### Power

```UNIT 4
Work, Energy, and Power
ConcepTest 7.4 Elastic Potential Energy
How does the work required to
1) same amount of work
stretch a spring 2 cm compare
2) twice the work
with the work required to
3) 4 times the work
stretch it 1 cm?
4) 8 times the work
ConcepTest 7.4 Elastic Potential Energy
How does the work required to
1) same amount of work
stretch a spring 2 cm compare
2) twice the work
with the work required to
3) 4 times the work
stretch it 1 cm?
4) 8 times the work
The elastic potential energy is 1/2 kx2. So in the second case,
the elastic PE is 4 times greater than in the first case. Thus,
the work required to stretch the spring is also 4 times greater.
ConcepTest 7.6 Down the Hill
Three balls of equal mass start from rest and roll down different
ramps. All ramps have the same height. Which ball has the
greater speed at the bottom of its ramp?
4) same speed
for all balls
1
2
3
ConcepTest 7.6 Down the Hill
Three balls of equal mass start from rest and roll down different
ramps. All ramps have the same height. Which ball has the
greater speed at the bottom of its ramp?
4) same speed
for all balls
1
2
3
All of the balls have the same initial gravitational PE,
since they are all at the same height (PE = mgh). Thus,
when they get to the bottom, they all have the same final
KE, and hence the same speed (KE = 1/2 mv2).
Follow-up: Which ball takes longer to get down the ramp?
ConcepTest 7.7a Runaway Truck
A truck, initially at rest, rolls
down a frictionless hill and
attains a speed of 20 m/s at the
bottom. To achieve a speed of
40 m/s at the bottom, how many
times higher must the hill be?
1) half the height
2) the same height
3)  2 times the height
4) twice the height
5) four times the height
ConcepTest 7.7a Runaway Truck
A truck, initially at rest, rolls
down a frictionless hill and
attains a speed of 20 m/s at the
bottom. To achieve a speed of
40 m/s at the bottom, how many
times higher must the hill be?
Use energy conservation:
 initial energy: Ei = PEg = mgH
 final energy: Ef = KE = 1/2 mv2
Conservation of Energy:
Ei = mgH = Ef = 1/2 mv2
therefore:
gH = 1/2 v2
So if v doubles, H quadruples!
1) half the height
2) the same height
3)  2 times the height
4) twice the height
5) four times the height
Friday November 11th
POWER
8
TODAY’S AGENDA
Friday, November 11
 Bowling Ball Demo
 Power
 Hw: Practice E (All) p177
Practice F (All) p181
UPCOMING…





Mon:
Tue:
Wed:
Thur:
Fri:
Problem Quiz 1 (Practice A, B, & C)
Problems @ the Boards
Problem Quiz 2 (Practice D, E, & F)
Problems @ the Boards
TEST 5
Chapter 5
Section 4 Power
Rate of Energy Transfer
• Power is a quantity that measures the rate at which
work is done or energy is transformed.
P = W/∆t
power = work ÷ time interval
• An alternate equation for power in terms of force and
speed is
P = Fv
power = force  speed
Resources
11
Power
Power is the rate at which work is done –
Average Power 
Work Energy Transformed

Time
Time
In the SI system, the units of power are Watts:
1Watt  1
Joule
Second
The difference between walking and running up
these stairs is power – the change in gravitational
potential energy is the same.
Energy
Power
Power is also needed for acceleration and for moving against
the force of gravity.
The average power can be written in terms of the force and the
average velocity:
v
F
d
W Fd
P

 Fv
t
t
Energy
Power (Problem)
A 1000 kg sports car accelerates from rest to 20 m/s in 5.0 s.
What is the average power delivered by the engine?
Power = 40,000 W
Energy
END
15
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