If someone pushes on a box on a horizontal floor with a horizontal force of 17.8 N, but the box does not move, what is the static friction (Fs) between the box and the floor? Explain.

The next question is:
If the box just starts to move with a horizontal force of 29.5 N, what is the maximum static friction (Fs,max)?

I know these are solvable with the current information, but I feel like I'm missing something... I am quite lost. I am not sure what formula can solve these with the given info.

In my textbook, it says Fs = -Fapplied

Does this mean Fs really just equals negative 17.8 N, for the first question?

Thanks!

1 answer

If it is not moving, the fricion must equal the pushing force.

if it moves at 29.5 N
then
29.5 is the max static force