2. Pulling hard: A block B of mass mg rests as shown on a bracket A of mass mA.

Question

2. Pulling hard: A block B of mass mg rests as shown on a bracket A of mass mA. The coefficient of friction between the block and the bracket is , same for the static and kinetic cases. There is no friction elsewhere (which means that the bracket A will slide). The pulley and string are ideal: both with negligible mass and the string is non- stretchable. The surfaces stay in contact all time, do not consider possible tilting or falling sideway. Use g-9.80m/s 1. What is the largest pull P that can be exerted without block B sliding with respect to bracket A? Derive your result using symbols.

Explanation / Answer

Horizontal Forces On Block B are

P towards left by the string

friction f ie u*mB*g towards the right by A

acceleration of B= (P-u*mB*g )/mB towards left

Horizontal Forces On Block A are

2P towards RIGHT by the PULLEY

friction f ie u*mB*g towards the left by A

acceleration of A= (u*mB*g-2P )/mA towards left

For no slipping , acceleration of both A and B should be same In the limiting case

Therefore (P-u*mB*g )/mB= (u*mB*g-2P )/mA

Or P = u*mB*g(mB+mA)/(mA+2mB)

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