A little rolling sphere

A small solid steel sphere of total mass 0.1 kg0.1~\mbox{kg} and radius 1 cm1~\mbox{cm} rolls without slipping with an initial speed viv_i on a table. It eventually rolls onto a thin sheet of paper. As the ball is moving on the paper you suddenly move the paper horizontally at a speed of 1 m/s1~\mbox{m/s} for 2 seconds2~\mbox{seconds} perpendicular to initial velocity of the sphere. The sphere may slip on the paper during this time. You then stop the paper, the sphere keeps rolling/slipping, but eventually rolls off the paper back onto the table. When the sphere is back to rolling without slipping on the table, it has a final speed vfv_f. What is vf/viv_f/v_i?

Details and assumptions

  • The coefficients of static and kinetic friction of the paper with the sphere are μs=0.5\mu_s=0.5 and μk=0.4\mu_k=0.4.
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