What is the minimum angle for box to start slipping?

[anubis01]

Homework Statement

A box of textbooks of mass 24.0 Kg rests on a loading ramp that makes an angle θ with the horizontal. The coefficient of kinetic friction is 0.25 and the coefficient of static friction is 0.36.

a)As the angle is increased, find the minimum angle at which the box starts to slip
b)At this angle, find the acceleration once the box has begun to move
c)At this angle, how fast will the box be moving after it has slid a distance 4.8 m along the loading ramp?

Homework Equations

f=un
n=mgcosθ

The Attempt at a Solution

a)f_s=u_sn=ma=0
u_smgcosθ=0
θ=cos^-1(-umg)
θ=cos^-1(-0.36*24*9.8)
θ=cos^-1(-84.67)
This is pretty much the only question I'm having trouble with, b and c I can figure out once I find θ. As always any help is much appreciated.

 

[Doc Al]

What forces act on the box? Just before it starts to slip, what's the net force on the box?

 

[anubis01]

the forces that act on the box are f_g and f_s and the net force will be zero just before it starts so.
-mg+u_smgcosθ=0
θ=cos^-1(mg/umg)

 

[Doc Al]

the forces that act on the box are f_g and f_s and the net force will be zero just before it starts so.

Good. (But don't forget the normal force.)

-mg+u_smgcosθ=0

Weight acts vertically; friction acts parallel to the incline. To combine forces in an equation, take components parallel to the incline.