Does Newtons 3rd law mean that half of the energy is wasted?

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This may sound dumb to some folks, but lets say I fire a gun. 1000N of force goes into the bullet, and another 1000N of force goes into my body. Even if i strap the gun to the ground, it will just apply 1000N of force to move the earth by a tiny amount. Because of this, does it mean that it isn’t possible to have 2000N of force going to the bullet with the same parameters as before?

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Anonymous 0 Comments

Newton 3 tells us that forces come in pairs (not apples). A force is a push or a pull. When you have a force it is the force of some object on some subject, due to some interaction. For example, if you throw a ball there is a force of you, on the ball, due to the contact between you and the ball.

For the Newton 3 pair, we switch around the subject and the object, switch around the direction, but keep everything else the same (same interaction).

So if you throw a ball, there is a force of you on the ball. There is an equal and opposite force of the ball on you.

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Energy is not force. Energy tells us how much something has been forced, and how much it could force other things. When looking at mechanics problems like these, we can look at them in terms of forces, or we can look at them in terms of energy (or we can look in terms of momentum). We get the same overall answer, but we’re using a slightly different set of tools to get there.

When you throw the ball you do work on it; you give it energy. You lose energy, the ball gains energy.

If we do this properly the maths gets rather complicated, but in simplest terms the work done by a force is given by the magnitude of the force, multiplied by the distance the thing being forced moves *in the direction of the force*.

So when you throw the ball, the force of you on the ball is in the direction you are moving the ball. So you do work on the ball; the ball gains energy.

But if we look at it the other way around, the force of the ball on you (the Newton3 pair) is in the opposite direction to the direction the ball is moving, meaning we get a negative sign in the energy; you *lose* energy, because you are doing work on the ball.

Newton3 gives us conservation of energy.

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Both ways of looking at this we only have one interaction. You are throwing the ball. But that interaction has a symmetry to it; if the ball gains energy, you lose energy. If you force the ball, the ball forces you. All we’re doing when splitting it up is looking at the two different sides to the interaction.

> 1000N of force goes into the bullet, and another 1000N of force goes into my body.

So applying it to this case; the gun applies a force of 1000N to the bullet. The bullet applies 1000N of force to the gun [with some other stuff going on, but we’re simplifying]. But that is only one interaction. We cannot somehow shift that to get 2000N to the bullet. In terms of energy, most of the energy will be going into the bullet, from the gun [from the chemicals that are exploding]. The gun loses energy, the bullet gains energy.

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As an aside; momentum is what happens when we sum our force over *time*, rather than distance moved (which gives us energy). So just as Newton3 gives us conservation of energy, if we take it into the energy world, Newton3 gives us conservation of momentum if we take it into the momentum world.

And if we’re really sneaky, once we get into working in 4-dimensions (with Special Relativity, and time being our 0th dimension), we may notice that energy is the time component, and momentum the space components, of the combined energy-momentum 4-dimensional thingamy.

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