A box of books weighing 330 N is shoved across the floor of an apartment by a force of 440 N exerted downward at an angle of 35.0° below the horizontal. If the coefficient of kinetic friction between box and floor is 0.57, how long does it take to move the box 4.00 m, starting from rest?

Answer 1

This is a somewhat involved problem.

First, you have to break the pushing force into horizontal and vertical components.

Fh=330cos35
Fv=330sin35 (goingdownward.)

Now, you have to figure friction retarding force.
frictionforce=mu(mg+downwardforce)
calculate that.

Then, you use
Net force= mass*acceleration
Fh-frictionforce= mass*acceleration
and you calcuate acceleration.

Finally, near the end, finding the time to move the box.

distance=1/2 a t^2
you know distance, and a. solve for time.