The Law of Conservation of Momentum

[temaire]

Homework Statement

This is more of a theoretical problem than a practical one. I am having a bit of difficulty understanding the concept of inelastic collisions and conservation of momentum. The law states that during inelastic collisions, total momentum is conserved, but total kinetic energy is not. But then I think to myself: if kinetic energy decreases in an inelastic collision, then the velocity of the colliding objects must decrease, which then means that the total momentum of the system decreases. However, this is contrary to the law. Can someone clear this up for me?

Homework Equations

$$p=mv$$

The Attempt at a Solution

Like I said, this is more of a theoretical problem, so there shouldn't be a need to show any work.

 

[Dick]

Compare your problem to an actual example. A 1kg mass moving at 1m/s to the right collides with a 1kg mass moving at 1m/s to the left and they stick together. The result is a stationary 2kg mass. The velocities decreased, did the momentum? Remember momentum is a vector quantity.

 

[baba89]

I understand your confusion about the concept of inelastic collisions and conservation of momentum. Let me try to clarify it for you.

First, let's review the law of conservation of momentum. It states that in a closed system, the total momentum before a collision is equal to the total momentum after the collision. This means that the total momentum of the system remains constant, regardless of the type of collision.

Now, let's look at inelastic collisions. In these types of collisions, kinetic energy is not conserved. This means that the objects involved in the collision lose some of their kinetic energy, usually in the form of heat, sound, or deformation. This decrease in kinetic energy does not violate the law of conservation of momentum because the objects also experience an equal and opposite change in momentum.

To understand why this is the case, let's consider a simple example. Imagine two identical objects colliding in an inelastic manner. Before the collision, both objects are moving at the same velocity, and therefore have the same momentum. During the collision, some of their kinetic energy is lost due to the factors mentioned earlier. However, the objects still have the same mass and velocity, so their momenta remain the same. The decrease in kinetic energy is offset by an increase in momentum, so the total momentum of the system remains constant.

In conclusion, the law of conservation of momentum still holds true in inelastic collisions because the decrease in kinetic energy is compensated by an increase in momentum. I hope this explanation helps to clear up your confusion. Remember, as scientists, it is important to question and seek understanding, so keep up the good work!