solutions 9 - Patel, Kinal Homework 9 Due: Oct 5 2007, 7:00...

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Patel, Kinal – Homework 9 – Due: Oct 5 2007, 7:00 pm – Inst: D Weathers 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. The due time is Central time. 001 (part 1 oF 1) 10 points A time-varying net Force acting on a 1 . 9 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 = 1 . 3 m / s , d = - 2 . 4 m / s 2 , and e = 1 . 3 m / s 3 , with x in meters and t in seconds. ±ind the work done on the particle in the frst 2 . 9 s oF motion. Correct answer: 385 . 227 J. Explanation: Since the Force is time dependent W Z x f x i ~ F · d~x = Z x f x i ma dx = m Z x f x i dv dt dx = m Z x f x i dv dx dx dt dx = m Z v f v i v dv = 1 2 mv 2 f - 1 2 mv 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 = dx dt = b + 2 dt + 3 et 2 v i = 1 . 3 m / s , and (1) v f = (1 . 3 m / s) + 2 ( - 2 . 4 m / s 2 ) (2 . 9 s) +3 (1 . 3 m / s 3 ) (2 . 9 s) 2 = 20 . 179 m / s , (2) where t i = 0 s and t f = 2 . 9 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 (1 . 9 kg) h (20 . 179 m / s) 2 - (1 . 3 m / s) 2 i = (386 . 832 J) - (1 . 6055 J) = 385 . 227 J . keywords: 002 (part 1 oF 1) 10 points Robin pushes a wheelbarrow by exerting a 121 N Force horizontally. Robin moves it 83 m at a constant speed For 24 s. What power does Robin develop?
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This note was uploaded on 10/22/2010 for the course PHYS PHYS 1710 taught by Professor Weathers during the Fall '07 term at North Texas.

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solutions 9 - Patel, Kinal Homework 9 Due: Oct 5 2007, 7:00...

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