Why does energy transfer during collisions?

[omega-centauri]

TL;DR Summary

I have a student that insists knowing "why" energy transfers. Anyone have any ideas for me?

We were doing an experiment where you put a tennis ball on top of a basket ball, and release to the floor. The tennis ball goes flying high and the basketball hardly bounces at all. We also measured the initial bounce of each independently.

We're talking about impact and momentum, energy transfer, collisions, etc. and the student is wondering why both balls didn't just bounce the way the did when the balls were by themselves, why one was impacted by the other. We did a number of other collision experiments, and each time the student isn't convinced until they understand the "why" energy has to transfer. Any ideas?

 

[phinds]

To the extent that such "why" questions can be answered, they will differ depending on the type of energy. Transfer of heat energy is different than transfer of mechanical energy is different from transfer of electrical energy to heat or to mechanical motion, so personally I think it's a fools errand to try to answer "why" questions outside of just looking at what the math says.

In the specific case of the big/little balls, the smaller ball, when on top, gets the considerable added boost of having indented the top of the larger ball and thus is taking advantage of both the bounce of the larger ball off of the floor plus the bounce off of the top of the larger ball. It really seems pretty intuitive when you really think about what's happening.

 

[jbriggs444]

I do not have a good answer for you. Only a couple of suggestions.

It is clear that one cannot dig an answer out of simple mathematics. An outcome where basketball plus tennis ball arrive together and leave together is permitted. It conserves both energy and momentum. It is perhaps surprising for a student who has consistently encountered textbook problems to face a situation where conservation laws by themselves do not lead to a single prescribed outcome.

It is tempting to try to describe the interaction as a sequence of two collisions. The basketball with the ground first and the tennis ball with the basketball after. Certainly, that sequence would have the right qualitative result -- the tennis ball would fly away rapidly upon encountering a moving basketball.

And indeed, one can wave hands rapidly to demonstrate that in a relevant sense, the collision of the tennis ball with basket ball takes place after the collision of the basketball with the floor. Look at the position graph of basketball and tennis ball over time. The lines start out parallel downward and the basket ball begins accelerating upward. Slowly at first then more rapidly as the collision progresses and the force from the floor increases. To a rough approximation, the motion of the basketball is simple harmonic motion. The tennis ball however, does not decelerate as rapidly. Instead of encountering a fixed floor, it is encountering a slow-at-first and rapidly-thereafter decelerating basketball. Its onset of significant deceleration will be delayed.

Alternately (and still waving hands wildly), postulate a moment at which tennis ball and basketball are both at rest. This is the imagined halfway point in the collision when everything is at maximum deflection. The tennis ball is dented into the basket ball -- the distance between the two has decreased. During the rebound it is clear that the distance between them must increase. The tennis ball will rebound more rapidly than the basketball. And, by Newton's third law, the basketball must rebound less strongly as a result.

 

[Nugatory]

This might be easier to visualize in terms of forces rather than energy transfer. When the two balls are dropped together, there is a downwards force on the basketball that is not present when it is rebounding alone, and likewise there is an upwards force on the tennis ball that is not present when it is rebounding alone.

Consider the situation at the moment when the basketball is most compressed, squished on its underside by contact with the floor and squished from above by the downwards-moving tennis ball. You'll see where these additional forces come from.
[Edit: Looks like @jbriggs444 beat me to it it - last paragraph of his post above]

 

[jbriggs444]

Edit: Looks like @jbriggs444 beat me to it it - last paragraph of his post above

I would not want to rely over-much on that explanation. It has a theoretical flaw: There is no assurance that there is actually a moment when both basketball and tennis ball are simultaneously at rest.

It is theoretically possible that the tennis ball could come to rest before the basketball has done so. It could then rebound, achieving the same final velocity as the basketball, only earlier. This would require that the top of the basketball come to a stop before the basketball as a whole does. Although perplexing, such a circumstance does not seem outright impossible. [If we can imagine spherical cows then perhaps we can also contemplate complicated non-spherical basketballs]

 

[Nugatory]

I would not want to rely over-much on that explanation.

I wouldn't either but it is pretty much how I was able to come to see the behavior as somewhat reasonable and intuitive... and I think that's all we're looking for in this thread.

 

[russ_watters]

This might be easier to visualize in terms of forces rather than energy transfer.

Agreed; conservation of energy and momentum can provide a good before and after picture of what happens, but they don't describe what happens during the collision ("elastic" is an input assumption, not an output). The forces and dynamics of the collision are the next level down.

The balls can be modeled as spring-mass systems pushing against/bouncing off each other (though perhaps not with a constant k).

 

[Cutter Ketch]

I can sympathize. Explanations based on conserved quantities are often unsatisfying. They must be true, so the answers are correct, but the details of how are missing.

In the case of stacked balls the interaction is very cool, and not completely obvious. See this article https://www.google.com/amp/s/phys.org/news/2015-07-two-ball-problem.amp

A pretty successful model of what happens is that an elastic wave is launched at the point of contact of the basketball with the floor. It propagates symmetrically around the sphere coming back together and concentrating on the opposite side producing a large kick for the tennis ball.

I remember a nuclear physics class a million years ago where the same explanation was used to describe anomalously high energy pieces flying off nuclei during collisions. The idea was demonstrated by inserting a golf pencil into a large “super ball” (if anybody but me remembers that term) and dropping it with the inserted pencil pointing up. If you would like to try this be warned that the pencil becomes a dangerous projectile.

 

[vanhees71]

I guess you can discuss this with the laws of elastic scattering: First the balls fall together. Then the basket ball hits the floor (which you can consider as an infinitely large mass) and is reflected, i.e., it bounces off with the velocity it reached at impact, and with this velocity it collides with the tennis ball. Now you can calculate which velocity the basket and tennis ball then has and using this as initial condition for the motion in the constant gravitational field of the Earth how high both go. That's enough to explain the observations, though it doesn't answer the student's question. To answer this in detail is very complicated since you'd have to treat the balls as elastic bodies and describe the dynamics of the impact and reaction of the balls in detail.