Two identical balls roll across the top of a table on parallel paths. One of the balls has to roll down into and up out of a dip in the table. The other ball rolls on the flat all the time. Which ball gets to the far side of the table first, and why?.
Firs, I would think we'd have to consider the dip to be smooth so there's be no point the ball going through it actually hit something, with a knocking sound.
Also, if the dip is not a linear feature hit perpendicular to its axis, then one must assume it's center is traversed as in a circular depression. Otherwise, as was indicated in a previous post, the ball could be deflected right or left so as not to make it to the other side at all.
I don't think the gravity can be isolated from the forward motion, as the incline will divert some of the gravitational force horizontally. Think of a car or bicycle going downhill.
By conservation of energy, the dipped ball will be going at the same speed on the far side of the dip as it entered, so it speeds up and then returns to its original speed, even considered horizontally.
So, since it traversed part of its course at a higher speed (horizontal component considered), it must arrive sooner than the level ball.
Posted by Charlie
on 2009-11-05 12:05:56