How Do Inelastic Collisions Distribute Energy Between Heat and Sound?

In summary, the conversation discusses how to predict the amount of energy lost as heat and sound in inelastic or partially elastic collisions. The analogy of an electrical circuit is used, with the concept of energy being dissipated as heat if there is no radiation of electromagnetic waves. The idea of maximizing radiation by making the circuit physically large and adding capacitance is also mentioned. The conversation concludes with the possibility of a damped sine wave oscillation and the difficulty in predicting the amount of sound energy radiated in colliding masses due to the complexity of the physical structure.
  • #1
DuckAmuck
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In collisions that are inelastic or partially elastic, how can we predict how much of the energy lost to the surroundings becomes heat, and how much becomes sound? What determines that fraction?
 
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  • #2
My own field is electrical engineering and I often translate problems such as these into an electrical analogy when seeking a simple solution.
A moving mass is equivalent to an inductor having zero loss resistance, with its ends connected together and with a circulating current. Rather like a superconductor magnet. To represent a collision, we can connect two of these together and then suddenly cut a common shorting wire so the current now passes through both. The momentum is conserved, L1I1 L2I2 = L3I3. However, energy is lost. The question arises, where does it go? If there is no radiation of EM waves, it dissipates as heat. To maximise radiation, we would make the circuit physically large, so that radiation resistance appears and dissipates some of the energy. We might also add capacitance to the circuit to obtain a damped sine wave oscillation. The radiation resistance of structures can be calculated - that is antenna engineering. The same happens for colliding masses. The size and shape of the physical structure will dictate how much energy is radiated by coupling to the air. There is the possibility of a damped sine wave oscillation caused by springiness in the system. But I don't think that in general it will be practicable to calculate the acoustic radiation resistance for something like colliding balls and to predict the sound energy radiated.
 

1. What is an inelastic collision?

An inelastic collision is a type of collision in which the total kinetic energy is not conserved. In other words, some of the kinetic energy is lost during the collision and is converted into other forms of energy, such as heat or sound.

2. How is an inelastic collision different from an elastic collision?

In an elastic collision, the total kinetic energy is conserved and there is no loss of energy. This means that the objects involved in the collision bounce off each other and retain their original shapes and velocities. In an inelastic collision, the objects may stick together or deform, and some of the kinetic energy is lost.

3. What factors affect the amount of energy lost in an inelastic collision?

The amount of energy lost in an inelastic collision depends on the materials of the objects involved, the speed and mass of the objects, and the angle and direction of the collision. Objects with higher mass or greater elasticity will generally experience less energy loss in a collision.

4. How is the conservation of momentum applied in inelastic collisions?

The law of conservation of momentum states that the total momentum of a closed system remains constant. In an inelastic collision, the total momentum before the collision is equal to the total momentum after the collision, even though some of the kinetic energy may be lost.

5. What are some real-life examples of inelastic collisions?

Inelastic collisions occur in many everyday situations, such as when a car collides with a tree or when a ball is caught by a catcher's mitt. Other examples include a bullet hitting a target, a baseball bat hitting a ball, or a person jumping onto a trampoline. In each of these cases, some of the kinetic energy is lost and converted into other forms of energy.

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