Block Held by Spring

Question

The coefficient of static friction can be determined using the following procedure. A block is held against a vertical wall by compressing a spring attached to the block.

If the spring has a spring constant = 531 N/m and requires a compression of 3.7 cm to just keep the block from slipping, what is the static friction coefficient between the wall and the 4.5 kg block?

Answer 1

The spring force is equal to the max static friction force:

kx = mgμ_s therefore, μ_s = kx/mg where x is the compression, which must be expressed in meters