Two masses, m1 = 1 kg and m2 = 2kg, are connected together via a massless string

Question

Two masses, m1 = 1 kg and m2 = 2kg, are connected together via a massless string running over a massless, frictionless pulley, initial, the system is at rest with m2 on the ground and m1 hanging in the air. You are holding the pulley up via its handle. What upward force must you supply to the pulley handle to maintain the stated static configuration? With what maximum force can you pull upward on the pulley handle and still have m2 remain always on the ground? If you pull upward on the pulley handle with a force 100N, what will be the tension T in the string? If you pull upward on the pulley handle with a force 15N, what will be the upward accelerations of mi and m2?

Explanation / Answer

a)

Equating forces in vertical for the pulley,

F = (m1*g*2) = 1*9.8*2 = 19.6 N

b)

Now, equating forces,

Fmax = (m1+m2)*g = (1+2)*9.8= 29.4 N <------answer

c)

Writing equations of motion,

F = 2T

So, T = F/2 = 100/2 = 50 N <----------answer

d)

a = 0 m/s2

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