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 1 m, calculate:
1) the height to which bob A will rise after collision.
2) the speed with which bob B starts moving.
Neglect the size of the bobs and assume the collision to be elastic.

Answer 1

1) An elastic collision is one where there is no net loss in kinetic energy in the system due to the collision. Both momentum and kinetic energy are conserved quantities in elastic collisions.

When bob \(A\) strike to an identical ball at rest then bob \(A\) transfer its entire momentum to the momentum to the ball on the table and does not rise at all.

When bob A reaches at the position of bob B, the P.E of A converts into K.E where bob A transfers its momentum to bob B and bob A becomes itself in rest after elastic collision. So bob A will not rise.

Final Answer: Bob A does not rise at all.

2) As the collision is elastic and two balls have the same mass, therefore bob \(A\) transfers its entire momentum to the ball \(B\) and bob \(A\) does not rise at all. After a collision, bob \(A\) comes to rest and bob \(B\) moves with speed of bob \(A\).

\(\dfrac{1}{2}mv^{2}=mgh\)

or, \(v=\sqrt{2gh}\)

Here, \(g=9.8~m/s^{2}\)

\(h=1~m\)

Substituting the values, we get

\(v=4.42~m/s\)

Final Answer: 4.42 m/s