Calculate the vertical acceleration a of the 100lb cylinder

Calculate the vertical acceleration a of the 100-lb cylinder for each of the two cases illustrated. Neglect friction and the mass of the pulleys.

Solution

>> Case (a).

Let acceleration = a

Now, Considering 150 b block, it will move downward

=> 150*32.2 - T = 150*a ....(1).....

>> and Considering Block 100 lb, it will move upwards,

=> T - 100*32.2 = 100*a .......(2).......

>> Adding (1) and 92),

=> 50*32.2 = 250*a

=> Acceleration, a = 6.44 ft/s²

>> Case (b).

Now, T = 150*32.2

So Considering 100 lb , as it will move upwards

=> So, T - 100*32.2 = 100*a

=> 50*32.2 = 100*a

=> Acceleration, a = 16.1 ft/s²