Question

For the apparatus shown in the figure, there is no slipping between the cord and the surface of the pulley. The blocks have mass of 3.0 kg and 5.7 kg, and the pulley has a radius of R and a mass of 15.4 kg. The moment of inertia of the pulley is EMR. What is the acceleration of the 5.7 kg mass? (Enter your answer in units of m/s2. Only enter the number using 2 significant figures.)

Answer 1

string is Ti and that in the NI Suppose the tension in the left string is ! right string is T2 - Suppose the block of mass 5.7 kg goes down a acceleration a and the other block of mass 3 kg up with the same acceleration. His will also be tangential acceleration gth sim of the pulley as string/core does not slip on the sim. He angular acceleration of the pulley will be mass 3 kg moves d=a the equation of motion of the two masses and the polley are- R (5.718 - T2 = 5.49 -0 T, - 13.0) g = (30) Q - © Tz R - TIR = Ida I - putting all the value of T1, T2 and I from eq" T2 = 5.79 -9.79 T= 5-7 (8-a) - © from eq" TI 318+a) | - IP MRS - 6

② ,6 and 6 in ③ putting the value from weget (T) - Ti) Rate (T) - TI) R = Į MR?: a (T2-T1) = Ima , M = 15.4k.g. 5-7(9-0) - 3 (9+a) = I x 15.4 xq (5.79-39) -39-5.70 = 7.79 = 7.70 +8.79 2.7 g 2-79 = (16.4) a = 2.7 g 22.7 x 9.8 16.4 9=1613 m/s2 Ta=lıb1 m/s27