Problem 8-43 2 dim. collision - Part 4

Two balls of equal mass m undergo a collision. One ball is initially stationary. After the collision, the velocities of the balls make angles of \(31.1^\circ\) and \(48.9^\circ\) relative to the original direction of motion of the moving ball.

(a) Draw a diagram showing the initial and final situations. If you are uncertain about the final directions of motion, remember that momentum is conserved.

(b) If the initial speed of the moving ball is \(2.25\; m/s\), what are the speeds of the balls after the collision?

(c) Is this collision elastic? Justify your answer.

[Ans. (a) \(1.18\; m/s\) at \(48.9^\circ\);   (b) \(1.72 \;m/s\) at \(31.1^\circ\)    (c) \(no\)]

Accumulated Solution

\(2.25 = (0.6574) v{_1}' + (0.8563) v{_2}' \; \text{ Eqn.# 1} \\ v{_2}' = 1.459\; v{_1}' \; \text{Eqn# 2}\)

\(2.25 = (0.6574) v{_1}' + (0.8563)(1.459) v{_1}' \\ v{_1}' = 1.18 \;m/s\)

From \(\text{Eqn # 2}\):   \(v{_2}' = 1.459\; v{_1}' = 1.459(1.18) = 1.72\;m/s\)

For a collision to be elastic:

(A)  Only momentum need be conserved.

(B)  Both momentum and kinetic energy must be conserved.

(C)  Momentum must be conserved but kinetic energy must be lost.