{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# 9 - roofner(bar784 Homework 9 Weathers(17104 This print-out...

This preview shows pages 1–2. Sign up to view the full content.

roofner (bar784) – Homework 9 – Weathers – (17104) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A time-varying net force acting on a 4 . 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 . 4 m , b = 2 . 2 m / s , d = - 3 . 4 m / s 2 , and e = 0 . 83 m / s 3 , with x in meters and t in seconds. Find the work done on the particle in the first 3 . 6 s of motion. Correct answer: 213 . 678 J. Explanation: Since the force is time dependent W integraldisplay x f x i vector F · dvectorx = integraldisplay x f x i m a dx = m integraldisplay x f x i d v dt dx = m integraldisplay x f x i d v dx d x dt dx = m integraldisplay v f v i v dv = 1 2 m v 2 f - 1 2 m v 2 i . Therefore work done on the particle is the change in kinetic energy. For this case, W = Δ K = K f - K i = 1 2 m ( v 2 f - v 2 i ) , where the velocity is found by differentiating the displacement: v = d x dt = b + 2 d t + 3 e t 2 v i = 2 . 2 m / s , and (1) v f = (2 . 2 m / s) + 2 ( - 3 . 4 m / s 2 ) (3 . 6 s) +3 (0 . 83 m / s 3 ) (3 . 6 s) 2 = 9 . 9904 m / s , (2) where t i = 0 s and t f = 3 . 6 s . Evaluation of the velocity at the initial and final times gives the desired result. W = K f - K i = 1 2 m ( v 2 f - v 2 i ) = 1 2 (4 . 5 kg) bracketleftBig (9 . 9904 m / s) 2 - (2 . 2 m / s) 2 bracketrightBig = (224 . 568 J) - (10 . 89 J) = 213 . 678 J . 002 (part 1 of 3) 10.0 points A 1650 kg car accelerates uniformly from rest to a speed of 10 . 3 m / s in 4 . 43 s. Find the work done by the net force on the car during this time interval Correct answer: 87524 . 2 J.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}