Question

2. A uniform, solid cylinder with mass M and radius 2R is on an incline plane with angle of inclination of 6. A string is attached by a yoke to a frictionless axle through the center of the cylinder so that the cylinder can rotate about the axle. The string runs over a disk-shaped pulley with mass M and radius R that is mounted on a frictionless axle through its center. A block of mass M is suspended from the free end of the string. The string doesn't slip over the pulley surface, and the cylinder rolls without slipping on the incline. (a) Draw all forces acting on the cylinder, the pulley, and the block (b) Find the tensions in the string on both sides of the pulley (c) Find the magnitude of the acceleration of the block after the system is released from rest. (d) Use energy method to find the velocity of the block when it descends by a distance h.

Answer 1

Solution body diagam block Fee an Ma -O Fee body diagyam of hirnd Suppose it h as angulat aceoaton - Jd2 cylin der Fyee body diagem of a N2 o 1ling aithou slipping Cylindey

3) 2-Mg Sine m C4) mg Sine N2 Cylindes angulas aceletation of Nou Fo PUlley Mg For o tate wheje x is to lengih will be dis placement block the angle de dt dy/dt R dwe R FXum eay

Fm aa t), 2) AS MA2 Ma Add Ca ond eq (b 3 ma Scbstitule ma Paon ea(3 In the apove eauation Mg sino -mg -1 sin & 2. -2] Sino Value in e Substitule 3 Ma - 3a 3g sine t -3%Sine 19 7-3 Sine a as

Fom ea (O Mg-, Ma - Ma Mg - Mg C3sine] 1-C1-35in 6 Sine - i6 sine i S MCsine) Fas d initial enexgy velocity op a block V Kinetic enegy of block Poten tia enexgy of biock -mgh 기억 Pulley angulay velocity of a w2 kinetic enegy Puny 2 루x(2비) 루 -kinetic enegy ofo Cylmdey anslaticna Rotaion t

mv m M2 mg hsing Do tentia enegy of Cyindes Should be To ta enesgy Same Gmvstmtmyh sine 2+ 1t3 m mgh C-sin e) O gCI-sine) 를 mve V gh Cr-sine) ghCi-sine