Question

A 100kg box is laying still in a wooden box. What is the horizontal force needed to start the crate moving

Answer 1

We assume, that mass of the wooden box without 100 kg box << $m=100\, kg$ box. Then the horizontal force needed to start the crate moving is

$$F=\mu mg,$$

where $\mu$ is the coefficient of static friction between the wood and the surface on which the crate rests.

For example, average of static friction between wood and metal is $\mu_{w,m}=0.4$ [1]. So, with $g=9.8 \, m/s^2$ we have

$$F=0.4\cdot 100 \cdot 9.8=392\, N.$$

[1] http://www.engineershandbook.com/Tables/frictioncoefficients.htm