Two ice skaters have masses m 1 and m 2 and are initially stationary. Their skat

Question

Two ice skaters have masses m1 and m2 and are initially stationary. Their skates are identical. They push against one another, as shown below, and move in opposite directions with different speeds. While they are pushing against each other, any kinetic frictional forces acting on their skates can be ignored. However, once the skaters separate, kinetic frictional forces eventually bring them to a halt. As they glide to a halt, the magnitudes of their accelerations are equal, and skater 1 glides 3 times as far as skater 2. What is the ratio m1/m2 of their masses?

Explanation / Answer

v^2 =2ad

so v1^2 =2 x a x 3 x d

v1 = sqrt(6ad)

v2^2 = 2ad

v2 = sqrt(2ad)

balancing momentum,

m1v1 = m2v2

m1/m2 = v2/v1 = s1rt(2ad) / sqrt(6ad) = 1 / sqrt(3) = 0.577

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