Conservation of momentum and loss of energy in inelastic collisions

In summary, during inelastic collisions, the total momentum in the system remains the same while the kinetic energy is lost as heat or sound. This is because momentum is a vector quantity and energy is a scalar quantity. The loss of energy does not affect the momentum of the system, as momentum is not dependent on energy. Therefore, the momentum remains constant even as the amount of energy in the system decreases.
  • #1
mahela007
106
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I just learned that, in elastic collisions, the total momentum in the system is preserved while a certain amount of kinetic energy is lost.
I know that kinetic is energy may be lost in the form of heat or sound. Isn't the same energy responsible for keeping the two objects in motion and preserving their momentum? How then does the momentum remain the same when the amount of energy in the system decreases?
 
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  • #2
mahela007 said:
I just learned that, in elastic collisions, the total momentum in the system is preserved while a certain amount of kinetic energy is lost.
I know that kinetic is energy may be lost in the form of heat or sound. Isn't the same energy responsible for keeping the two objects in motion and preserving their momentum? How then does the momentum remain the same when the amount of energy in the system decreases?

You need to read again where you learn all this.

In elastic collision, BOTH momentum and KE are conserved.

Zz.
 
  • #3
Opps. My mistake. I made a small typing error. What I meant was "inelastic".
 
  • #4
Momentum is a vector. Energy is a scalar. Say you have 2 vectors of equal magnitude pointing in opposite directions = 0. Now subtract lots of little vectors representing the energy loss as heat in all directions (ie. non-directionally). Now the vector sum is still 0.
 
  • #5
atyy said:
Momentum is a vector. Energy is a scalar. Say you have 2 vectors of equal magnitude pointing in opposite directions = 0. Now subtract lots of little vectors representing the energy loss as heat in all directions (ie. non-directionally). Now the vector sum is still 0.

umm...
So what you are saying is that the loss of heat energy in all directions adds up to zero. Therefore it can make no change to momentum?
 
  • #6
mahela007 said:
Isn't the same energy responsible for keeping the two objects in motion and preserving their momentum?

mahela007 said:
umm...
So what you are saying is that the loss of heat energy in all directions adds up to zero. Therefore it can make no change to momentum?

You seem to believe that energy causes momentum. It doesn't.

Consider a motionless boulder poised at the top of a cliff. It has a lot of energy but no momentum.

And conversely, an object doesn't consume energy to keep it moving. Such would be an Aristotelian, rather than a Newtonian, model of the world.
 
  • #7
"You seem to believe that energy causes momentum."
That's exactly what I was thinking.
Since it is true that an object with momentum has kinetic energy, I assumed that a loss of energy would be accompanied by a loss of momentum.
But I still don't understand why a loss of energy has no effect on momentum.
 
  • #8
mahela007 said:
Since it is true that an object with momentum has kinetic energy,
An object with momentum has macroscopic kinetic energy (associated with its center of mass movement). But it also has plenty of random kinetic energy (internal, thermal energy).
I assumed that a loss of energy would be accompanied by a loss of momentum.
Sure, if a single object loses macroscopic kinetic energy (due to some force acting on it) it also loses momentum. But in an inelastic collision between two objects, the net momentum of the system remains unchanged. But the momentum of each object changes, and thus the macroscopic kinetic energy of each object changes. When all is said and done, in an inelastic collision the momentum of the system remains the same while the total macroscopic kinetic energy is lower. (That "lost" energy becomes random thermal energy.)
 
  • #9
mahela007 said:
Since it is true that an object with momentum has kinetic energy, I assumed that a loss of energy would be accompanied by a loss of momentum.
But I still don't understand why a loss of energy has no effect on momentum.

Yes, a single object that has momentum also has kinetic energy. If you slow it down, then both the momentum and kinetic energy decrease. But a system of objects can have kinetic energy, but no momentum. Recall atyy's observation that one is a scalar and the other is a vector.

Imagine two balls of putty speeding towards each other. The total momentum is zero, even though the total kinetic energy is not. When they collide, the kinetic energy converts into heat. But remember the momentum is already zero. How could it lessen?
 
  • #10
First of all, thanks for your replies.
I understood the puttyball example but I didn't understand the how force being a scalar quantity and momentum being a vector quantity could explain the conservation of momentum
 
  • #11
mahela007 said:
I understood the puttyball example but I didn't understand the how force being a scalar quantity and momentum being a vector quantity could explain the conservation of momentum
Both force and momentum are vector quantities. Kinetic energy is a scalar.
 
  • #12
Oh. After a little thinking I understand what's happening,. Thanks for all your replies.
 

FAQ: Conservation of momentum and loss of energy in inelastic collisions

1. What is conservation of momentum and how does it apply to inelastic collisions?

Conservation of momentum is a fundamental law in physics that states that the total momentum of a closed system remains constant. In an inelastic collision, the objects stick together and move with a common velocity, but the total momentum before and after the collision remains the same. This means that the sum of the individual momenta of the objects before the collision is equal to the sum of the individual momenta after the collision.

2. What is the difference between elastic and inelastic collisions?

In an elastic collision, the objects bounce off each other and the total kinetic energy of the system is conserved. In an inelastic collision, the objects stick together and some of the kinetic energy is lost to other forms of energy, such as heat or sound.

3. How is the loss of energy calculated in an inelastic collision?

The loss of energy in an inelastic collision can be calculated by taking the difference between the initial kinetic energy of the system and the final kinetic energy of the objects after the collision. This lost energy is converted into other forms of energy, such as heat or sound.

4. Can the law of conservation of momentum be violated in inelastic collisions?

No, the law of conservation of momentum is a fundamental law of physics and cannot be violated. In an inelastic collision, the total momentum of the system remains constant, even though some of the kinetic energy is lost.

5. How does the coefficient of restitution relate to the conservation of momentum and loss of energy in inelastic collisions?

The coefficient of restitution is a measure of the elasticity of a collision. In an inelastic collision, the coefficient of restitution is less than 1, indicating that some of the energy is lost. The conservation of momentum still applies, but the loss of energy can be calculated by using the coefficient of restitution in the equation for kinetic energy.

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