Question #110555

Using the energy conservation law determine the following...

If the minimum velocity needed by the skater to pass the loop is 5.42m/s, what is the minimum initial height that allows the skater complete the loop?

If the minimum velocity needed by the skater to pass the loop is 5.42m/s, what is the minimum initial height that allows the skater complete the loop?

Expert's answer

So that skater does not leave the loop it is necessery that "w_n=v^2\/R\\geq g" then "v_{min}=\\sqrt{gR}"

and "R=v^2_{min}\/g." As "v^2_{min}\/2+mg\\sdot2R=mgH" hence "v^2_{min}\/2=g(H-2v^2_{min}\/g)"

hence "H=\\frac{5v^2_{min}}{2g}" then "H\\approx7.5m"

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