Particles Connected By Pulleys

If two particles of differing masses are connected be a string that passes over a smooth pulley – so there is no friction - as shown below, then the particles will start to move – the heavier particle with massmoving down.

We can find the acceleration and tension for each particle in the above system using the method shown below if we have the following two requirements met:

The string is light and inextensible. This means that the weight of the string does not appear in any equation, and that the accelerations of both particles are the same.

We resolve vertically for both particles, in the direction of acceleration.

For (1)

For (2)

(1)+(2) gives

Both sides factorise to give

From