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A large crate with mass m rests on a horizontal floor. The static and kinetic coefficients...

A large crate with mass m rests on a horizontal floor. The static and kinetic coefficients of friction between the crate and the floor are μs and μk, respectively. A woman pushes downward on the crate at an angle θ below the horizontal with a force F⃗ .

What is the magnitude of the force vector F⃗  required to keep the crate moving at constant velocity?

If μs is greater than some critical value, the woman cannot start the crate moving no matter how hard she pushes. Calculate this critical value of μs.

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