A 45-kg box containing a new bicycle has just arrived in the front porch and two brothers are fighting over it. The first brother pulls with a five of 52 N, while the second brother pulls on the opposite direction with a force of 125 N. What is the minimum coefficient of static friction that will prevent the box from moving?

0.17

Explanation:

Draw a free body diagram. There are five forces on the box:

Weight force mg pulling down

Normal force Fn pushing up

Applied force 52 N pulling to the left

Applied force 125 N pulling to the right

Friction force Fnμ pulling to the left

Sum of the forces in the y direction:

∑F = ma

Fn - mg = 0

Fn = mg

Fn = (45) (9.8)

Fn = 441

Sum of the forces in the x direction:

∑F = ma

125 - 52 - Fnμ = 0

Fnμ = 73

μ = 73 / Fn

μ = 73 / 441

μ = 0.17