Puzzler

[ivyfic]

Here's a brain teaser for you:

I'm finishing up an article on the All-American Soap Box Derby. The Derby is for engine-less carts; the only thing accelerating the racers down the hill is gravity. One boy tried to cheat by holding a bowling ball between his legs and letting it go at the top of the hill so it would roll forward and hit the nose. The theory is that this would give his cart a little extra boost.

Here's the question: Would the cart go any faster? If so, why and under what circumstances?

I've already called my Physics major brother and figured it out--I'm just wondering how smart my f-list is. *evil grin*

Comments

[gryphonrose.livejournal.com]

No idea--but if he let it go and it hit him in the groin, bounced, and hit him in *his* nose it would make for an exciting race! :)

[edgehopper.livejournal.com]

If he timed it right so that he pushed the ball forward while the cart was still being held, and the ball hit the nose after the cart was released, it would help. By doing that, the cart+ball system would already have some momentum while being held, and the speed of the cart would increase when the ball hit the nose--almost like getting a running start. If he tries this after the cart's released, though, the cart would slow down when he initially pushes the ball, and then go back to regular speed when it hits the nose, actually increasing his net time on the run.

[ivy03.livejournal.com]

I don't see how it would lose speed. (I'm assuming an idealized version of the cart here, like a Physics 101 problem -- so no wheels slipping, no friction of the axle turning, etc. I'm also assuming he's just releasing the ball, not pushing it.) The only force being applied to the cart is gravity, and that acts on the mass. So whether you treat the cart+bowling ball as one system or the cart and the bowling ball seperately and then add them together -- it's going to be the same. The bowling ball, in rolling toward the front of the cart, could not gain any more energy than it would just being part of the cart.

However, it would give you a boost if you let it go before the starting gate fell. As my brother explained it, this would be a false start -- part of the system is starting to accelerate before the start of the race. So you wouldn't be going any faster than if you let the cart go a little early.

[edgehopper.livejournal.com]

The system doesn't lose speed, but the cart alone does for the short period of time when the ball is moving independently, so the net time for the run will be greater. For another way of thinking about it: The center of gravity of the cart-ball system will cross the finish line at the same time no matter what. However, moving the ball forward moves the center of gravity of the system forward relative to the cart, causing the nose to cross the finish line later than it would have otherwise.

[ivy03.livejournal.com]

Aaaah... that makes sense. See, I really just feel better about all this stuff if I can do the math. I know I have my PHY 103 notes somewhere...

[ivy03.livejournal.com]

Want another physics brain teaser?

[cubby-t-bear.livejournal.com]

Oh. And here I was ready to start talking about nonlinear frictional forces. Well, mathematicians exist to make life complicated :)

[shnayder.livejournal.com]

Ditto :-)