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On a frictionless horizontal table a plank P (length 1 m) and a small block Q (negligible size) are set moving in the same direction with speeds 3 m/s and 6 m/s respectively. The block, initially at one end of the plank, slides relative to the plank and just stops slipping exactly when it reaches the far end of the plank. If the mass of the plank is twice that of the block, determine the coefficient of friction between them.

1. 1/3
2. 1/2
3. 2/3
4. 1

Correct answer: 1/3

Solution

Momentum conservation gives a common velocity of 4 m/s. Energy lost to friction equals friction force times relative sliding distance (1 m), which fixes mu = 1/3.

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