(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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?

2. Relevant equations

kinematics(for x-motion)

mgsinθ = ks*mgcosθ

F=mgsinθ-k*mgcosθ

3. 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.

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# Using coefficients of static and kinetic friction

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