acceleration question please help!?

Question

The coefficients of static and kinetic friction between a 559 crate and the warehouse floor are 0.665 and 0.420, respectively. A worker gradually increases his horizontal push against this crate until it just begins to move and from then on maintains that same maximum push.

What is the acceleration of the crate after it has begun to move?

Please show steps on how to work.

Answer 1

When the worker just gets the crate to move, his force, Fp, matches that of the static drag.

Fp = Fs = Cs x N

where

N is the normal force (in this case just the weight of the crate)
Cs is the coefficient of static friction.

The drag once the crate is moving is:

Fk = Ck x N

The drag force opposes the pushing force so the net force is the difference:

Fn = Fp - Fk

Acceleration = force divided by mass or:

A = Fn/M

(I don't know if the 559 is weight or mass. Remember that:

Weight = Mass x Gravitational acceleration (around 9.8 m/s^2) so you can convert between them.)