A box of textbooks of mass 25.3 kg rests on a loading ramp that makes an angle (ALFA) with the horizontal. The coefficient of kinetic friction is 0.260 and the coefficient of static friction is 0.330 .
A) As the angle (ALFA) 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 4.60m along the loading ramp?
A) Use the static friction coefficient for this one. Call it Us. When the maximum friction coefficient equals the downhill component of the weight, slipping begins. Call the angle A
M g sin A = M g cos A * Us
Us = tan A
A = arctan (0.33) = 18.3 degrees
B) Once slipping starts, the friction coefficient is lowered to Uk. The net force down the ramp is
F = M g sin A - Mg cos A * Uk
and the acceleration is F/M
Solve for the acceleration, a.
C) W = sqrt(2 a X), where X is the distance moved. Use the 'a' from part B.
Thank you very much !
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