A box of textbooks of mass 24.4 kg rests on a loading ramp that makes an angle \

Question

A box of textbooks of mass 24.4 kg rests on a loading ramp that makes an angle lpha with the horizontal. The coefficient of kinetic friction is 0.230 and the coefficient of static friction is 0.350.

A)As the angle lpha 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.
Take the free fall acceleration to be g = 9.80 m/s^2.
C) At this angle, how fast will the box be moving after it has slid a distance 5.40 m along the loading ramp?
Take the free fall acceleration to be g = 9.80 m/s^2.

Explanation / Answer

us*mgcos(alpha)=mg sin(alpha)=>us=tan(alpha)[us is coeff of static friction] =>alpha= arctan(0.350)=19.29 degree B)gsin(alpha)-ukgcos(aplha)=1.1099m/sec^2[uk is coeff of kinetic friction] C)v^2=u^2+2*a*s [u=0] =>v=3.44m/sec

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