Question

Two ice skaters have masses m₁ and m₂ and are initially stationary. Their skates are identical. They push against one another, as in Figure 7.10, 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 twice as far as skater 2. What is the ratio m₁/m₂ of their masses?

Answer 1

using work energy theroem

ma d = 0.5 m v^2

v^2 = 2 a d

so

(v1/v2) ^2 = 2a d1/2 a d2

v1/v2 = sqrt (2)

now using conservation of momentum

m1 v1 = m2 v2

m1/m2 = v2/v1

m1/m2 = 1/sqrt(2)

m1/m2 = 0.707

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