# hw31 - Muraj, Hamza Homework 31 Due: Apr 17 2006, 4:00 am...

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Muraj, Hamza – Homework 31 – Due: Apr 17 2006, 4:00 am – Inst: Florin 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – fnd all choices be±ore answering. The due time is Central time. 001 (part 1 o± 1) 10 points A 65 kg man in a 3 . 9 kg chair tilts back so that all his weight is balanced on two legs o± the chair. Assume that each leg makes contact with the ²oor over a circular area o± radius 1 . 4 cm. The acceleration o± gravity is 9 . 8 m / s 2 . Find the pressure exerted on the ²oor by each leg. Correct answer: 548289 Pa. Explanation: Given : M man = 65 kg , M chair = 3 . 9 kg , and r = 1 . 4 cm = 0 . 014 m . The area o± one o± the legs is A = π r 2 and the ±orce exerted by one leg on the ²oor is F = 1 2 ( M man + M chair ) g Thus the pressure exerted on the ²oor by one leg is P = F A = ( M man + M chair ) g 2 π r 2 = (65 kg + 3 . 9 kg) ( 9 . 8 m / s 2 ) 2 π (0 . 014 m) 2 = 548289 Pa . 002 (part 1 o± 2) 10 points Consider a vertical dam o± width w and height h ±rom the bottom to the waterline. h w What is the total horizontal ±orce on the dam? 1. F = ρ g w h 2 2. F = 1 4 ρ g w h 2 3. F = ρ g w 2 h 4. F = 1 3 ρ g w 2 h 5. F = 1 2 ρ g w 2 h 6. F = 1 2 ρ g w h 2 correct 7. F = 1 4 ρ g w 2 h Explanation: Basic Concept: Variation o± pressure with depth. Solution: The total ±orce acting on the dam is the integral o± the pressure on the sur±ace o± the dam F = Z h 0 dy w P = Z h 0 dy w ρ g y = 1 2 ρ g w h 2 . 003 (part 2 o± 2) 10 points Consider a new dam where the height is dou- bled and the width is only one third o± the original value. The ratio o± the total ±orce exerted on the new dam to that on the original dam F new F is given by 1. F new F = 1 3 2. F new F = 2 3

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Muraj, Hamza – Homework 31 – Due: Apr 17 2006, 4:00 am – Inst: Florin 2 3. F
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## This note was uploaded on 04/12/2010 for the course PHY 58195 taught by Professor Turner during the Spring '09 term at University of Texas.

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hw31 - Muraj, Hamza Homework 31 Due: Apr 17 2006, 4:00 am...

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