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, v^{2} = 4^{2} + 2as
a = 3.6 m/sec^{2} 6^{2} = 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