In a pulley system, two blocks are connected by a rope as shown below. The coefficient of static friction between block A and the surface is 0.8. Block A has a mass of 20kg. What is the minimum mass that block B can have so that block A moves?

Hi there!

We can begin by doing a summation of forces for each block.

Block A:

This block has the force of tension (in direction of acceleration +) and static friction (opposite direction -) acting on it. Thus:

Block B:

This block has the force of tension (opposite of acc. -) and gravity (in direction of acc +), working on it.

Add both of the expressions and solve for the maximum mass of Block B.

To find the minimum value, we can set a = 0, so:

The block must weigh > 16 kg for block A to move.

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