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 30 feet. 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 loop. Known: Unknown: Strategy: Solution:

Explanation / Answer

Known :

diameter of loop , d = 30 feet

radius of loop = 30/2 = 15 feet

unknown :

speed of skater at the top of loop , v

height of hill is h

STratery :
find minimum speed needed at the top of loop

Use conservation of energy to find the minimum height of hill

Solution :

for the speed at the top of hill

m * g = m * v^2/r

32.17 = v^2/15

v = 22 feet/s

Now , Using conservation of energy

0.5 * m * v^2 = m * g * (h - d)

0.5 * 22^2 = 32.17 * (h - 30)

h = 37.5 feet

the minimum height of hill is 37.5 feet

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