Work and energy work sheet.
Work = F dll or Work = Fll d
dll is the distance moved parallel to the force and Fll is the component of force parallel to
the distance moved.
Find the work done by each force F as the object moves through
the distance d.
F=10 N
(I)
F=10 N
(II)
d=4.0 m
d=4.0 m
d=4.0 m
(III)
F=10 N
A) If 20 Joules (20 J) of work (W) is done in moving a crate 2.0 meters (d)
in the same direction as the applied force how large is the force (F)?
Info:The friction force always opposes the direction of motion as in Figure
II above.
If an object has 20 J of kinetic energy, the friction force must do -20 J of
work to bring it to rest.
B) When the friction force acting on an object is 5N (F) and the object has
20 J of kinetic energy (KE=W), how far will it slide (d) before stopping?
Kinetic Energy = 1/2mv2
i) What is the kinetic energy of a 2.0 kg ball traveling at a speed of 1.0 m/s? __________
ii) what if its speed is 2.0 m/s (instead of 1.0 m/s)? __________
iii) what if its speed is 3.0 m/s (instead of 1.0 m/s) ? __________
iv) what if its speed is 4.0 m/s (instead of 1.0 m/s)? __________
v) When the speed of an object doubles its kinetic energy ________________
6) What is the kinetic energy of a 2.0 kg ball traveling at a speed of 1.0 m/s? __________
(see above)
7) What if its speed is 1.0 m/s but its mass is 4.0 kg (twice as large as 2.0 kg) ?
__________
8) What if its speed is 1.0 m/s but its mass is 6.0 kg (triple the original 2.0 kg) ?
__________
9) When the mass of an object doubles its kinetic energy _________________
Two identical cars A and B are traveling at speeds of 20 m/s and 40 m/s respectively.
Each slams on the brakes and skids to a stop. Since the cars are identical, each will
experience the same braking force (F) so the additional work required to stop the faster
car will come from its additional skid distance (d).
10) How much more kinetic energy does B have compared to A (1X (the same), 2x, 3x,
4x, ......)
11) How much more work must be done by friction to stop B compared to that required
to stop A? Remember Work=∆KE
12) How much further will B skid than A?
13) Car A travels at a speed of 30 mi/hr and skids to a stop in 20 meters. How far will an
identical car B skid before stopping if it is traveling at a speed of 90 mi/hr?
Potential energy = (mg)h or wh (w=weight in N)
The gravitational potential energy gained by an object as it is lifted up equals the work
required to lift it.
1) What is the potential energy relative to the floor of a 30 kg boy who is 3.0 m above the
floor?
2) What is the potential energy relative to the floor of a 60 kg boy who is 3.0 m above the
floor?
3) What is the potential energy relative to the floor of a 30 kg boy who is 6.0 m above the
floor?
Conservation of Energy
Energy can neither be created nor destroyed but only transformed from one form into
another.
As an object falls from a height its potential energy is transformed into kinetic energy.
4) The picture below shows a 10 N ball (m=1.0 kg) falling from a height of 10.0 m. Each
image of the ball is separated by 2.5 meters. Fill in the values for the potential energy
(PE) and kinetic energy (KE) for each location.
w=10N
PE=_______ J
KE= 0.00 J
PE=_______ J
KE= __________
PE=_______ J
KE= __________
PE=_______ J
KE= __________
PE= 0.00 J
KE= __________
10.0 m
5) At what height is the kinetic energy equal to the potential energy?
6) At what height is the kinetic energy three times the potential energy?
Mechanical Power
Power is defined as the rate at which work is done (or energy delivered).
power
work energy

time
time
or
Energy Power time
E  Pt
The unit of measure for power is a Watt (1Watt=1Joule/sec)
1) How much work is required to lift a 40 N weight 2.0 meters above the ground?
(remember work = force x distance)
2) If this work is done in 1.0 sec how much power is needed?
3) If this work is done in 2.0 sec how much power is needed?
4) If this work is done in 0.5 sec how much power is needed?
5) How much work is required to give a 20 kg car a speed of 10 m/s?
6) If this work is done in 1.0 sec how much power is needed?
7) If twice this amount of work is done in twice the time (2.0 sec), how much
power is needed?
The kilowatt-hour is a common unit of energy
(1 kW-hr=1000 Watts x 3600 s =3,600,000 Joules)
To find the energy consumed in units of kW-hr simple multiply the power (in kWatts) by
the time (in hours). For example, a 2000 Watt heater running for 4 hours will use an
amount of energy E given by
E=2 kW x 4 hrs=8 kW-hrs
Presently 1 kW-hr costs about $0.08 in the Pacific Northwest so 8 kW-hrs costs about 64
cents ($.64)

How much energy is used in operating a 4000 Watt hot water heater for 10 hrs?

How much will this cost?

