Question

(Figure 1) illustrates an Atwood's machine. Let the masses of blocks A and B be 9.00 kg and 2.00 kg, respectively, the moment of inertia of the wheel about its axis be 0.220 kg. m², and the radius of the wheel be 0.120 m. There is no slipping between the cord and the surface of the wheel. 

Part A 

Find the magnitude of the linear acceleration of block A. 

Part B 

Find the magnitude of linear acceleration of block B. 

Part C 

Find the magnitude of angular acceleration of the wheel C. 

Part D 

Find the tension in left side of the cord.

Part E 

Find the tension in right side of the cord. 

Answer 1

1) linear acceleration of block A:

a = (ma - mb) *g/(ma + mb + I/r^2)

a = (9-2)*9.8/(9+2+15.27)

a = 68.6/26.27

a = 2.611 m/s^2

2) linear acceleration of block B is

a = - 2.611 m/s^2

3) angular acceleration of C is

angular acceleration = a/r

A = 2.611/0.12

A = 21.76 rad/s^2

4) tension in left rod is

Fb = 2*(9.8 + 2.611)

Fb = 24.822 N

5) tension In right rod is

Fa = 9*(9.8 - 2.611)

Fa = 64.701 N