How to answer questions involving pulleys?

Question

A small ball,P, of mass 0.8kg is held at rest on a smooth horizontal table and is attached to one end of a thin rope. The rope passes over a pulley that is fixed at the edge of the table. The other end of the rope is attached to another small ball Q of mass 0.6kg that hangs freely below the pulley. Ball P is released from rest with the rope taut with P at a distance of 1.5m from the pulley and with Q at a height of 0.4m above the ground. Ball Q hits thefloor and doesn't rebound. The balls are modelled as particles the rope as a light inextensible string and the pulley as smooth and small. Using this model,

a) show that the acceleration of Q as it falls is 4.2ms-2

b)Find the time taken by P to hit the pulley from the instant when P is released

c)State one limitation of the model that will affect the accuracy of your answer to part (a)

Answer 1

This is where the adage: "A picture is worth a thousand words" is more than 100% correct! I don't see any way to understand this question entirely without a drawing... THat being said, the key to understanding and working all pulley problems is making free-body diagrams where the strings are cut and every single body (each ball, and the pulley itself) is represented as a body either in equilibrium (not accelerating) or accelerating due to forces acting on it. Then you will have a series of simple equations of motion or of static equilibrium. You will likely have many variables, and if you have as many variables as equations, they can be solved. Also you should realize that a tension in one end of a rope is equal and opposite to a tension in the other end. All static equations are a form of "THe sum of the forces in ___ direction (x or y) = 0 " and all equations of motion are some form of "The sum of the forces in ____ direction (x or y, unless there are bodies caused to roll which have mass, which brings in torque and rotational acceleration) = mass x acceleration of that body"