Homework 9 Sol.

# Homework 9 Sol. - Abd Elhai Mohamed – Homework 9 – Due...

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Unformatted text preview: Abd Elhai, Mohamed – Homework 9 – Due: Apr 17 2008, 3:00 pm – Inst: Dr Kevin Dean 1 This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. This is ONLINE HOMEWORK No. 9 It is due by 06:00 AM Abu Dhabi Time on Tuesday 15 April (9:00 PM Monday 14 April, Texas time). 001 (part 1 of 2) 5 points The turntable of a record player rotates at a rate of 49 . 6 rev / min and takes 62 s to come to rest when switched off. Calculate the magnitude of its angular ac- celeration. Correct answer: 0 . 0837759 rad / s 2 . Explanation: Angular acceleration is given by, α = Δ ω Δ t The number of revolutions (or rather the an- gle) the turntable makes before coming to rest is, θ = ωt + 1 2 αt 2 Notice that ω and α have opposite signs since the turntable is decelerating. 002 (part 2 of 2) 5 points Calculate the number of revolutions it makes before coming to rest. Correct answer: 25 . 6267 rev. Explanation: keywords: 003 (part 1 of 2) 5 points Four particles with masses 5 kg, 3 kg, 4 kg, and 5 kg are connected by rigid rods of negli- gible mass at the corners of a rectangle. The origin is at the center of the figure. x y O ω 4m 8 m 5 kg 3 kg 4 kg 5 kg What is the moment of inertia about the y-axis? Correct answer: 272 kg · m 2 . Explanation: Let : m 1 = 5 kg , top right m 2 = 3 kg , top left m 3 = 4 kg , bottom left m 4 = 5 kg , bottom right w = 8 m , and h = 4 m . Each mass is a distance r i = 4 m from the x-axis and X m i = 5 kg+3 kg+4 kg+5 kg = 17 kg , so I y = X m i r 2 i = r 2 i X m i = (4 m) 2 (17 kg) = 272 kg · m 2 . 004 (part 2 of 2) 5 points If the system rotates around the z-axis at an angular velocity of 7 rad / s, what is the kinetic energy of the system? Correct answer: 8330 J. Explanation: Let : ω = 7 rad / s The distance of each point from the z-axis is defined by r 2 i = h w 2 i 2 + • h 2 ‚ 2 = w 2 + h 2 4 , so Abd Elhai, Mohamed – Homework 9 – Due: Apr 17 2008, 3:00 pm – Inst: Dr Kevin Dean 2 I z = r 2 i X m i = w 2 + h 2 4 X m i = (8 m) 2 + (4 m) 2 4 (17 kg) = 340 kg · m 2 , and the rotational kinetic energy is K = 1 2 I z ω 2 = (340 kg · m 2 ) (7 rad / s) 2 2 = 8330 J . 005 (part 1 of 1) 0 points A massless rod of length L has a small mass m fastened at its center and another mass m fastened at one end. On the opposite end from the mass m , the rod is hinged with a frictionless hinge. The rod is released from rest from an initial horizontal position; then it swings down....
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Homework 9 Sol. - Abd Elhai Mohamed – Homework 9 – Due...

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