Find out the motion of the system, Mechanical Engineering

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.

Solution

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.

1302_Find out the motion of the system.png

Let Datum-level at the lowest level B′ of the block B.

801_Find out the motion of the system1.png

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.

Posted Date: 1/29/2013 7:12:22 AM | Location : United States







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