Phycics - Create assignment, 18042, Homework 9, Aug 03 at...

Info iconThis preview shows pages 1–3. 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: Create assignment, 18042, Homework 9, Aug 03 at 12:55 pm 1 This print-out should have 19 questions. Multiple-choice 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....
View Full Document

This document was uploaded on 04/15/2009.

Page1 / 7

Phycics - Create assignment, 18042, Homework 9, Aug 03 at...

This preview shows document pages 1 - 3. Sign up to view the full document.

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