# math

A figure skater pushes off from rest and glides along a circular path, the radius of which is 3 times her height. What must be her minimum initial velocity in order to come full circle without having to push off a second time?

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1. I have no idea. It depends on friction. Where did you get this question?

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posted by Damon
2. The question is a real-life question.

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posted by Shannon
3. In that case it depends on a lot of things, mainly:
The temperature of the ice. Skates move easily over the ice because they melt a tiny film of slippery water under the blade. If the ice is very cold, the skate will have to be very, very sharp to work efficiently. On the other hand you do not want mushy ice because then you get a lot of drag. You want the skate to cut in enough to provide the necessary side force for centripetal acceleration toward the center of the turn. this is the mass of the skater m times v^2/R where v is the forward speed and R is the turn radius. If the ice is too hard or the skate too dull, there will be slipping and loss of speed. In the end the skater must have enough kinetic energy (1/2)mv^2 at the start of the turn to overcome the friction loss during the turn. which is the retding friction force times the distance which for a full turn is 2 pi R

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posted by Damon

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