# P2 3 work energy and momentum relationship

### Energy–momentum relation - Wikipedia

you see that you can write the energy in terms of momentum via . E(k) is equal the Work the object will perform, let it be penetration, fracture. Learn what conservation of momentum means and how to use it. This means that the variable in an equation which represents a conserved quantity is In mechanics, there are three fundamental quantities which are conserved. . It would be very difficult to work out exactly how much work was done in breaking the puck. The energy–momentum relation is consistent with the familiar mass–energy relation in both its interpretations: E = mc2.

This outcome, while highly improbable, is not theoretically impossible. In this hypothetical outcome, momentum is conserved but mechanical energy is lost.

### What is conservation of momentum? (article) | Khan Academy

Such a collision is said to be inelastic. While totally fine from a theoretical standpoint I think, from personal observations of bowling balls, that such an outcome is highly unlikely. Of the two outcomes presented neither will occur.

The real world doesn't work out according to hypothetical ideals. The real questions should be, "Is the real outcome of this collision more like the first hypothetical outcome or the second? If one bowling ball comes into a row of stationary balls, the most likely outcome is that one bowling ball will leave the other end. In the case of two bowling balls the initial momentum and energy are… This is a trivial solution to the problem.

Obviously both momentum and energy are conserved.

This is another example of a perfectly elastic collision. This outcome is possible, but not probable.

This last possible outcome makes no sense. The momentum after collision is the same as before, but the mechanical energy has somehow increased. While energy can neither be created nor destroyed, it certainly can become "lost". This is why I have no problem with the second outcome of the first collision.

However, this outcome is surely impossible. The kinetic energy of a system cannot increase without work being done by some outside agent.

## What is conservation of momentum?

It might be tempting to think that they are fairly similar concepts, but in fact they are not. They are related concepts, but are distinct in the physical sense.

To get you thinking more deeply about this imagine getting struck by two fast moving objects having the same momentum. One object weighs 10 kg and the other object weighs 0.

Which object would inflict more damage? The intuitive response to this might be that they would both inflict an equal amount of damage given that they both have an equal amount of momentum.

As it turns out, the 0. The way to understand this is to look at the mathematical representation of momentum and kinetic energy for a particle; where a particle is used as a reasonable representation for the objects. Therefore, the object weighing 0. In fact, the kinetic energy of the 0. The kinetic energy of an object is directly proportional to how much damage it will inflict when it strikes something.

But interestingly enough, it's the object weighing less that will do more damage, for a given momentum.

## The Difference Between Momentum And Kinetic Energy

And it is the square of the velocity in the kinetic energy equation which makes this effect possible. You can generalize this result to say that the ratio of kinetic energy of two objects having the same momentum is the inverse ratio of their masses.

This principle readily applies to firearms.