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**Problem**

A mass of 2 kg is held at rest on a rough horizontal table with coefficient of friction μ = 0.5. A string is attached to the mass and is hung over a smooth pulley. A 1 kg mass is suspended from the other end of the string. The top of the pulley is at a height of 1 m above the table surface, and the 2 kg mass is initially at a horizontal distance of 2 m away from the pulley as illustrated in the diagram below.

i) Whilst the 2 kg mass is held at rest, what is the tension in the string?

The 2 kg mass is released so that it is free to move across the surface.

ii) What is the tension in the string immediately after the 2 kg mass is released?

iii) How far will the 2 kg mass have moved before it reaches its maximum speed?

**Solution**

i) This is obvious. If g = 10, then the tension T = mg = 10 N.

This rest is difficult. One needs to find a relation between the acceleration of the two masses, but it is not as straightforward as it seems, because the relative accelerations also depend on the instantaneous velocities and the angle between the relative velocities, right?

Any help appreciated.

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