What’s the difference between kinetic energy and momentum?

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I understand that they have two similar but different formula’s that both scale differently with velocity. I also understand that momentum has a direction ie. Vectored, and kinetic energy is directionless. What I can’t wrap my head around is how they are seperate properties with differing values and how it interacts with forces on an object.

For example, when an object collides with a wall, momentum drops to zero, the change in momentum requires the wall to exert force on the object and it involves some work done, and therefore energy. At the same time, the kinetic energy of the object is also released as heat(?)

In: 1

Momentum = mass * velocity
Kinetic energy = 1/2 * mass * velocity^2

In a collision, momentum is conserved, but if the collision is inelastic, some of the energy is converted to heat.

For example you have two pairs of 1kg and 10kg balls, one pair perfectly bouncy, the other is clay that sticks together when it touches.

If the small ball is moving left at 10m/s and the large ball is moving right at 1m/s and they hit squarely, the bouncy balls will just reverse their direction, the clay balls will become a stationary lump, with all the energy converted to heat.

Now, all the balls might start out with the same amount of momentum, but the small balls have more kinetic energy than the big balls. When you’re accelerating an object, the momentum is force * time, but kinetic energy is force * distance. The smaller balls move a longer distance in the same amount of time, so they require more energy to get the same momentum.

Momentum increases linearly with velocity. A 10kg object moving at 20 m/s has twice as much momentum as the same object moving at 10 m/s.

Kinetic energy is quadratic, because the formula for KE takes half of an object’s mass and multiplies it by the square of the velocity, thus doubling the velocity quadruples the kinetic energy.

Also, momentum is always conserved, meaning that the amount of momentum in a given system never changes, it’s merely transferred to other objects in that system. Kinetic energy, by comparison, can be converted into other forms of energy, depending on if the collision is elastic or inelastic.

The simplest way to differentiate between the two is this: Momentum is a description of the amount of mass in motion, while kinetic energy is a description of the amount of energy that object is carrying due to its motion.

If you shoot a billiard ball directly at another one, the first ball stops and the second one picks up all of the first’s momentum. But according to conservation of momentum, that’s only one of the possible endings. What could also happen is that the first one *bounces back*, and the second ball picks up more speed than the first originally had. The reason this doesn’t happen is that this second scenario has more energy and so is prohibited by conservation of energy.

Basically if you only had one of the laws then any collision would have an infinite number of “legal” results, but with both there is exactly one result.

To understand momentum and energy, you need to see these equations:

momentum = force * time
energy = force * distance

They both measure the “pushiness” of an object, but they do it in different measures: one do it in time, another – in space.

* Momentum is time-pushiness: it measures how many “seconds of push” an object have. It is related to stopping time.
* Energy is distance-pushiness: it measures how many “meters of push” an object can do. It is related to stopping distance.

It is also easy to explain, why one depends on **v**, and another on v^(2). When the object goes twice the speed, it takes twice the time to stop it – so its time-pushiness (momentum) scales by 2. But the distance-pushiness (energy) goes by a factor of 4: not only the object moves *twice as long*, it also goes *twice as fast!* So the speed has double effect on the distance.

> For example, when an object collides with a wall, momentum drops to zero, the change in momentum requires the wall to exert force on the object and it involves some work done, and therefore energy. At the same time, the kinetic energy of the object is also released as heat(?)

Collision with a wall is a bad example; the wall is usually so much heavier than the object that it doesn’t seem to move at all. So it’s better to look at two objects of roughly similar mass colliding.

When one object meets the other, it will transfer momentum to it until both have the same velocity. You now have both objects moving, but at a lower speed than the original speed of the first object. As kinetic energy scales with the square of speed, the sum of kinetic energy will be lower than the original kinetic energy; the difference has been transformed into deformation.

If one of the objects is made of putty or soft clay, that’s the end of it. The deformation energy is transformed into heat; the two objects now stick together and move as one. That’s called an inelastic collision. In an elastic collision, the deformation energy is transformed back into kinetic energy, dished out to the two objects in reverse proportionality to their mass, such that the total momentum stays the same; the two objects now fly away from each other. Most real-world collisions are somewhere in between, with part of the deformation energy being transformed into heat or sound.