## Physics Problem

Mechanics, discrete, statistics, ...
PurpleBlu3s
Posts: 73
Joined: Mon Sep 19, 2011 6:49 pm

### Physics Problem

Hi, the following was a question in a Physics Olympiad paper I saw during my A-levels (which were a few years ago now). I cannot remember the answer nor work it out.

There are two identical balls, travelling at the same speed towards either a hill or a trough. If you were to draw the outline of the hill, then reflect it vertically, you would have the outline of the trough. So the question is, which ball is travelling faster after getting past its obstacle (assume the initial speed is great enough to make it past the obstacle)?

At the time I thought that their speeds should be the same, but my teacher said that in fact one of the balls (and I can't remember which) was travelling faster. The reason given was fairly short (but again, I can't remember it). I was reminded recently of it and have been curious to know the answer and explanation. So I would greatly appreciate any thought on the solution.

Thanks.

wrongrook
Posts: 396
Joined: Sat Oct 17, 2009 10:39 pm

### Re: Physics Problem

One argument is that air resistance will increase non-linearly with speed, so the ball going through the trough might be expected to be faster and meet with more air resistance, and come out slower.

However, this is likely to be a negligible effect so probably the proper answer is something else?

PurpleBlu3s
Posts: 73
Joined: Mon Sep 19, 2011 6:49 pm

### Re: Physics Problem

wrongrook wrote:One argument is that air resistance will increase non-linearly with speed, so the ball going through the trough might be expected to be faster and meet with more air resistance, and come out slower.

However, this is likely to be a negligible effect so probably the proper answer is something else?
I think that as long as the effect is there I don't think it matters how small it is. Friction increases linearly doesn't it, so that wouldn't be relevant?

thundre
Posts: 356
Joined: Sun Mar 27, 2011 10:01 am

### Re: Physics Problem

If you neglect friction, they end up going the same speed, but the one that went into the trough will be ahead because it was going faster for a time. If the question was "Which will reach the finish line first?", that's the answer.

If the question was "Which will have the higher speed?" I'd have to go with Wrongrook's answer.

PurpleBlu3s
Posts: 73
Joined: Mon Sep 19, 2011 6:49 pm

### Re: Physics Problem

thundre wrote:If you neglect friction, they end up going the same speed, but the one that went into the trough will be ahead because it was going faster for a time. If the question was "Which will reach the finish line first?", that's the answer.

If the question was "Which will have the higher speed?" I'd have to go with Wrongrook's answer.
The question is for their speed, not the first to get there. So it does sound like the air resistance argument best answers this question.