Question

Block b moves to the right with a constant velocity v0 the velocity of body a relative to b is

Answer 1

Answer:

Vab = Vo/2

Explanation:

To understand the scenario, first see the figure.

Now length of rope is constant = L;

So ;

L = (Xb – Xf) + 2(Xb+Xa)

Here Xa is the distance of Block A pulley from origin.

Here Xb is the distance of Block B pulley from origin.

Here Xf is the distance from the centre.

L = (Xb – Xf) + 2(Xb+Xa)

L = 3Xb – Xf – 2Xa  …………………. Eq(1)

Differentiating eq(1) with respect to t;

dL/dt   =  3dXb/dt  - dXf/dt  - 2 dXa/dt

0 = 3 Vb – 0 – 2Va

Va = 3/2 Vb

Vb= Vo

Va= 3/2Vo

Vab = Va – Vb;

        = 3/2 Vb – Vb;

        = Vb/2;

        = Vo/2

Towards right as Vab is positive