Question

A ball with a mass of `6 kg` is rolling at `16 m/s` and elastically collides with a resting ball with a mass of `1 kg`. What are the post-collision velocities of the balls?

Answer 1

These momentum problems are the first in physics where you're responsible for managing a (relatively) large number of variables.

Explanation:

Recall,

`nu_A - nu_B = nu_B' - nu_A'`

Which is derived starting from,

`m_A(nu_A-nu_A') = m_b(nu_B' - nu_B)` `(1)`

`m_A(nu_A^2 - nu_A^('2)) = m_B(nu_B^('2) - nu_B^2)` `(2)`

(a restatement of the law of conservation of momentum and energy, respectively).

Then, by factoring out (2), and dividing the expansion by (1).

From here, since ball B is at rest, it's easy. Consider,

`nu_A = nu_B' - nu_A'`

`=> nu_B' = nu_A +nu_A'`

Now, consider the conformity with the law of conservation of momentum, and substituting this variable in,

`nu_A = nu_A' + nu_A + nu_A'`

`nu_A' = (0"m")/"s"`,

and by extension,

`nu_A = nu_B' = (16"m")/"s"`

From this calculation, we can understand that:

In perfectly elastic collisions, all of the energy or momentum is transferred perfectly from one body to the other, if one is at rest.