A ball of mass 6.2 kg and radius 10 cm rolls without slipping horizontally at 5.

Question

A ball of mass 6.2 kg and radius 10 cm rolls without slipping horizontally at 5.3 m/s and hits a spring attached to a wall. What is the maximum change in length of the spring if the spring constant k=30600N/m in cm? (Assume the floor is frictionless)

A ball of mass 6.2 kg and radius 10 cm rolls without slipping horizontally at 5.3 m/s and hits a spring attached to a wall. What is the maximum change in length of the spring if the spring constant k=30600N/m in cm? (Assume the floor is frictionless)

Explanation / Answer

I = (2/5)*m*r^2 + m*r^2 = (7/5)*m*r^2

w = v/r

KE = 0.5*I*w^2 = 0.5*(7/5)*m*v^2 = (7/10)*m*v^2

PE = 0.5*K*x^2

KE = PE

(7/10)*m*v^2 = 0.5*K*x^2

(7/10)*6.2*5.3*5.3 = 0.5*30600*x^2

x = 0.089 m = 8.9 cm = 9 cm nearly

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