A little rolling sphere

A small solid steel sphere of total mass $0.1~\mbox{kg}$ and radius $1~\mbox{cm}$ rolls without slipping with an initial speed $v_i$ 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 $1~\mbox{m/s}$ for $2~\mbox{seconds}$ 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 $v_f$. What is $v_f/v_i$?

Details and assumptions

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