Find the value of force to move a system:

The system of particles shown in the figure given below is initially at rest. Find the value of force F which should be applied so that system acquires velocity of 6m/sec after moving 5m.

Sol: Given,

Initial velocity u = 0

Final velocity v = 6m/sec

Distance traveled s = 5m

For finding acceleration, use relation, v²  = 4²  + 2as

a = 3.6 m/sec²  6²  = 0 + 2a X 5                                                                                     ... (i)

Apply relation F = ma,

Let T = Tension in string, same for both side

Using relation F = ma, for block A T - 100 = ma

T - 100 = (100/9.81) X 3.6                                                                                                             ...(ii)

Using relation F = ma, for block B

100 + F - T = ma

100 + F - T = (100/9.81) X 3.6                                                                                                            ...(iii)

Add equation (2) and (3), we get

F = 2[(100/9.81) X 3.6]

F = 73.5N                                                                          .......ANS