1. UNIT 4 Work, Energy, and Power

2. 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 7.4Elastic Potential Energy ConcepTest 7.4 Elastic Potential Energy

3. 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 1/2 kx 2 elastic PE is 4 times greater work required to stretch the spring is also 4 times greater The elastic potential energy is 1/2 kx 2. 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 7.4Elastic Potential Energy ConcepTest 7.4 Elastic Potential Energy

4. ConcepTest 7.6Down the Hill 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

5. ConcepTest 7.6Down the Hill ConcepTest 7.6 Down the Hill same initial gravitational PE same height same final KEsame speed 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 mv 2 ). 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?

6. ConcepTest 7.7aRunaway Truck 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

7. ConcepTest 7.7aRunaway Truck 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: E i = PE g = mgH initial energy: E i = PE g = mgH E f = KE = 1/2 mv 2 final energy: E f = KE = 1/2 mv 2 Conservation of Energy: E i = mgH = E f = 1/2 mv 2 E i = mgH = E f = 1/2 mv 2 gH = 1/2 v 2 therefore: gH = 1/2 v 2 So if v doubles, H quadruples!

8. Friday November 11 th 8 POWER

9. TODAYS AGENDA Bowling Ball Demo Power 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

10. 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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12. 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: Energy

13. 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 Power Energy

14. 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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