Question

A 4kg box is initially sitting at an horizontal floor with a Coefficent of stable friction miu=04. a horizontal pushing forces is applied to the box What is the maximum pushing force that can be applied with out moving the box?​

Answer 1

By Newton's second law, the net vertical force on the box is

∑ F[vertical] = n - mg = 0

where n = magnitude of normal force and mg = weight of the box. It follows that

n = mg

so that static/stable friction has a maximum magnitude of

f = µn = 0.4 mg

The box stays at rest up to the point that the applied force matches this magnitude of about 0.4 (4 kg) g ≈ 16 N.