(Solved): A small ball, P, of mass 0.8kg, is held at rest on a smooth horizontal table and is attached to one ...

A small ball,

, of mass

, 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,

, of mass

, that hangs freely below the pulley. Ball

is released from rest, with the rope taut, with

at a distance of

from the pulley and with

at a height of

above the horizontal floor, as shown in Figure 1. Ball

descends, hits the floor and does not rebound. The balls are modelled as particles, the rope as a light and inextensible string and the pulley as small and smooth. Using this model, (a) show that the acceleration of

, as it falls, is

(5) (b) find the time taken by

to hit the pulley from the instant when

is released. (6) (c) State one limitation of the model that will affect the accuracy of your answer to part (a). (1)