Problem 8-34 Elastic collision - Part 2 - A

A superball of mass \(22\; g\) rolls with a speed of \(3.5\; m/s\) toward another (stationary) superball of mass \(27\; g\). If the balls have a head-on elastic collision, what are the velocities magnitudes and directions) of the balls after the collision?
[Ans. \(3.1\; m/s\) forward and \(0.4\; m/s\) backward]

Accumulated Solution

Diagram of ball.

\(m_1\; v_1 = m_1\; v{_1}'+ m_2\; v{_2}'\)

Let's put in the numbers we know:
\((22)(3.5) = (22) v{_1}' + (27) v{_2}' \\ 3.5 = v{_1}' + 1.227\; v{_2}' \;   \text{Eqn. #1}\)

Note: In problems like this we can use mixed units that would be improper elsewhere. We have used gm for mass and m/s for velocity. It was not necessary to convert \(gm\) to \(kg\) as that would only introduce the same multiplying factor on both sides of the equation.

This collision is 'elastic', that means:

(A)  Maximum \(E_K\) is lost in the collision.

(B)  Some \(E_K\) is lost in the collision.

(C) \(E_K\) is conserved.