Your company is designing an apparatus for an ice skating show. An ice skater wi

Question

Your company is designing an apparatus for an ice skating show. An ice skater will start from rest and slide down an ice-covered ramp. At the bottom of the ramp, the skater will glide around an ice-covered loop which is the inside of a vertical circle before emerging out onto the skating rink floor. For a spectacular effect, the circular loop will have a diameter of hf=22 ft . Your task is to determine the minimum height from the rink floor to the top of the ramp for the skater to make it around, the skater briefly loses contact with the ice at the top of the loop.

Explanation / Answer

for the skater to briefly lose contact at the top ,

mg = m * v^2/r

g in ft/s^2 = 32.17 ft/s^2

here r = D/2 = 22/2 = 11 ft

32.17 = v^2 /(11)

v = 18.81 feet/s

let the minimum height needed is h

using conservation of energy

mg* h = 0.5 * m * v^2

32.17 * h = 18.81^2 * 0.5

h = 5.5 feet

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