7.10 - Interactive checkpoint: another one dimensional collision problem
Two balls move toward each other
and collide head-on in an elastic
collision. What is the mass and final
velocity of the green ball?
Answer:m 2 = kg
vf2 = m/s
7.11 - Physics at play: clicky-clack balls
The law of conservation of momentum and the nature of elastic collisions underlie the functioning of a desktop toy: a set of balls of equal mass
hanging from strings. This toy is shown in the photograph above.
You may have seen these toys in action but if you have not, imagine pulling back one ball and releasing it toward the pack of balls. (Click on
Concept 1 to launch a video.) The one ball strikes the pack, stops, and a ball on the far side flies up, comes back down, and strikes the pack.
The ball you initially released now flies back up again, returns to strike the pack, and so forth. The motion continues in this pattern for quite a
while.
Interestingly, if you pick up two balls and release them, then two balls on the far side of the pack will fly off, resulting in a pattern of two balls
moving. This pattern obeys the principle of the conservation of momentum as well as the definition of an elastic collision: kinetic energy
remains constant. Other scenarios that on the surface might seem plausible fail to meet both criteria. For instance, if one ball moved off the
pack at twice the speed of the two balls striking, momentum would be conserved, but the KE of the system would increase, since KE is a
function of the square of velocity. Doubling the velocity of one ball quadruples its KE. One ball leaving at twice the velocity would have twice
the combined KE of the two balls that struck the pack.
However, it turns out this is not the only solution which obeys the conservation of momentum and of kinetic energy. For instance, the striking
ball could rebound at less than its initial speed, and the remaining four balls could move in the other direction as a group. With certain speeds
for the rebounding ball and the pack of four balls, this would provide a solution that would obey both principles. Why the balls behave exactly
as they do has inspired plenty of discussion in physics journals.Clicky-clack balls
Momentum conserved
Elastic collision: kinetic energy
conserved(^154) Copyright 2007 Kinetic Books Co. Chapter 07