Question

Two blocks A and B having masses m₁ 1 = kg and m₂ = 4 kg are arranged as shown in Figure. The pulleys P and Q are light and frictionless. All blocks are resting on the horizontal floor and pulleys are held such that strings remain just taut. At moment t=0, a force F=30N starts acting on the pulley P along vertically upward direction as shown in the Figure: Determine 

(a) The time when blocks A and B lose contact with ground, 

(b) The velocity of A when B loses contact with ground, 

(c) The height raised by A till this instant.

Answer 1

F = 30t N

⇒ T = 10 t

wt. of A = 10 m₁ = 10 N

(a) Block A loses contact when T = weight

10t = 10

t = 1 s

Similarly 2T = 10m₂ when B loses contact

20t = 10(4)

t = 2s

(b) Net force on A F_A = 10 t – 10 (t > 1)

Answer 2

(a) t_A =1sec, t_B = 2sec,

(b) v_A = 5m /s 

(c) \(\frac{5}{3}\) m