Energy Loss in Inelastic Collision

Question

If we take a tennis ball and drop it from a certain height above the ground on earth, it collides inelastically, with the maximum height it can reach reducing after each collision due to loss of energy to the atmosphere, sound energy and to change the vibrational energy of both the ball and the floor.

Now consider the same experiment in vacuum. The lost energy shouldn't escape to the atmosphere to heat it up, or to contribute to producing sound; it can only change the internal energies of the floor and the ball itself. Is the amount of energy loss the same? If yes, then can we say that dropping a ball in vacuum heats it up more than it could've heated up in an atmosphere full of air? This would be the case if the maximum possible height reached by the ball after each collision would remain the same.

Answer 1

In an inelastic collision, does a ball get hotter if it is dropped in a vacuum?

Short answer: Yes, the ball gets hotter if it cannot lose energy to sound. All the kinetic energy lost to the ball's internal pressure wave during impact is converted into thermal energy. In the case of impact in an air environment, a portion of that pressure wave energy is lost to sound.

Elaboration

• Impact: Upon impact, the kinetic energy of the ball is converted into the potential energy of lattice compression.
• Elastic Collision: In a fully elastic collision, all of that lattice compression recoils, and repels the ball back upwards at the same speed.
• Inelastic Collision: In an inelastic collision, a portion of the compressive energy is transmitted through the ball's material. In effect, the energy associated with the pressure wave has disconnected from the rebound kinetic energy of the ball, resulting in its reduced height on the bounce.
• Reflection: The pressure wave travels through the material and strikes a surface on the other side of the ball. The pressure wave causes the surface of the material to first bulge outward and then retract. The recoil regenerates a pressure wave going the opposite direction, which will continue to a surface on the other side of the ball, where it will bounce, etc. This continues until the pressure wave disperses its cohort of oscillating kinetic-potential energy into thermal energetic disorder.
• Sound Production: If air surrounds the ball, an increment of the pressure wave's energy is transmitted to the air when the pressure wave causes the surface to bulge and retract. This causes compression and decompression of the air surrounding the ball, producing the sound we hear.
• Vacuum Reflection: When a vacuum surrounds the ball, the surface deforms outward and recoils back inward due to the impact of the pressure wave. But, all the energy striking the surface reflects back into the bulk material of the ball. No kinetic and potential energy is lost to the surrounding air.
• Multiple Reflections: The pressure wave bounces from surface to surface. The waves produce complex surface distortions due to their variable path length between their points of reflection and their opposing spherical inner surface. The variable path length produces a dispersion of the pressure waves' energy, resulting in a rapid decay into random motion.
• Thermal Energy Decay: The pressure waves eventually fully decay into randomly directed momentum, which is recognized as thermal energy.
  1) The major decay/dispersion effect is due to the pressure waves' loss of coherence with each reflection. The variable path lengths between generation and reflection of each segment of the pressure wave result in a non-coherent phase relationship between the various segments of the pressure wave. That is, the pressure waves hit and reflect at different times, interfere, and quickly disperse the coherent pressure wave energy into random directions. The conversion of pressure wave energy into thermal energy occurs much faster than would be expected by the rate of loss of coherent to random energy in an elastic material. Note that in a resonant elastic structure, like a bell or gong, where reflections reinforce and stay coherent, the sound is heard much longer than in a non-resonant structure like a spherical ball.
  2) A minor loss of pressure wave energy occurs in a metallic or stiff/elastic materials due to inelastic losses during inter-atomic collisions. This occurs due to the off-center force transmission during atom collision.
• Conclusion: Vacuum vs. Air Thermal Energy Conversion: An increment of energy is lost to the creation of a pressure wave internal to a stiff-elastic ball after the impact of the ball-surface in an inelastic collision. The pressure wave will convert completely into thermal energy if it cannot lose energy to the production of air vibration/sound.

Answer 2

The lost energy shouldn't escape to the atmosphere to heat it up, or to contribute to producing sound; it can only change the internal energies of the floor and the ball itself.

Such an inelastic collision in a vacuum will result in an increase in temperature of the ball and floor which means an increase in the internal energy of the ball and floor. As already noted, no energy is converted to sound in a vacuum. But even in a vacuum you can have internal energy loss by means of radiant (electromagnetic) waves emitted by the ball and floor in a vacuum .

Hope this helps.

Answer 3

In a vacuum energy loss is reduced to a great extent right??there is no way energy can escape by means of sound or heat.... So wont the collision tend to be alot more elastic..cant be sure itll be perfectly elastic cause very little of the energy can be transmitted to the ground sometimes...but overall it'll be elastic...

There is very less chance that the ball will get heated up in vacuum compared to the atmosphere....cause for the ball to get heated during the motion...some sort of resistive force should act on it (mostly air resistence.thats how energey escapes as heat when done in normal conditions)...but this is not possible in vacuum...