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HW15_Solutions

# HW15_Solutions - hiarker(srh959 homework 15 Turner(58220...

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hiarker (srh959) – homework 15 – Turner – (58220) 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A hot rod of mass 1400 kg, starting from rest reaches a speed of 190 m / s in only 17 . 7 s. What is the average output power? 1. 1 . 42768 MW correct 2. 0 . 000424527 MW 3. 0 . 0150282 MW 4. 0 . 0806601 MW 5. 2 . 85537 MW Explanation: The average output power is equal to the kinetic energy acquired divided by the total time, so P = 1 2 mv 2 t = (1400 kg) (190 m / s) 2 2 (17 . 7 s) · mW 10 6 W = 1 . 42768 MW 002 10.0 points A car with a mass of 1 . 29 × 10 3 kg starts from rest and accelerates to a speed of 12.4 m/s in 10.3 s. Assume that the force of resistance remains constant at 347.9 N during this time. What is the average power developed by the car’s engine? Correct answer: 11785 . 6 W. Explanation: Let : m = 1 . 29 × 10 3 kg , v f = 12 . 4 m / s , Δ t = 10 . 3 s , and F r = 347 . 9 N . v f = a Δ t and Δ x = 1 2 a t ) 2 since v i = 0 m/s, and F = m a + F r , so P = F Δ x Δ t = F · 1 2 a t ) 2 Δ t = F a Δ t 2 = ( m a + F r ) v f 2 = parenleftBig m v f Δ t + F r parenrightBig · v f 2 = bracketleftbigg (1290 kg)(12 . 4 m / s) 10 . 3 s + 347 . 9 N bracketrightbigg × 12 . 4 m / s 2 = 11785 . 6 W . 003 10.0 points A car weighing 8200 N moves along a level highway with a speed of 83 km / h. The power of the engine at this speed is 75 kW. The car encounters a hill inclined at an angle of 7 . 3 with respect to the horizontal. If there is no change in the power of the engine, and no change in the resistive forces acting on the car, what is the new speed of the car on the hill?

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