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Momentous Momentum in "The Music Man"

In the 1962 film, The Music Man, a conman named Harold Hill tricks the people of River City, Iowa into buying musical instruments. If only they had studied a little physics, they would have never been so easily fooled. Everyday Einstein delves into the classic movie to discuss the importance of momentum.

 
By
Lee Falin, PhD,
March 7, 2014
Episode #091

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Conservation of Momentum

One of the things you often hear about associated with momentum is something called conservation of momentum. This principle says that if one object collides with another object, the total momentum of the objects after the collision will be the same as the total momentum of the objects before the collision.

If you’ve ever seen one of those desk toys where metal balls knock back and forth while suspended on strings (usually called a Newton’s cradle), you’re seeing conservation of momentum in action. As the swinging ball collides with the row of stationary balls, its momentum is transferred to the ball on the end, which causes it to swing out. Then that ball swings back and the process should (according the conservation of momentum) continue forever. Except it doesn’t.

There’s a slight caveat to conservation of momentum, which says it only holds true for elastic collisions. An elastic collision (which has nothing to do with stretchy things), is one where no kinetic energy is lost. Every time that little metal ball swings back and hits another ball, some energy is converted into sound and heat. After a while, so much energy has been changed to sound and heat, that the ball no longer has enough momentum to cause the other ball to move, and the toy comes to a halt.

We’ve Got Trouble My Friend

So what does any of this have to do with playing pool? When the cue ball strikes another ball, some of its momentum is transferred to the second ball, causing it to move (hopefully towards a pocket). Now, things don’t always work out exactly as you might expect, and that’s because the angle and spin of the ball, as well as the friction from the surface of the table affects things. A detailed look at the physics of pool is actually quite complicated, but the general principle of conservation of momentum will always hold true.

It’s also important to consider how mass and velocity can both impact momentum. Let’s say you have a standard size cue ball, which has a mass of about 0.2 kg. If the ball is moving with a velocity of 2 m/s, then the momentum of that cue ball is 0.4 kg m/s. Since the cue ball has close to the same mass of the other balls, when it strikes them it usually stops moving, (or at least slows down considerably) because it has transferred most of its momentum into the other balls. 

If you were to greatly increase the mass of the cue ball, however, using one with a mass of 20kg, you’d noticed that as it hit the other balls it wouldn’t slow down very much. That’s because it has so much momentum (20 kg * 0.4 m/s = 8 kg m / s) that it is a lot harder to slow down. 

Conclusion

So now you know more about momentum and how it’s related to mass and velocity. You also know how the conservation of momentum works, and that the introduction of a pool table to your community isn’t necessarily a disaster.

If you liked today’s episode, you can become a fan of Everyday Einstein on Facebook or follow me on Twitter, where I’m @QDTeinstein. If you have a question that you’d like to see on a future episode, send me an email at everydayeinstein@quickanddirtytips.com.

Pool table and collision toy images courtesy of Shutterstock.

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