A mass mB is on a slope inclined by angle with respect to the horizontal. The co

Question

A mass mB is on a slope inclined by angle with respect to the horizontal. The coefficient of kinetic friction between mB and the slope is k. Its downhill side is connected by an ideal cord that passes over a massless, frictionless pulley and connects to a hanging mass mH. At time t = 0 mB is moving upslope with initial velocity v0. (A) Derive an expression for the acceleration of the blocks in terms of mB, mH, k, g, and . (B) If the sliding block travels upslope for a distance s and comes to v = 0, and remains at rest after coming to a halt, what can you say about the coefficent of static friction, s?
0 B H

Explanation / Answer

A) Applying Newtons law on the blocks,

mHg - T = mHa

T + mB g sin theta - uk mB g cos theta = mBa

a = ( mHg +mB g sin theta-uk mB g cos theta ) / (mH+mB)

B) newtons law on two blocks,

T = mHg

T = us mBg cos theta - mBg sin theta

Minimum us = (mHg +mBg sin theta) /(mBg cos theta)

  

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