Question

5. (20 points) Two blocks are connected by a massless string over a pulley. Block 1 has mass m = 65kg and is on a horizontal table. Block 2 has mass m2 = 10kg and is on a ramp inclined at angle 0 = 53.13. The pulley has a mass M = 16kg and radius R = 25m and can be treated like a disk with uniform mass distribution. The string never slips against the pulley TTI m2 a) Suppose my travels 2.5m to the right when my reaches the bottom of the ramp. What is the angular speed of the pulley when my reaches the bottom of the ramp? The ramp and the table are frictions and the system is initially at rest. b) Lot T, denote the force of tension on m, and let T, denote the force of tension on me. Find the magnitude of T, and the magnitude of 7

Answer 1

ТІ m, = 65 kg mi lokg T m2 M = 46 kg R = 0,25 M mi For m, ma Ti For m2 maa I 10 11 12 13 My g sino - Tz For fully Tz R - TIR = I a I a R 14 15 = I am 116 a 117 118 I R2 a 19 78.399 20 a = eli 2 2/2 Tz - Ta edding all equation - m g sino (m, + m₂ + 10 x 9.8 x Sin 53.13 65 +10 + Ź MRR2 65 +10 + 46 O. O M/S2 Now time required to travell 2.5M so ut+ ļ at² 2.5 = ot ļxo.8 x t => t = 2.5 sec Now For Pully I = I MR² = { x 46(0.25) ² 1.4375 kg-m². 213 by mi 24 25 N

0.8 - 3.2 god port? D. Now a = R 0.25 Now f wi tat = 0 +3.2 x 2.5 wf w 8 read/sec (b Now By Eg. T = m, a = 65x0.8 = 52N T = Now By Eq I a 1.4375 x 0.8 (0,25) Tz - T, R2 18.4 Tz - Ti T2 T + 18.4 = 52 +18.4 7014 N Ci