? (b) What is the height of point A?
3) The length of the ropes on a playground swing is 2.0 m. (a) What is the maximum speed attainable on
the swing if the maximum value of θ is 60o ? (b) If a 50-kg person is playing the swing, what is the
maximum kinetic energy he can attain?
4.) When a force of 120.0N is applied to a certain spring, it causes a stretch of 2.25cm. What is the
potential energy of this spring when it compressed by 3.50cm?