Speed of recoil

Classical Mechanics Level 4

A solid sphere rolls on a horizontal surface without slipping at linear velocity v v and collides elastically with a fixed, smooth vertical wall. Find the speed of the sphere after it has started rolling without slipping away from the wall.

v 3v/7 7v/3 9v/7

Mohit Vyas by Mohit Vyas , 23, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

3 solutions

Jaivir Singh
Apr 27, 2014

APPLY CONSERVATION OF ANGULAR MOMENTUM ABOUT POINT OF CONTACT JUST AFTER COLLISION AND WHEN BODY STARTS PURE ROLLING MOTION. ANGULAR MOMENTUM IS CONSERVED BECAUSE FRICTION IS ACTING AND ITS TORQUE WILL BE ZERO ABOUT POINT OF CONTACT

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Manish Bhandari
Apr 25, 2014

let F be frictional force acting on the sphere and R be the radius of the solid sphere... Suppose the velocity before collision be V and angular velocity be W similarly after collision linear velocity be V' and angular velocity be W'... let "t" be the time for which frictional force acts after collision... then the equations can be given as... for linear motion... F.t = M(V-V') for rotational motion... F.R.t = 2/5MR*R(V'/R + V/R) by solving above we get V' = 3V/7

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Satvik Choudhary
Sep 10, 2015

Since friction must do some negative work energy must decrease and thus velocity will decrease there is only one option.

Although it is not a proper solution it can be useful sometimes.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...