Riding a Loop-the-loop. A car in an amusement park ride rolls without friction around the track shown in the figure. It starts from rest at point at a height above the bottom of the loop. Treat the car as a particle.

1. What is the minimum value of (in terms of) such that the car moves around the loop without falling off at the top (point)?

2. If the car starts at height and the radius is, compute the speed of the passengers when the car is at point, which is at the end of a horizontal diameter.

3. If the car starts at height and the radius is, compute the radial acceleration of the passengers when the car is at point, which is at the end of a horizontal diameter.

4. If the car starts at height and the radius is, compute the tangential acceleration of the passengers when the car is at point, which is at the end of a horizontal diameter.

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