A 25.0-kg box of textbooks rest on a loading ramp that makes an angle a with the horizontal

kinetic-friction
minimum-angle

#1

A 25.0-kg box of textbooks rest on a loading ramp that makes an angle a with the horizontal. The coefficient of kinetic friction is 0.25, and the coefficient of static friction is 0.35.
a) As the angle a 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 it will the box be moving after it has slid 5.0m along the inclined plane?

Answer:

Think of it logically, the force stopping the box on the incline from slipping is the static friction force between the slope and the box. So the slipping force has to be more than the static friction

sin(A)mg\textgreatercos(A)mgs

where s is coefficient of static friction

cancel m and g to obtain this

sin(A)\textgreatercos(A)s

make ratio of sinA and cosA into tan A

tan−1(s)\textgreaterA

it has to be more than 19.29, so it is 19.3 degrees

Part b) is where you write the forces in newton’s 2nd law and find value of a using m,g,s and angle A in part a…you should get 0.002m/s^2

Part c) is where you do the same in part b except use kinetic friction coefficient instead of static friction coefficient…you get 0.9m/^s2