Question regarding inelastic collisions

In summary, the kinetic energy after an inelastic collision is not always equal to 1/2 the total momentum squared divided by the total mass. The final kinetic energy can vary depending on the degree of inelasticity and can range from the initial kinetic energy to zero. Two equal masses with equal and opposite velocities colliding and sticking together will result in zero kinetic energy.
  • #1
Vector1962
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8
Concerning inelastic collisions: Is it true the kinetic energy after the collision is equal to 1/2 the total momentum?
 
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  • #2
CORRECTION:
Concerning inelastic collisions: Is it true the kinetic energy after the collision is equal to 1/2 the total momentum squared divide by total mass?
 
  • #3
The kinetic energy has a range of values after the collision depending on just how inelastic the collision is.

The largest value the final kinetic energy could have would be equal to the initial kinetic energy, but this only happens in the limit that the collision becomes elastic.

The smallest value the final kinetic energy could have would be the kinetic energy if after the collision the particles stick together. This value depends on the ratio of the two masses, and the ratio of the two initial velocities. It is not simply half the initial kinetic energy (though I'd have to work it out to see if that's indeed the smallest possible value over all initial masses and velocities).
 
  • #4
jfizzix said:
The smallest value the final kinetic energy could have would be the kinetic energy if after the collision the particles stick together. This value depends on the ratio of the two masses, and the ratio of the two initial velocities. It is not simply half the initial kinetic energy (though I'd have to work it out to see if that's indeed the smallest possible value over all initial masses and velocities).

Two equal masses with equal and opposite velocities colliding and sticking together will yield zero kinetic energy.
(Think head-on SPLAT!).
 
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  • #6
Vector1962 said:
CORRECTION:
Concerning inelastic collisions: Is it true the kinetic energy after the collision is equal to 1/2 the total momentum squared divide by total mass?
In a perfectly inelastic collision, all the participants will stick together after the collision. The resulting momentum will be ##m_{tot}v_{cm}##. Yes, the resulting kinetic energy is ##\frac{1}{2}m_{tot}{v_{cm}}^2 = \frac{1}{2}\frac{(m_{tot}v_{cm})^2}{m_{tot}}##
 
  • #7
excellent. thanks for all the reply's.
 

1. What is an inelastic collision?

An inelastic collision is a type of collision in which the total kinetic energy of the system is not conserved. This means that some of the kinetic energy is lost during the collision, usually due to the deformation of objects involved or the production of heat and sound.

2. How is the kinetic energy lost during an inelastic collision?

The kinetic energy is lost due to the deformation of objects involved in the collision. This deformation results in the conversion of kinetic energy into other forms such as heat and sound.

3. What is the difference between an inelastic collision and an elastic collision?

An elastic collision is a type of collision in which the total kinetic energy of the system is conserved. This means that no kinetic energy is lost during the collision, and the objects involved bounce off each other without any deformation. In an inelastic collision, some of the kinetic energy is lost due to deformation or the production of heat and sound.

4. Can an inelastic collision have a coefficient of restitution?

No, an inelastic collision cannot have a coefficient of restitution. The coefficient of restitution is a measure of the elasticity of a collision, and since an inelastic collision involves the loss of kinetic energy, it cannot have an elastic property.

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

Some examples of inelastic collisions include a car crash, a ball hitting the ground and not bouncing back to its original height, and a person landing on a trampoline and not bouncing back to their original height. In all of these examples, some of the kinetic energy is lost due to deformation or the production of heat and sound.

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