Power Page: 456
Big Ideas Details Unit: Energy, Work & Power
Power
Unit: Energy, Work & Power
NGSS Standards/MA Curriculum Frameworks (2016): N/A
AP Physics 1 Learning Objectives/Essential Knowledge (2024): 3.5.A, 3.5.A.1,
3.5.A.2, 3.5.A.3, 3.5.A.4
Mastery Objective(s): (Students will be able to…)
• Calculate power as a rate of energy consumption.
Success Criteria:
• Variables are correctly identified and substituted correctly into the
appropriate equations.
• Algebra is correct and rounding to appropriate number of significant figures is
reasonable.
Language Objectives:
• Explain the difference between total energy and power.
Tier 2 Vocabulary: power
Notes:
power: a measure of the rate at which energy is applied or work is done. The
average power is calculated by dividing work (or energy) by time.
E W K + U
Pavg = = =
t t t
Power is a scalar quantity and is measured in Watts (W).
1 W = 1 sJ = 1 Nsm = 1 kgsm3
2
Note that utility companies measure energy in kilowatt-hours. This is because
W
P = , which means energy = W = Pt.
t
Because 1 kW = 1000 W and 1 h = 3600 s, this means
1 kWh = (1000 W)(3600 s) = 3 600 000 J
Fd d
Because W = F d , this means Pavg = = F = F vavg
t t
However, if we use the instantaneous velocity instead of the average velocity, this
equation gives us the instantaneous power:
Pinst = F v = Fv cos
Physics 1 In Plain English Jeff Bigler
Power Page: 457
Big Ideas Details Unit: Energy, Work & Power
AP® Power in Rotational Systems
In a rotational system, the formula for power looks similar to the equation for power
in linear systems, with force replaced by torque and linear velocity replaced by
angular velocity:
P = Fv P =
linear rotational
Solving Power Problems
Many power problems require you to calculate the amount of work done or the
change in energy, which you should recall is:
W = F|| d if the force is caused by linear displacement
Kt = 12 mv 2 − 12 mvo2 * if the change in energy was caused by a change in
velocity
= 12 m(v 2 − vo2 )
Ug = mgh − mgho if the change in energy was caused by a change in
= mg h height
Solving Rotational Power Problems
AP® Power is also applicable to rotating systems:
W = if the work is produced by a torque
K r = 12 I 2 − 12 Io2 if the change in energy was caused by a change in
angular velocity
= 12 I ( − )
2 2
o
Once you have the work or energy, you can plug it in for either W, K or U , use
the appropriate parts of the formula:
W K + U
P= = = Fv =
t t
and solve for the missing variable.
* Kt is translational kinetic energy. This is the only form of kinetic energy used in CP1 and honors
physics. The subscript t is used here to distinguish translational kinetic energy from rotational kinetic
energy (Kr), because both are used in AP® Physics.
Physics 1 In Plain English Jeff Bigler
Power Page: 458
Big Ideas Details Unit: Energy, Work & Power
Sample Problems:
Q: What is the power output of an engine that pulls with a force of 500. N over a
distance of 100. m in 25 s?
A: W = Fd = (500)(100) = 50000 J
W 50000
P= = = 2000 W
t 25
Q: A 60. W incandescent light bulb is powered by a generator that is powered by a
falling 1.0 kg mass on a rope. Assuming the generator is 100 % efficient (i.e., no
energy is lost when the generator converts its motion to electricity), how far
must the mass fall in order to power the bulb at full brightness for 1.0 minute?
A: Ug mg h
P= =
t t
(1)(10) h
60 =
60
3600 = 10 h
3600
h = = 360 m
10
Note that 360 m is approximately the height of the Empire State Building. This is
why changing from incandescent light bulbs to more efficient compact
fluorescent or LED bulbs can make a significant difference in energy
consumption!
Physics 1 In Plain English Jeff Bigler
Power Page: 459
Big Ideas Details Unit: Energy, Work & Power
Homework Problems
1. (S) A small snowmobile has a 9 000 W (12 hp) engine. It takes a force of
300. N to move a sled load of wood along a pond. How much time will it
take to tow the wood across the pond if the distance is measured to be
850 m?
Answer: 28.3 s
2. (M) A winch, which is rated at 720 W, is used to pull an all-terrain vehicle
(ATV) out of a mud bog for a distance of 2.3 m. If the average force applied
by the winch is 1 500 N, how long will the job take?
Answer: 4.8 s
3. (S) What is your power output if you have a mass of 65 kg and you climb a
5.2 m vertical ladder in 10.4 s?
Answer: 325 W
4. (M) Jack and Jill went up the hill. (The hill was 23m high.) Jack was carrying
a 21 kg pail of water.
a. (M) Jack has a mass of 75 kg and he carried the pail up the hill in 45 s.
How much power did he apply?
Answer: 490.7 W
b. (M) Jill has a mass of 55 kg, and she carried the pail up the hill in 35 s.
How much power did she apply?
Answer: 499.4 W
Physics 1 In Plain English Jeff Bigler
Power Page: 460
Big Ideas Details Unit: Energy, Work & Power
honors & AP® 5. (M – honors & AP®; A – CP1) The maximum power output of a particular
crane is P. What is the fastest time, t, in which this crane could lift a crate
with mass m to a height h?
(If you are not sure how to do this problem, do #6 below and use the steps to
guide your algebra.)
mgh
Answer: t =
P
6. (S – honors & AP®; M – CP1) The maximum power output of a particular
crane is 12 kW. What is the fastest time in which this crane could lift a
3 500 kg crate to a height of 6.0 m?
(You must start with the equations in your Physics Reference Tables and
show all of the steps of GUESS. You may only use the answer to question #5
above as a starting point if you have already solved that problem.)
Hint: Remember to convert kilowatts to watts.
Answer: 17.5 s
AP® 7. (M – AP®; A – honors & CP1) A 30 cm diameter solid cylindrical flywheel
with a mass of 2 500 kg was accelerated from rest to an angular velocity of
1 800 RPM in 60 s.
a. How much work was done on the flywheel?
Answer: 5.0 105 N m
b. How much power was exerted?
Answer: 8.3 103 W
Physics 1 In Plain English Jeff Bigler
