Collision Q: Why Energy Transfer Max w/ Same Mass Particles

[asdf1]

why is energy transfer a maximum when colliding particles have the same mass?

 

[Nam_Sapper]

why is energy transfer a maximum when colliding particles have the same mass?

Let's thinik about it:
Take a huge heavy lead ball with a lot of energy flying out of a cannon. Let's say the gunpowder/cannon arrangement is pretty efficient, transferring most of the gunpowder energy to the cannonball.

Now imagine the cannonball hits a butterfly while flying through the air. I think you'll agree that while the butterfly is now squashed flat, and traveling at the same speed as the cannonball, since it is stuck to it, the actual energy to move the butterfly at said speed isn't very much, since the butterfly is light in weight.

Since we know the weight of the butterfly, we can calculate the exact amount of energy that has been transferred to the butterfly. This is subtracted from the energy the cannonball had before impact, and rather obviously, the energy left over hasn't changed much.

That is, the maximum energy the butterfly can get is limited to the amount it took to squash it, the amount it took to stop its movement in the opposite direction, and the final amount it absorbed in being carried by the cannonball. This amounts to diddly squat. The majority of the energy of the cannonball is still with the cannonball.

So in actual fact, very little energy was transferred, due to the mismatch between the masses of the cannonball and butterfly. And this makes good common sense.

We can reverse the argument by simply pretending we started with the butterfly.

The butterfly begins with very little energy, and although it loses it all to the cannonball, and absorbs a heck of a lot more relative to its own energy, this still amounts to diddly squat when compared to the total energy of the system that includes the cannonball.

That is, most of the energy of the system just stayed where it started from, still with the cannonball. It is only if we ignore the energy in the cannonball entirely that we fool ourselves into thinking the energy was efficiently transferred.

True, the energy in the butterfly was very efficiently absorbed/cancelled by the cannonball. But this ignores the embarrassing fact that most of the energy in the system stayed where it was.

Part of the problem is point of view. When we talk about efficiency of energy transfer, we usually mean a ratio, i.e., we compare the total energy available to the amount actually transferred. For the efficiency to be meaningful, we obviously want to include all the energy available.

Of course we could be deliberately cheating in not reporting the other massive chunk of energy that didn't get transferred, like corporations often do when they report record 'profits' and hide record losses while paying their CEOs boatloads of your cash. But that would not be very scientific.

Parallel in Electronics

Notice that something very similar happens in electric circuits. Only there it is called 'Impedance Matching'. When you join two devices together, usually by a two-wire link, the electricity flows in a circuit (circle) through a resistance inside the source (say a battery) and out and through another resistance (say a lightbulb) in the 'sink' (the receiver).

If the resistances are equal, you have maximum 'efficiency' of power transfer, but the voltage (pressure) is divided equally between the battery and the lightbulb. In this case however, the battery heats up at least as much as the lightbulb: probably a 'bad' situation...and the battery is quickly used up. (ouch).

Now imagine you increase the resistance of the lightbulb. The total resistance (the two resistors in series) is more, so overall, less current flows. However, more effective (useful) voltage appears across the load (sink/bulb) of the total voltage available (a battery is a 'fixed' voltage source). This now means that the (new) bulb actually burns brighter, since most of the energy is now used by the bulb, and very little is wasted as heat inside the battery.

But now, if you continue to increase the resistance of the bulb, you are also choking off the current, since the total resistance just keeps going up. Its a law of diminishing returns. At some point, the total power available to the bulb begins to drop again, as the electricity is choked off. These cross-over points on a graph are called the Maximum Power Usage point and the Maximum Efficiency point etc.

So you have to decide, based upon your purpose at hand, what ratio of resistance (battery internal to load internal) you want. If you want to transfer maximum power, but you don't care about efficiency, you do one thing. If you want maximum efficiency, or maximum battery-life, or maximum power to the load, then you do something else.

 

[OnTheCuttingEdge2005]

You can also fire two Cannon Balls at each other and weld them together with the head on energy they acquired.

A 22 Cal Long Magnum shell fires at one mile a second, Two 22 Cal bullets hitting head on at a combined force of 2 miles a second, Isn't welding fun!

 

[asdf1]

thank you very much! :)