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# (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,

`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 horizontal floor, as shown in Figure 1. Ball

`Q`

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

`Q`

, as it falls, is

`4.2ms^(-2)`

(5) (b) find the time taken by

`P`

to hit the pulley from the instant when

`P`

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

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