Problem 8-34 Elastic collision - Part 5 - A

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

Accumulated Solution

Diagram of ball.

m1v1=m1v1′+m2v2′3.5=v1′+1.227v2′Eqn. #1m1v12=m1v1′2+m2v2′23.52=v1′2+1.227v2′2Eqn. #2

Eqn.#1v1′=3.5−1.227v2′v1′2=3.52−8.589v2′+1.506v2′2

Substitute in Eqn.#2:

3.52=3.52−8.589v2′+1.506v2′2+1.227v2′2

 

Notice that the 3.52 subtracts away and then one power of v2′ can be cancelled from the remaining terms leaving:
 
0=1.506v2′−8.589+1.227v2′
 
which can be solved for v2′

 

Do this before continuing.

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