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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 Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. 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