# Energy Lost During Purely Inelastic Collisions

• jon4444
In summary, the conversation discusses the application of conservation of momentum to a theoretical problem of a moving object having a purely inelastic collision with a stationary object in a single dimension. The velocity and masses of the objects determine the amount of energy lost, which is equal to the energy required for smashing and deformation during the collision. The interpretation of this situation is correct and the energy loss can be calculated using a specific equation.

#### jon4444

I'm curious about how the math comes out when you apply conservation of momentum to the theoretical problem of a moving object having a purely inelastic collision with another stationary object in a single dimension. Since the velocity of the combined object is entirely determined by the initial speed of the moving object and the masses of the objects, these parameters also determine the amount of energy lost (when you compare the kinetic energy of the initial object versus that of the combined object).
But shouldn't energy loss be related to how much smashing and deformation goes on during the collision? Is there another interpretation I'm missing?

jon4444 said:
I'm curious about how the math comes out when you apply conservation of momentum to the theoretical problem of a moving object having a purely inelastic collision with another stationary object in a single dimension. Since the velocity of the combined object is entirely determined by the initial speed of the moving object and the masses of the objects, these parameters also determine the amount of energy lost (when you compare the kinetic energy of the initial object versus that of the combined object).
But shouldn't energy loss be related to how much smashing and deformation goes on during the collision? Is there another interpretation I'm missing?
You have assumed that the two objects smash together and then continue to move together as one object. The energy lost to the smashing and deformation required to reach that state is exactly equal to the kinetic energy loss.

jon4444 said:
these parameters also determine the amount of energy lost (when you compare the kinetic energy of the initial object versus that of the combined object).
Yes.

jon4444 said:
shouldn't energy loss be related to how much smashing and deformation goes on during the collision?
Yes. The two amounts are the same.

But shouldn't energy loss be related to how much smashing and deformation goes on during the collision?
But shouldn't smashing and deformation be related to energy loss? Or even, determined by it.

so, say certain materials require a certain amount of energy to join together (the smashing and deformation)--this essential sets a critical condition for if you could have an inelastic condition (i.e., only under certain relative masses and initial speed).
Is that a correct interpretation of the situation?

jon4444 said:
so, say certain materials require a certain amount of energy to join together (the smashing and deformation)--this essential sets a critical condition for if you could have an inelastic condition (i.e., only under certain relative masses and initial speed).
Is that a correct interpretation of the situation?
Yes, for example, if a material has an elastic region and a plastic region in its stress strain curve then you would not get a plastic collision at low energies.

Since the OP asked about the maths, then (for the record) energy loss in a perfectly inelastic collision is given by:

## ΔE = ½μΔv^2 ##

where μ is the reduced mass of the colliding objects and Δv their relative velocity.

jon4444

## 1. What is the definition of a purely inelastic collision?

A purely inelastic collision is a type of collision in which kinetic energy is not conserved. This means that the total kinetic energy of the system before the collision is not equal to the total kinetic energy after the collision.

## 2. How is energy lost during a purely inelastic collision?

In a purely inelastic collision, energy is lost in the form of heat, sound, and deformation of the objects involved in the collision. This is due to the fact that the objects stick together after the collision, resulting in a decrease in kinetic energy.

## 3. Is the total momentum conserved in a purely inelastic collision?

Yes, the total momentum of the system is still conserved in a purely inelastic collision. This means that the total momentum before the collision is equal to the total momentum after the collision, even though the kinetic energy may not be conserved.

## 4. How does the coefficient of restitution affect the energy lost during a purely inelastic collision?

The coefficient of restitution, which is a measure of the elasticity of a collision, affects the amount of energy lost during a purely inelastic collision. A higher coefficient of restitution means that the objects involved in the collision will bounce off each other more, resulting in less energy lost.

## 5. Can the amount of energy lost during a purely inelastic collision be calculated?

Yes, the amount of energy lost during a purely inelastic collision can be calculated by subtracting the final kinetic energy from the initial kinetic energy. This can also be expressed as a percentage of the initial kinetic energy, known as the coefficient of restitution.