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Unformatted text preview: Create assignment, 18042, Homework 9, Aug 03 at 12:55 pm 1 This printout should have 19 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. The due time is Central time. Holt SF 08E 01 10:04, highSchool, numeric, > 1min, wording variable. 001 A solid cylinder with a mass of 4.10 kg and a radius of 0.050 m starts from rest at a height of 2.00 m and rolls down a 30 . ◦ slope, as shown. The acceleration of gravity is 9 . 81 m / s 2 . What is the translational speed of the cylin der when it leaves the incline? Correct answer: 5 . 11468 m / s. Explanation: Basic Concepts: v = rω I = 1 2 mr 2 KE trans = 1 2 mv 2 KE rot = 1 2 Iω 2 PE g = mgh Conservation of mechanical energy: PE i + KE i = PE f + KE f Given: m = 4 . 10 kg r = 0 . 050 m h = 2 . 00 m θ = 30 . ◦ v i = 0 m / s g = 9 . 81 m / s 2 Solution: v i = 0 m/s and h f = 0 m, so PE i = KE f PE i = KE trans,f + KE rot,f mgh = 1 2 mv 2 f + 1 2 Iω 2 f mgh = 1 2 mv 2 f + 1 2 µ 1 2 mr 2 ¶ ‡ v f r · 2 gh = 1 2 v 2 f + 1 4 v 2 f = 3 4 v 2 f v 2 f = 4 3 gh v f = r 4 3 gh = r 4 3 (9 . 81 m / s 2 )(2 m) = 5 . 11468 m / s Three Particle System 10:04, calculus, numeric, > 1 min, normal. 002 Three particles of mass 4 kg, 2 kg, and 3 kg are connected by rigid rods of negligible mass lying along the y axis and are placed at 3 m, 2 m, and 4 m , respectively as in the figure. The system rotates about the x axis with an angular speed of 2 rad / s . Contrary to what is observed in the figure, consider the masses to be point particles. 3 m 2 m 4 m 2 rad / s x 4 kg 2 kg 3 kg Find the moment of inertia about the x axis. Correct answer: 92 kgm 2 . Explanation: Create assignment, 18042, Homework 9, Aug 03 at 12:55 pm 2 Let : m 1 = 4 kg , m 2 = 2 kg , m 3 = 3 kg , y 1 = 3 m , y 2 = 2 m , y 3 = 4 m , and ω = 2 rad / s . The total rotational inertia of the system about the x axis is I = X m i r 2 i = 92 kgm 2 , where, r i =  y i  . 003 Find the total rotational energy of the sys tem. Correct answer: 184 J. Explanation: Since ω = 2 rad / s , the total rotational energy is E = 1 2 I ω 2 = 1 2 (92 kgm 2 )(2 rad / s) 2 = 184 J . 004 Find the linear speed of the top particle of mass 4 kg in the figure. Correct answer: 6 m / s. Explanation: The linear speed of each particles are v i = r i ω v 1 = r 1 ω = (3 m)(2 rad / s) = 6 m / s . Decelerated Grinding Wheel 10:06, trigonometry, numeric, > 1 min, nor mal. 005 The motor driving a grinding wheel with a ro tational inertia of 0 . 1 kgm 2 is switched off when the wheel has a rotational speed of 20 rad / s. After 6 s, the wheel has slowed down to 16 rad / s....
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This document was uploaded on 04/15/2009.
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