More about the ball on the curve

In the ball on the curve problem, you were asked to calculate the speed of the ball when it reached the bottom of the curve, given the vertical height of the curved section:

The temptation would be to use suvat by saying that the acceleration was 9.81m/s2 and that the distance s was given by h.

This would be the wrong thing to do because 9.81 is only the acceleration at A.

At B, it is the dotted component that points in the direction of motion that causes the acceleration. This is smaller than the weight, so the acceleration has reduced.

And at the end, when the ball is moving horizontally, it no longer accelerates at all.

So to solve the problem, we use an energy argument:

Say that gravitational potential energy at the top = kinetic energy at the bottom

assuming that no energy has been wasted by a transformation into thermal energy by friction.

Thus





And