How much energy is consumed in operating ten 100 Watt light bulbs for 12 hrs
during the day?
How much will this cost?
Work and energy work sheet.
Work = F dll or Work = Fll d
dll is the distance moved parallel to the force and Fll is the component of force parallel to
the distance moved.
Find the work done by each force F as the object moves through the distance d.
F=10 N
(I)
F=10 N
(II)
d=4.0 m W=40 J
d=4.0 m W=-40 J
d=4.0 m
(III)
F=10 N W=0.0 J
A) If 20 Joules (20 J) of work (W) is done in moving a crate 2.0 meters (d) in the
same direction as the applied force how large is the force (F)?
F=W/d=10 N
Info:The friction force always opposes the direction of motion as in Figure II above.
If an object has 20 J of kinetic energy, the friction force must do -20 J of work to bring it
to rest.
B) When the friction force acting on an object is 5N and the object has 20 J of
kinetic energy (KE=W), how far will it slide (d) before stopping?
d= W/F = KE/F = 20J/5N = 4.0m
Kinetic Energy = 1/2mv2
i) What is the kinetic energy of a 2.0 kg ball traveling at a speed of 1.0 m/s? KE=1.0J
ii) what if its speed is 2.0 m/s (instead of 1.0 m/s)? KE=4.0J
iii) what if its speed is 3.0 m/s (instead of 1.0 m/s) ? KE=9.0J
iv) what if its speed is 4.0 m/s (instead of 1.0 m/s)? KE=16.0J
v) When the speed of an object doubles its kinetic energy quadrouples
6) What is the kinetic energy of a 2.0 kg ball traveling at a speed of 1.0 m/s? KE=1.0J
(see above)
7) What if its speed is 1.0 m/s but its mass is 4.0 kg (twice as large as 2.0 kg) ? KE=2.0J
8) What if its speed is 1.0 m/s but its mass is 6.0 kg (triple the original 2.0 kg) ? KE=3.0J
9) When the mass of an object doubles its kinetic energy _doubles
Two identical cars A and B are traveling at speeds of 20 m/s and 40 m/s respectively.
Each slams on the brakes and skids to a stop. Since the cars are identical, each will
experience the same braking force (F) so the additional work required to stop the faster
car will come from its additional skid distance (d).
10) How much more kinetic energy does B have compared to A (1X (the same), 2x, 3x,
4x, ......) B has 4x more KE than A
11) How much more work must be done by friction to stop B compared to that required
to stop A? Remember Work=∆KE Four times more work to stop B than to stop A
12) How much further will B skid than A? B will skid four times farther since the
force stopping both is the same (identical cars)
13) Car A travels at a speed of 30 mi/hr and skids to a stop in 20 meters. How far will an
identical car B skid before stopping if it is traveling at a speed of 90 mi/hr? 3 times
faster 9 times the KE skids 9 times farter 180 meters
Potential energy = (mg)h or wh (w=weight in N)
The gravitational potential energy gained by an object as it is lifted up equals the work
required to lift it.
1) What is the potential energy relative to the floor of a 30 kg (w=300N) boy who is 3.0
m above the floor? 900J
2) What is the potential energy relative to the floor of a 60 kg(w=600N) boy who is 3.0 m
above the floor? 1800 J
3) What is the potential energy relative to the floor of a 30 kg boy who is 6.0 m above the
floor? 1800 J
Conservation of Energy
Energy can neither be created nor destroyed but only transformed from one form into
another.
As an object falls from a height its potential energy is transformed into kinetic energy.
4) The picture below shows a 10 N ball (m=1.0 kg) falling from a height of 10.0 m. Each
image of the ball is separated by 2.5 meters. Fill in the values for the potential energy
(PE) and kinetic energy (KE) for each location.
5) At what height is the kinetic energy equal to the potential energy? 5.0 m
6) At what height is the kinetic energy three times the potential energy? 2.5 m
Mechanical Power
Power is defined as the rate at which work is done (or energy delivered).
power
work energy

time
time
or
Energy Power time
E  Pt
The unit of measure for power is a Watt (1Watt=1Joule/sec)
1) How much work is required to lift a 40 N weight 2.0 meters above the ground? 80 J
(remember work = force x distance)
2) If this work is done in 1.0 sec how much power is needed? 80 W
3) If this work is done in 2.0 sec how much power is needed? 40 W
4) If this work is done in 0.5 sec how much power is needed? 160 W
5) How much work is required to give a 20 kg car a speed of 10 m/s? 1000 J=KE
6) If this work is done in 1.0 sec how much power is needed? 1000 W
7) If twice this amount of work is done in twice the time (2.0 sec), how much
power is needed? 1000 W
The kilowatt-hour is a common unit of energy
(1 kW-hr=1000 Watts x 3600 s =3,600,000 Joules)
To find the energy consumed in units of kW-hr simple multiply the power (in kWatts) by
the time (in hours). For example, a 2000 Watt heater running for 4 hours will use an
amount of energy E given by
E=2 kW x 4 hrs=8 kW-hrs
Presently 1 kW-hr costs about $0.08 in the Pacific Northwest so 8 kW-hrs costs about 64
cents ($.64)

How much energy is used in operating a 4000 Watt hot water heater for 10 hrs?
40kW-hrs

How much will this cost? $3.20=40kW-hr*$0.08/(1 kW-hr)

How much energy is consumed in operating ten 100 Watt light bulbs for 12 hrs
during the day? 12 kW-hr
How much will this cost? 96 cents