(Mainly need help with #2! Please explain.) A steel ball rolls down an incline i

Question

(Mainly need help with #2! Please explain.)

A steel ball rolls down an incline into a looptheloop of radius R.

1. What minimum speed must the ball have at the top of the loop in order to stay on the track?

This one I have: v = square root of (gR)

2. At what vertical height on the incline in terms of the radius of the loop must the ball be released in order for it to have the required minimum speed at the top of the loop? ?!

3. What are the sensations of the riders if the roller coaster has a minimum speed or a greater speed at the top of the loop?

Explanation / Answer

for the second part
To stay on the track;-
=>mv^2/R = mg
=>v^2 = gR
Thus by PE(total) = KE(top) + PE(top)
=>mgH = 1/2mv^2 + mg x 2R
=>mgH = 1/2 x m x gR + 2mgR
=>H = R/2 + 2R
=>H = 5R/2

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