Phyisics question below

Question

A spring with a force constant of 120N/m is used to puch a 0.27kg block of wood against a wall. Find the minimum compression of the spring needed to keep the block from falling, given that the coefficient of static friction between the block and the wall is 0.46.

Answer 1

First we need to know the weight W of the block. We can use W=mg.

We get W = mg = (0.27 kg)(9.8 m/s²) = 2.6 N

The force of static friction is given by F = μ_sN.

We are given μ_s = 0.46. The minimum force of friction required is equal to the weight of the block. so we can solve for N.

0.46N = 2.6 N

N = (2.6 N)/0.46 = 5.7 N

To push the block with 5.7 N of force, the compression x must satisfy kx = 5.7 N.

We are given k = 120 N/m so

x = (5.7 N) / (120 N/m) = 0.048 m = 4.8 cm.