Using coefficients of static and kinetic friction

[Crusaderking1]

Homework Statement

A box of textbooks of mass 24.6 kg rests on a loading ramp that makes an angle theta with the horizontal. The coefficient of kinetic friction is 0.23 and the coefficient of static friction is 0.35.

A. As the angle theta 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 5.3 m along the loading ramp?

Homework Equations

kinematics(for x-motion)

mgsinθ = ks*mgcosθ

F=mgsinθ-k*mgcosθ

The Attempt at a Solution

A. 24.6*9.80sinθ=0.35*24.6*9.80cosθ

241.08sinθ=84.378cosθ

tan^-1 = 19.29°

B. F=(24.6)(9.80)sinθ-0.23(24.6)(9.80)cosθ

F=241.08sinθ-55.4484cosθ

F=27.305 N

27.305/24.6 = 1.109 m/s^2

C. 5.3= .5(1.109)t^2

3.09 = t

then, 0+ (1.109)(3.09) = 3.4 m/s

I have no idea is this is right or not. I'm not sure if I should have used 0.23 or 0.35 for part A but I'm assuming static(0.35) because that is what it needs to "start" moving. Thanks.

 

[danielakkerma]

It seems to me, at first hand, that you've done everything accurately, though abit cumbersome in my view.
You were absolutely right to use the static friction coefficient as long as the box was still quasi-stationary(on the "brink") so to speak, but, once it got rolling, the application of Kinetic factors is essential.
Following the algebra is trivial and a trifle, and from my perspective, the physics is a-okay.
Good job!
Daniel
P.S
I might first help to etch out the formulae via signs and symbols, and plug in only at the end of the process; Saves unit hassles and possible sign/truncation errors.