Acar starts from rest at point a, a height h above the ground, and rolls freely (no resistance or drag) down a track and around a circular loop of radius r. (a) from what minimum height h (in terms of r) should the car start in order to just barely make it all the way around the loop without losing contact? [hint: what minimum speed must the

Explanation:

We use the Energy conservation theorem, in the initial point (h=H, velocity=0, because the car starts from rest) and at the point maximum in the loop (h=2*R ).

     1

but at the top of the loop the car does a circular movement, so the Newtons equation must be fulfilled:

N is the normal force applied by the loop on the car.

The minimal case occurs when the Normal is equal to zero:

      2

We replace 2 in 1, and we solve to find H:

layers of the earth affect the waves and these effects are seen on instruiments such as seimometers