Homework 10'-solutions

Homework 10'-solutions - kaplan (hmk378) Homework 10...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: kaplan (hmk378) Homework 10 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 5 . 2 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 . 9 m , b = 1 . 1 m / s , d =- 2 m / s 2 , and e = 0 . 5 m / s 3 , with x in meters and t in seconds. Find the work done on the particle in the first 4 . 5 s of motion. Correct answer: 468 . 951 J. Explanation: Since the force is time dependent W integraldisplay x f x i vector F dvectorx = integraldisplay x f x i ma dx = m integraldisplay x f x i dv dt dx = m integraldisplay x f x i dv dx dx dt dx = m integraldisplay 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. For this case, W = K = K f- K i = 1 2 m ( v 2 f- v 2 i ) , where the velocity is found by differentiating the displacement: v = dx dt = b + 2 dt + 3 et 2 v i = 1 . 1 m / s , and (1) v f = (1 . 1 m / s) + 2 (- 2 m / s 2 ) (4 . 5 s) +3 (0 . 5 m / s 3 ) (4 . 5 s) 2 = 13 . 475 m / s , (2) where t i = 0 s and t f = 4 . 5 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 (5 . 2 kg) bracketleftBig (13 . 475 m / s) 2- (1 . 1 m / s) 2 bracketrightBig = (472 . 097 J)- (3 . 146 J) = 468 . 951 J . 002 (part 1 of 3) 10.0 points A 1930 kg car accelerates uniformly from rest to a speed of 10 . 9 m / s in 3 . 74 s....
View Full Document

This document was uploaded on 10/26/2011 for the course PHYS 1710 at North Texas.

Page1 / 4

Homework 10'-solutions - kaplan (hmk378) Homework 10...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online