Question

The bob A of a pendulum released from horizontal to the vertical hits another bob B of the same mass at rest on a table as shown in figure.
If the length of the pendulum is 1m, calculate
(a) the height to which bob `A` will rise after collision.
(b) the speed with which bob `B` starts moving.
Neglect the size of the bobs and assume the collision to be elastic.

Answer 1

When ball A reaches bottom point its velocity is horizontal, hence we can apply conservation of linear momentum in the horizontal direction.
(a) Two balls have same mass and the collisaoitn between them is elastic. Therefore, ball A transfers its entire linear momentum to ball B. Hence, ball A will come to at rest after collision and does not rise at all

(b) Speed with which bob B starts moving
=speed with which bob hits bob B
`=sqrt(2xx9.8xx1)`
`=sqrt(19.6)`
`=4.4m//s`
NOTE: When the bob A is at the bottommost point, its velocity is velocity is horizontal and tension is the external force on the bob but still momentum can be considered to be conserved in horizontal because the tension has no effect in horizontal direction at the horizontal point.