Find out the motion of the system:
Block (A) of mass M A = 40 kg is resting on coarse table having coefficient of friction = 0.1. This is tied up with an inextensible rope (a b c d) passing over the smooth and mass-less pulleys P1 and P2 and end (d) is at the fixed support is illustrated in Figure. Another mass MB = 10 kg is hanging from pulley P2.Find out the motion of the system.
Figure illustrated the block A and B as connected in the system. Pulley P2 has rope on its either side or therefore movement of P2 or block B is half the movement of block A.
∴ If V is the velocity of block A, V/2 is the velocity of block B.
Likewise, if a is the acceleration of A, a/2 is the acceleration of B.
∴ For block A, V 2 = 2 a s --------- (I)
Weight of B = WB = 10 × g
Let A′ and B′ be the final positions of block A and B respectively as illustrated in the figure.
Let Datum-level at the lowest level B′ of the block B.
40 g ( H + (s/2) ) + 10 (s/2) × g = 40 g (H + (s/2) + M A (V 2 /2) + (M B/2) (V /2)2 + F × s
∴ 5 g s = (V 2/2) (40 +( 10/4) )+ 0.1 × 40 g s ---------- (II)
From Eq. (I) and (II)
5 g s - 4 g s = (2 a/2) s (42.5)
∴ a = 0.23 m / sec 2 along AA.