Question

The following problem is not multiple choice. Final numerical answer is not sufficient to get full credits on the problem. You need to explain what you did and what you used to get your answers. A solid cylinder of radius 20 cm and mass 12 kg starts from rest and rolls without slipping a distance L=8 m down a roof that is inclined at angle 30°. (a) What is the angular speed of the cylinder about its center as it leaves the roof? (b) The roof's edge is at height H=6 m. How far horizontally from the roof's edge does the cylinder hit the level ground? H

Answer 1

© L=sm m=12kg R 20cm = 0.2m o L h = 30° a) The velocity whene the cylinder leaves the roof is given by agh it k?R? where K = radius of gyantion of cylinder. pe h = L sen o = 8x sin 30 4 m. agh agh i v = CS Scanned with CamScanner 1 + (Riva) R2 (312)

2x9.8ly 4 x 2 3 = 7.23 mls : So angula velocity, 7:23 w = R (Ans) = 36:17 rad Is b ) vcoso Ha Gm v sino vertical distance, a H=6m vertical initial velocity, U = V sino = 7.23 x sin 30 u=3.62 m/s acceleration, а 11 go 29.81 m/s? CS Scanned with CamScanner

H =utt ļ at? time 't is given by > + 3.62t 6 20. 6 = (3.62xt)+(v 9.81x t?) 4.922 solving this and degree equation, t = 0.797 S .: Horizontal distance horizontal velocity & time - V eos ext =7.23(Los 30) x 0.797 4.99 m CAns) CS Scanned with CamScanner

u TH h = t + ata u=46 m/s 0 -60° t = 65. a) vertical distance h is givenby vo= usino H * K. h ucose a = -9.8lmis? x -9.8xt? = u sinoxt + á 646x Sin 60 x6)-(à *9.8 9.886') 62.44 m Cans) - h CSScanned with CamScanner

b) vertical relocity V = Vot at = usin 60 + 69.8) x 6 = 46x Sindo - 9.8 x 6 on mains mots =-18.96 mis Cans) horizontal velocity doesnot change. VH = U cose = 46 x cos 60 Y = 23 mois .: velocity of impact JVP+ veren = 29.81 mls (Aus) c) Maximum height it is given by u? Sin? H = 46² x (Sin 60) ag 2x 9.8 (Ans) Jj 80.89 m CS Scanned with CamScanner