Study Guide

Energy and Momentum - Impulse

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Any time a force is applied to an object, its momentum is going to change. This change in momentum is called impulse (abbreviated I). And it really isn't a new quantity at all—just another name for changing momentum: I = Δp.

We can find how much the momentum of an object is going to change by looking at the magnitude of the force applied to it (F) and the length of time the force acts (Δt):

I = FΔt

This means an object's momentum is just the end result of applying a force to it for some time. Fair enough—non-zero momentum means an object is moving. If its moving, chances are someone pushed it at some point.

But wait. Why are we even talking about changes in momentum when the law of conservation of momentum clearly states momentum can never increase or decrease? That's exactly what Luke Skywalker said before Yoda lifted a starfighter out of the Dagobah swamp. Yoda taught him a thing or two about forces' (and the Force's) ability to change momentum.

The law of conservation of momentum applies to isolated systems—collections of objects we cut off from the outside world. Two billiard balls rolling around on a pool table? Momentum is definitely conserved. But when you hit one with a pool cue, you're transferring momentum from an object outside the system (that is, the cue—which gets momentum from your arm muscles, which get momentum from your steak dinner the night before).

Yoda's not violating the law of conservation of momentum; he's just applying an outside force to the X-wing/swamp system. This force is allowed to change the total amount of momentum in the system, but once it stops acting, you better believe the law of conservation of momentum is still calling the shots.

Of course, if our "isolated system'' wasn't actually isolated at all and instead comprised the entire universe, there wouldn't be such a thing as an outside force. That tends to make the math a little tricky, though.

The beauty of isolated systems is that they allow us to ignore forces that are negligible compared to what we really care about. Does Mars affect Earth's rotation? Yes. Does it affect it anywhere close to the amount the sun affects Earth's rotation? Not a chance.* So when we talk about earth's orbit, we usually talk about an isolated system consisting of the sun and the earth (sometimes we let the moon hang out, too).

Common Mistakes

Being able to break a problem into sections and define isolated systems is key to solving problems in physics—but be careful not to forget the parts of the question you've temporarily ignored. Always check to make sure every force in the question is accounted for.

Brain Snack

While large solid or liquid chemical rockets are used to getting rockets out of earth's atmosphere, smaller ion thrusters are usually used to adjust satellites and things already in orbit. These small thrusters are often talked about as a means of deep-space exploration, because they have much higher specific impulse, a measure of how much force they can provide versus the amount of propellant they use per second.

Large chemical rockets use a lot of fuel very quickly, while small ion thrusters use small amounts of fuel over a long period of time. The small guys could be better for sending things to galaxies far, far away.

*The force of gravity between the earth and the sun is about 3.5 × 1022 N, while the force of gravity between Earth and Mars is about 5 × 1015 N on average—a difference of a factor of 7,000,000. Trying to figure out the effect Mars has on Earth's rotation is like trying to figure out whether the Titanic sank because the captain brought his terrier onboard.

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