UNIT 4 Work, Energy, and Power

UNIT 4Work, Energy, and Power

ConcepTest 7.4Elastic Potential Energy 1) same amount of work 2) twice the work 3) 4 times the work 4) 8 times the work How does the work required to stretch a spring 2 cm compare with the work required to stretch it 1 cm?

ConcepTest 7.4Elastic Potential Energy 1) same amount of work 2) twice the work 3) 4 times the work 4) 8 times the work How does the work required to stretch a spring 2 cm compare with the work required to stretch it 1 cm? 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 7.6Down 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 3 2 1

ConcepTest 7.6Down 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 3 2 1 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?

1)half the height 2) the same height 3)  2 times the height 4) twice the height 5) four times the height ConcepTest 7.7aRunaway 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 7.7aRunaway 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 = 1/2v2 So if v doubles, H quadruples!

Friday November 11th POWER

TODAY’S AGENDA Friday, November 11 • 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

Section 4 Power Chapter 5 Rate of Energy Transfer • Poweris 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

Power Power is the rate at which work is done – In the SI system, the units of power are Watts: The difference between walking and running up these stairs is power – the change in gravitational potential energy is the same. Energy

Power v F d Power is also needed for acceleration and for moving against the force of gravity. The averagepower can be written in terms of the force and the averagevelocity: 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

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UNIT 4 Work, Energy, and Power