Homework 9 Solutions

# Homework 9 Solutions - lim(kl9356 Homework 9 Weathers(17104...

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lim (kl9356) – Homework 9 – Weathers – (17104) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points A time-varying net Force acting on a 2 . 5 kg particle causes the object to have a displace- ment given by x = a + b t + d t 2 + e t 3 , where a = 2 . 2 m , b = 3 . 1 m / s , d = - 4 . 4 m / s 2 , and e = 2 m / s 3 , with x in meters and t in seconds. ±ind the work done on the particle in the frst 2 . 5 s oF motion. Correct answer: 420 . 437 J. Explanation: Since the Force is time dependent W i x f x i v F · dvx = i x f x i ma dx = m i x f x i dV dt dx = m i x f x i dx dx dt dx = m i v f v i V dV = 1 2 mV 2 f - 1 2 2 i . ThereFore work done on the particle is the change in kinetic energy. ±or this case, W = Δ K = K f - K i = 1 2 m ( V 2 f - V 2 i ) , where the velocity is Found by di²erentiating the displacement: V = dt = b + 2 dt + 3 et 2 V i = 3 . 1 m / s , and (1) V f = (3 . 1 m / s) + 2 ( - 4 . 4 m / s 2 ) (2 . 5 s) +3 (2 m / s 3 ) (2 . 5 s) 2 = 18 . 6 m / s , (2) where t i = 0 s and t f = 2 . 5 s . Evaluation oF the velocity at the initial and fnal times gives the desired result. W = K f - K i = 1 2 m ( V 2 f - V 2 i ) = 1 2 (2 . 5 kg) b (18 . 6 m / s) 2 - (3 . 1 m / s) 2 B = (432 . 45 J) - (12 . 0125 J) = 420 . 437 J . 002 (part 1 oF 3) 10.0 points A 1850 kg car accelerates uniFormly From rest to a speed oF 11 . 4 m / s in 3 . 25 s. ±ind the work done by the net Force on the car during this time interval Correct answer: 1 . 20213 × 10 5 J.

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Homework 9 Solutions - lim(kl9356 Homework 9 Weathers(17104...

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