Question

A solid sphere is rolling on a rough horizontal surface with linear speed v . It collides with a vertical wall elastically. Coefficient of friction on each surface is 0.5 .Find speed of sphere when it again starts rolling without slipping.

Answer 1

$F_fr=I\alpha$

$I=\frac{2}{5}mr^2$

$\alpha=\frac{5F_f}{2mr}$

After collision we have the equation

$\omega_f=-\omega+\alpha t\to\omega_f=-\omega+\frac{5F_f}{2mr} t$

$v_f=-v+r\alpha t\to v_f=-v+\frac{5F_f}{2m} t$

$v_f=-v+\frac{5}{2}(v-v_f)\to v_f=\frac{3}{7}v$ . Answer