Prove inelastic collision loses the most KE?

In summary, using the equation m1v1 + m2v2 = (m1 + m2)Vf, the energy retained or lost in a one-dimensional collision can be expressed in terms of the final velocities. To show that inelastic collisions have the most KE loss, an equation encompassing all possibilities should be used and expressed in terms of a single variable related to the final velocities.
  • #1
Chickensalad
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Homework Statement



Prove that inelastic collisions have the most KE loss of any type of collision (i.e. partially inelastic and elastic are the others)[/B]

Homework Equations


m1v1+ m2v2= (m1+m2)Vf

The Attempt at a Solution


I have solved for Vf in that Vf=(m1v1+m2v2)/(m1+m2), but I am totally unsure as to where to go from here [/B]
 
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  • #2
If you want to show it retains the least energy out of all the possibilities, then you will need an equation that encompasses all possibilities. Start with a general equation for one dimensional collision and express the energy retained (or the energy lost, if you think that will be more helpful) in terms of the final velocities.
You will then want to get it in terms of a single variable somehow related to the final velocities. Consider what relationship you are trying to establish, and what single function of the two would encapsulate that relationship.
 

1. What is an inelastic collision?

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

2. How is kinetic energy lost in an inelastic collision?

Kinetic energy is lost in an inelastic collision due to the deformation of the objects involved. When two objects collide, they exert forces on each other, causing them to deform. This deformation results in some of the kinetic energy being converted into other forms of energy, such as heat or sound.

3. Why does an inelastic collision lose more kinetic energy than an elastic collision?

In an elastic collision, the objects involved do not deform and all of the initial kinetic energy is conserved. However, in an inelastic collision, some of the kinetic energy is lost due to the deformation of the objects. This results in an inelastic collision losing more kinetic energy than an elastic collision.

4. How can the amount of kinetic energy lost in an inelastic collision be calculated?

The amount of kinetic energy lost in an inelastic collision can be calculated by subtracting the final kinetic energy from the initial kinetic energy. This can be represented by the equation KE lost = KE initial - KE final.

5. Can an inelastic collision ever gain kinetic energy?

No, an inelastic collision can never gain kinetic energy. Kinetic energy can only be lost in an inelastic collision due to the conversion into other forms of energy. This is because energy is conserved in all collisions, and the total amount of energy in a closed system cannot be increased or decreased.

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