The question is"Asolid sphere rolling on a rough horizontal surface with a linear speed v collides elastically with a fixed,smooth vertical wall.find the speed of the sphere after it has started pure rolling in the backward direction."
I don't want the solution.just tell me whats happening there.My approach goes this way.
Let THE SPHERE go rightward with a speed v.friction force acts leftward.for pure rolling v=r.so sphere has to rotate anticlockwise. decreases and also v decreases.at one stage vanishes.after some time becomes such that v=r.we have to find the velocity now right?
But i have some doubts.after this (v=r) how can it continue rolling?v decreases and increases .how can they maintain the relationv=r.
if it hits the wall before has vanished thenit is still rotatng anti clockwise and the v becomes leftward.now friction acting rightward increases and v decreases.now will it ever purely roll.
well, i think u got the concept of pure rolling wrong.if a force is not acting on a body performing pure rolling in the direction of it's velocity, the n friction shall not act !!
when the body hits the vertical wall, it must be given that the wall is frictionless. so now no effect on it's angular velocity just right after it hits the wall.but the wall now imparts a impulse to the body in the opposite direction, which causes it to tend to slide.due to friction, it shall again get the state of pure rolling !!
for more queries, contact at vishakp0001@gmail.com
As far as the question goes before collision the sphere is in pure rolling condition. Now the wall is smooth. There fore just after collision the angular velocity remains same in magnitude and direction but the linear velocity changes direction after collision. If the collision is elastic the magnitude will not change. There fore the sphere after collision has clockwise rotation and leftward linear motion and the friction direction now is towards right because the bottom most point has a resultant velocity towards right. Now the angular velocity and linear velocity both will reduce until the angular velocity will change its direction and becomes equal in magnitude to the ration of linear velocity to radius when, pure rolling starts. Now the friction dissappears.
Moderation Team
![[Post New]](/templates/default/images/icon_minipost_new.gif){kind=icon}
![[Up]](/templates/default/images/icon_up.gif "[Up]"){kind=icon}
0
.so sphere has to rotate anticlockwise.
2
