I was intrigued by a question that was raised in the modeling workshop at SPU this past summer. Does FΔx for a baseball caught by a mitt give the change in kinetic energy of the baseball or the change in total energy of the baseball (including a rise in thermal energy)?
My model says that it depends on what Δx is. If Δx is the displacement of the center of mass of the ball then FΔxcm would equal the change in kinetic energy. If Δx is the displacement of the point of application of the force on the ball then FΔxforce would give the change in total energy of the baseball. Since the ball compresses a bit Δxcm will be slightly greater in magnitude than Δxforce. Both the change in kinetic energy of the ball and the change in the total energy of the ball would be negative but the magnitude of the change in total energy would be smaller. The difference would account for the rise in thermal energy. So maybe FΔxcm is -100J and FΔxforce is -95J this would mean the ball lost 100J of kinetic energy and gained 5J of thermal energy is produced in the ball. The remaining 95J of thermal shows up elsewhere.
Now I want to try out this thinking on two more scenarios; (A) a rigid metal ball that is stopped by a glob of clay and (B) a glob of clay that is stopped by a rigid metal wall. Let's assume that in both scenarios the change in kinetic energy is 100J, so FΔxcm is -100J in both scenarios.
In scenario (A) the ball is rigid so FΔxforce would be the same as FΔxcm , -100J. So the rigid ball doesn't get any of the thermal energy directly. The glob of clay gets the entire 100J.
In scenario (B) the wall is rigid so FΔxforce would be zero. In this case the glob of clay get's the entire 100J of thermal energy. The rigid wall doesn't get any.
I guess the moral of my story is that whatever squashes gets the thermal energy. In the case of the baseball, the baseball doesn't squash much so it doesn't get a very big share. The mitt, arm, shoulder squash a lot and get most of the thermal energy.
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