A block of mass m1 is on top of a block of mass m2. Block 2 is connected by an ideal rope passing through a pulley to a block of unknown mass m3 as shown. The pulley is massless and frictionless. There is friction between block 1 and 2 and between the horizontal surface and block 2. Assume that the coefficient of kinetic friction between block 2 and the surface, μ, is equal to the coefficient of static friction between blocks 1 and 2.

Question

a) What is the value of m3 for which m1 and m2 are moving together at a constant speed? Express your answer in terms of some or all of the variables m1, m2, μ, and g. To write μ, use mu.

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b) The mass of block 3 has been changed such that block 1 and block 2 are moving together with a given acceleration of magnitude a. What is the magnitude and the direction of the force of friction exerted by block 2 on block 1? Express your answer in terms of some or all of the variables a, m1, m2, μ, and g. To indicate the direction, use a minus sign if the force is pointing to the left. To write μ, use mu.

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c) What is the minimum value of m3 for which block 1 will start to move relative to block 2? Express your answer in terms of some or all of the variables m1, m2, μ, and g. To write μ, use mu.

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Answer 1

For a)
mu*(m1+m2)

Answer 2

for b) m1 * a1