Chapter 11, Problem 007 In the figure, a solid cylinder of radius 13 cm and mass

Question

Chapter 11, Problem 007 In the figure, a solid cylinder of radius 13 cm and mass 16 kg starts from rest and rolls without slipping a distance L 4.3 m down a roof that ls inclined at angle e-39 (a) is the angular of the cylinder about Its center as it leaves the roof? (b) The roofs edge is at height H- 6.7 m. How far horizontally from the roofs edge does the cylinder the level ground? (a) Number Units (b) Number Units VIDEO MINI-LECTURE LINK TO SAMPLE PROBLEM LINK TO SAMPLE PROBLE LINK TO TEXT LINK TO SAMPLE PROBLE By accessing this Question Assistance, you will learn while you earn points based on the Point Potential Policy set by your instructor. licy I 2000-2012 lohn Wiler Sons Ins All Rights Reserved A Division of lohn wiley. sens assignment/rest/aglist,uniaN1002,

Explanation / Answer

m = 16 kg, r =13 cm , L = 4.3 m , theta = 39 degrees

From conservation of energy

KEtop =KE bottom of roof

0.5mv^2 +0.5Iw^2 = mgh

sin(39) = h/L

moment of ienrtia of solid cylinder I = 0.5mr^2/2

for without slipping condition v = rw

0.5mr^2w^2 + 0.5*0.5*mr^2w^2 = mgLsin(39)

(3/4)r^2w^2 = gLsin(39)

(3/4)0.13^2*w^2 = 9.8*4.3*sin(39)

w = 45.74 rad/s

(b) vox = rwcos(theta) = 0.13*45.74*cos(39)

vox = 4.62 m/s

voy = 0.13*45.74*sin(39) = 3.74 m/s

from kineamtic equaiton along vertical direction

H = voyt+0.5gt^2

H = 6.7 m

6.7 = 3.74*t +0.5*9.8*t^2

t = 0.848 s

x = vox*t = 4.62*0.848

x = 3.92 m

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