Boxes A and B in (Figure 1) have masses of 13.3kg and 4.8kg , respectively. The

Question

Boxes A and B in (Figure 1) have masses of 13.3kg and 4.8kg , respectively. The two boxes are released from rest. What would be the speed of the boxes when box B has fallen a distance of 0.50 m ? The coefficient of kinetic friction between box A and the surface it slides on is 0.20. Use conservation of energy.

Boxes A and B in (Figure 1) have masses of 13.3kg and 4.8kg , respectively. The two boxes are released from rest. What would be the speed of the boxes when box B has fallen a distance of 0.50 m ? The coefficient of kinetic friction between box A and the surface it slides on is 0.20. Use conservation of energy.

Explanation / Answer

Note that

Wncon = KEf - KEi + PEf - PEi

Note that the two boxes have the same velocity. Thus,

KEf = 1/2(mA + mB)vf^2

KEi = 0

PEi = mB g d

PEf = 0

Thus,

Wncon = 1/2(mA + mB)vf^2 - mgd

Also, note that

Wncon = Work of friction = -uk mA g d

Thus,

-uk mA g d = 1/2(mA + mB)vf^2 - mB g d

Plugging the given in and solving for vf,

vf = 1.076 m/s [ANSWER]

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