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# Bowling and the Conservation of Momentum

The law of conservation of momentum is one of the many natural laws of the universe that makes sports possible. Everyday Einstein explains the conservation of momentum by taking a trip to the bowling alley.

By
Lee Falin, PhD
Episode #041

Back when I was a poor college student, one of our family’s favorite activities was bowling. The reason for this was simple: it was cheap. The local college had a deal where you could bowl at their on-campus bowling alley for around \$0.50 per game. One of the best things about bowling (aside from the obligatory nachos) is that it provides a great setting for discussing the law of conservation of momentum.

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## Bowling with Ramps

Even though my poor college days are behind me, I still love to take my family bowling. When we take our young children, they always request “the ramp.” The ramp is a slightly broken looking steel frame that you could set a ball on top of, give it a slight push, and send it rolling down an incline and down the bowling lane.

The kids love the ramp because it makes their ball go straight. But despite the increased accuracy, they are sometimes disappointed that the ramp doesn’t give them that dynamic bowling pin explosion that my bowling ball causes (on the rare occasions when my ball actually stays out of the gutter).

Their first guess as to why this happens is that they were using lighter bowling balls. What’s a 6 lb ball compared to a 10 or 12, right? So off they ran to get a heavier ball. The heavier ball did help, but there was still something missing. They still lacked some key ingredient that was needed to send those bowling pins into a violent explosion. What their bowling balls lacked was velocity.

## Learn the Meaning of the Law

Back in 1687 when Newton wrote, Principia Mathematica Philosophiae Naturalis, some of the phrasing he used has led some scientists to think that although he was writing about motion in general, what he really meant was momentum.

Momentum is the mass of an object multiplied by its velocity. This means that while you might be able to catch a 90 mph fastball, you can’t catch a 90 mph truck. The fact that the truck has much more mass than a baseball means that a speeding truck has much more momentum than the best fastball could ever hope to achieve.

The law of conservation of momentum can be mathematically calculated as a direct result of applying Newton’s 3 laws of motion that we talked about in last week’s episode.

The law states that if two particles interact in a closed system, the total momentum of the two particles stays constant. In other words, if there are no other forces acting on a pair of objects, and they collide, the momentum of the first object plus the momentum of the second object before the collision is equal to the momentum of the first object plus the momentum of the second object after the collision.

## Back to the Game

So if you have a 10 lb bowling ball, rolling down the lane at 15 miles per hour, and it hits a single 3 pound bowling pin, some of the bowling ball’s momentum is going to be transferred to the pin. Assuming that the bowling ball doesn’t break, and that it slows down to 10 miles per hour after the collision, we can figure out the momentum of the bowling pin after the collision using this formula:

10 lb ball * 15 mph + 3 lb pin * 0 mph = 10 lb ball * 10 mph + 3 lb pin * X mph

Solving for X, we get around 16.7mph. So if what we said before was true, after the ball hits the pin, the pin will have a velocity of 16.7 mph.

Now, in the real world things don’t work out quite like that. For one thing, the ball loses velocity due to friction and drag as it travels down the lane. For another thing, the ball often strikes more than one pin, and then those pins strike each other, which muddles things even more. But if we ignore friction and drag, each time the pins run into each other, their momentum is conserved.

So if this momentum stuff is true and momentum equals mass times velocity, then isn’t it always better to use the heaviest bowling ball available for maximum explosiveness? Yes, but only if you’re really, really strong.

The thing about velocity is that it’s brought about through acceleration. And as we learned about in the episode on Newton’s 3 Laws of Motion, the second law of motion says that it takes a lot more force to accelerate a 10 lb ball than it does to accelerate a 6 lb ball. So while a 10 lb ball would have more momentum than a 6 lb ball, if they were moving at the same velocity, it takes a lot more force to get the 10 lb ball to reach that velocity.

This principle explains why no matter how heavy a ball the kids used with their ramp, they could never achieve the same dramatic effect with the pins that I could (assuming I actually hit the pins). Their bowling ball never reached the same velocity as mine.

## Conclusion

So that concludes our trip to the bowling alley and our introduction to the law of the conservation of momentum. As you might have guessed, the law of conservation of momentum isn’t limited to the bowling alley. It’s also the principle behind why you can hit a home run, why you can sink an 8-ball in the corner pocket, and why you can land a hole in one. Any time a sport involves one thing hitting something else, the law of conservation of momentum is on hand to make sure things behave properly.

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Isaac  Newton Stamp and Bowling images from Shutterstock