A spring with a force constant of 1.35x10^2 N/m is used to push a 0.270 kg block of wood against a wall, as shown in the figure. 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 0.410

weight of block = m g = 0.270 * 9.81 = 2.65 Newtons down

we need mu F = 2.85 Newtons up
so F = 2.85 / 0.41 = 6.46 N
6.46 = k x
x = 6.46 N / 135 N/meter = .0478 meter = 4.78 cm