# How much energy in return force?

Assuming I had a magic device able to discharge its stored energy in a directional force, and absorb the energy from the resulting return force (for every action, there is an equal and opposite reaction) which it could then discharge... What laws of physics are being violated? (basically, energy that would have moved the device, ignoring obstacles like ground, instead just gets stored as magic. This device can freely exchange between kinetic and magic energy, so 1KE absorbed is 1KE of discharge. And it is selective in what it converts to magic, so it is affected by gravity, it does not absorb that).

Looking at it from conservation of energy, this would be 100% efficient energy transfer (from kinetic, to magic to kinetic) so the device should have no power left after the discharge, but since there is energy in the return force... is there no return force or is the return force a fraction of the discharge force? If the later, what is that fraction?

The device just converts kinetic energy, to magic, to kinetic energy with 100% effecency. I just want a reality check on how this device works given that the energy absorb/discharge is the only exception to physics happening.

Just as an example, you charge the device by striking it with a hammer, than place a ball bearing next to the device (physically touching it), the device than discharges its energy into the ball as kinetic energy, and stores the recoil energy from the ball, which can than be used to launch another ball bearing. What would be the speed of each ball bearing? (assuming whatever makes the math easier/cleaner and doesn't violate physics)

• You seem to be freely mixing up 'force' and 'energy'. These are relatively different concepts, and I don't know how to make sense of your magic box because of it. If you just want it to absorb / release forces, then Captain America's shield (vibranium) might be a thing to check out. If you want it to store / release energy, then (I suspect) you could get a lot more flexibility in what you can do. Oct 19 '16 at 19:22
• @Lacklub F=MA, AKA, force is directly related to change in kinetic energy, with final change in kinetic energy being any force that isn't cancelled by another. But the device only converts energy. If force is not an indicator of energy (kinetic or potential) than please correct my understanding. Oct 19 '16 at 19:45
• Or is this more a Physics exchange question? Oct 19 '16 at 19:47
• I'm actually not sure, I check both here and there because I like answering these type of questions. But I suspect they'll have a problem with you breaking the laws of physics. As to force and energy: perhaps the clearest relationship to express the difference is KE = F*d, ie. the force multiplied by the distance the force acts over is the change in kinetic energy. If I press my hand against a wall and push, I am applying a force (which it absorbs) but it is gaining zero kinetic energy because it is moving zero distance. Oct 19 '16 at 19:52

There are two important but distinct concepts here: conservation of momentum and conservation of energy. When you talk about absorbing the return force, you're referring to momentum (force is a change in momentum over time).

The momentum of a moving object is $\vec{p} = m \vec{v}$, that is, momentum is mass multiplied by velocity. The arrow over velocity means the direction is important here; "momentum going east" is different from "momentum going west".

Conservation of momentum means that the total momentum of a closed system should remain constant. If one object loses momentum, another should gain it. This leads to Newton's third law: if I apply a change in momentum to something, it applies an equal and opposite change in momentum to me. Add $+p$ to one thing, add $-p$ to another, and the sum stays the same.

Kinetic energy, on the other hand, doesn't have a direction. $E_k = mv^2$. No matter which direction I'm moving, so long as I'm moving, I have positive kinetic energy.

Energy is also conserved, but it's much easier to lose it. In fact, the Second Law of Thermodynamics says you have to lose it. Energy can't be destroyed, but it can be turned into a form that's useless to you, and there's no practical way to prevent this from happening. (Though your magic very well could.)

For an example: suppose I have two metal balls, each weighing 1 kg. I put them on a straight track, then roll one of them east at 1 m/s, and the other one west at 1 m/s.

The total momentum is $p = 1 kgm/s + (-1) kgm/s = 0$. The total energy is $E_k = 1 kg mm/ss + 1 kgmm/ss = 2$.

Now the balls collide with each other, and stick together (a fully inelastic collision). So their velocities are both zero.

The total momentum afterward is $p = 0 + 0 = 0$, same as before. The total energy is $E_k = 0 + 0 = 0$. Where did all that energy go? It still exists, but it went out into the environment: some of it caused the air to vibrate, for example, making sound.

Now, for your magic box. Let's assume the magic box is already charged up with some amount of energy. You take one of my 1kg metal balls, and set it in front of the box. $p = 0$ and $E_k = 0$ since nothing is moving.

The box does its magic, and now the ball is flying east at 1 m/s. It's gained momentum of 1 kg meter per second east. But we know the total has to be zero, so something else needs to gain momentum of 1 kg meter per second west. The easiest solution is to give that momentum to the Earth, where it has no measurable effect because the Earth is so heavy. This is what happens to the equal-and-opposite momentum when you walk.

But the ball has also gained energy. It now has 1 kg meter-squared per second-squared of kinetic energy. Where did this come from? The obvious answer is: the box. But since this energy doesn't have a direction, the box can't "gain" anything in response. It now has a little bit less magic energy in it than before.

So you've expended some stored energy to move an object; in other words, you have a magic gun.

A converter of kinetic energy is a wonderful idea, but alas, there is no energy to be regained from recoil. The most you can get is momentum.

• So if I redefine the box as storing momentum, and able violate conservation of momentum by rotating it, I can basically just change the direction of travel without energy loss from entropy (assuming used on same object as was absorbed from)? Oct 19 '16 at 20:10
• I'd say the easiest modification is make it absorb kinetic energy, and release kinetic energy, with very little lost to entropy. Not breaking any laws, and it interacts with mass in the way you'd expect (hit it with a hammer at 1 m/s, and the stored energy will launch a marble at many times that). Oct 19 '16 at 20:14
• The amount of energy lost to entropy can also often be ignored. It's there, but most of the time it's small enough you don't need to care about it. Oct 19 '16 at 20:15
• So would I just be ignoring the momentum lost/gained from absorb/discharge? (if I put no limit on the device and say it works on objects the scale of planets?) Oct 19 '16 at 20:21
• A very well written answer. Kudos. Oct 19 '16 at 20:57