Other interesting exhibits were:
- the optics and illusions section, bending light and playing with diffraction and mirrors.
- a list of gene-based characteristics--e.g. "earlobe distinct/attached, ring finger longer/shorter than index, freckles/no freckles"--where you can select your choice for each option and see what percentage of people match your set of answers. Diana matched 36 of 100,000; I matched 12 in 100,000.
- three ramps, down which you can simultaneously roll three identical balls. The ramps all have the same start height, and the same end height, but the paths are different. The first one is a straight line from start to finish; the second is a steep drop at first, with most of the path nearly level; and the third is a section of a circle ("cycloid") which dips below level of the end point before coming back up. Which path is the fastest to get to the end point? On which ramp does the ball have the most energy at the end point?
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I think of you more as one in six billion than 3 in 100K.
My back of envelope 'frame of reference' calculations suggests:
Energy - In a frictionless world, all would be equal. The only energy in the system (assume your initial perturbation is infinitely small) is the conversion of potential energy from the altitude. The only wrinkle in this is friction. My theory is that the impact of friction is directly proportional to the length of the surface you run along and these paths have different lengths. So I'm betting the straight incline, being the shortest distance to be subject to friction, leaves the most potential energy converted to kinetic energy.
Fastest - The speed of something has to do with acceleration. My first guess was that the cycloid was the answer because the sharpest drop would occur here (depends on how sharp the drop in the other system was). But then I considered coming back up and out of the deepest point, you'd be bleeding momentum to friction.
When you reach ground level on this path, your energy would be (max potential energy based on height - some energy based on a small amount of friction on the downhill arc to that point), so a sizable portion of total potential energy from height.
After that, you should get a near zero change of energy from that point to the next point it hits ground level (the end of the ramp) as you gain some kinetic energy descending further then bleed it off again ascending. Again, friction instills some losses.
So you end up with friction loss on the first leg of the descent (to ground level), on the way to the lowest point, and on the way back up to ground level.
I think that since this path is still longer than the straight line incline from start to finish, it cannot in fact have superior ending energy. If my final answer about energy is 'straight incline plain is the best' then I must maintain that speed is also the best on that surface. I don't see how one of these paths could have the best output energy and not have the highest speed, since the ball weighs the same.
KE = mv^2.
v = sqrt (KE/m)
m = constant
So highest KE = highest v as far as I can see.
And if my theory about shortest path for least friction effect, I say simple incline plane is right for both.
Am I totally wrong?
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