UNIT 4 Work, Energy, and Power
Mar 28, 2015
UNIT 4Work, Energy, and Power
How does the work required to
stretch a spring 2 cm compare
with the work required to
stretch it 1 cm?
1) same amount of work
2) twice the work
3) 4 times the work
4) 8 times the work
ConcepTest 7.4 Elastic Potential Energy
How does the work required to
stretch a spring 2 cm compare
with the work required to
stretch it 1 cm?
1) same amount of work
2) twice the work
3) 4 times the work
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 7.4 Elastic Potential Energy
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?
1
4) same speed
for all balls
2 3
ConcepTest 7.6 Down the Hill
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).
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?
1
4) same speed
for all balls
2 3
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?
1) half the height
2) the same height
3) 2 times the height
4) twice the height
5) four times the height
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!
Friday November 11th
8
POWER
TODAY’S AGENDA
Bowling Ball DemoPower
Hw: Practice E (All) p177 Practice F (All) p181
UPCOMING…
Mon: Problem Quiz 1 (Practice A, B, & C) Tue: Problems @ the Boards Wed: Problem Quiz 2 (Practice D, E, & F) Thur: Problems @ the Boards Fri: TEST 5
Friday, November 11
Copyright © by Holt, Rinehart and Winston. All rights reserved.
ResourcesChapter menu
Section 4 Power
Chapter 5
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
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Power
Power is the rate at which work is done –
The difference between walking and running up these stairs is power – the change in gravitational potential energy is the same.
In the SI system, the units of power are Watts:
TimeWork
Power Average Time
dTransforme Energy
SecondJoule
1Watt1
Energy
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
tW
P t
Fd Fv
Power
Energy
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 (Problem)
Energy
Power = 40,000 W
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END