A 0.060kg tennis ball, moving with a speed of 2.50m/s, collides head-on with a 0
ID: 1991234 • Letter: A
Question
A 0.060kg tennis ball, moving with a speed of 2.50m/s, collides head-on with a 0.090kg ball initially moving away from it at a speed of 1.15m/s. Assuming a perfecly eleastic collision, what are the speed and direction of each ball after the collision?Can someone show all steps and explain in detail how to do it using two equation (the energy before = energy after, and momentum before = momentum after), not the relative velocity way because i dont know how to do it that way, and want to learn using two equations.
(when i use two equations i get it into the form (2/9)V1'^2 - (4/3)V1' * V2' + (53/18)m^2/s^2 but cant use the quadratic formula because the middle term has the final velocity for both obects
Explanation / Answer
Treat bthis as a one-dimensional problem since it is a head-on collision. There is no motion in perpendicular directions.
Problems of this type are most easily done in a coordinate system that moves with the center of mass. Then transform back to laboratory cordinates. You can also treat it only in lab coordinates as two equations in two unknowns, but it takes longer.
The speed of the center of mass of the two balls is Vcm
= (0.06*2.5 + 0.09*1.15)/0.15
= 1.69 m/s
In a coordinate system traveling with the CM, the smaller ball approaches with velocity 2.50-1.69 = 0.81 m/s and the larger ball approaches with a velocity 1.69-1.15 = 0.54 m/s
Both balls reverse direction and keep the same speed in the CM system. The preserves total momentum and kinetic energy.
In laboratory coordinates, the final velocity of the smaller ball is 1.69 - 0.81 = 0.88 m/s (forwards) and the final velocity of the larger ball is
0.54 + 0.81 = 1.35 m/s (also forwards)
physics - joy, Thursday, August 19, 2010 at 11:27am
thanks :D but where did the 0.15 come from? :) what equation did you use?
physics - drwls, Thursday, August 19, 2010 at 11:56am
0.15 (kg) is the total mass of both balls. You need it in the denominator to get the speed at which the center of mass moves.
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