Welcome to NRICH.

 
Collision and coeeficient of restitution
By Anonymous on Wednesday, November 29, 2000 - 04:08 pm:

Hi,

I could not figure out the following and would appreciate some help. Thanks.

A small smooth sphere of mass 3kg moving on a smooth horizontal plane with a speed of 8 ms/sec collides directly with a sphere of mass 12kg which is at rest. Given that the spheres move in opposite directions after the collision, obtain the inequality satisfied by e.

By Kerwin Hui (Kwkh2) on Wednesday, November 29, 2000 - 06:04 pm:

Write out the equation for the conservation of linear momentum, and Newton's law of restitution:

24=3u+12v
8e=v-u

Solve for u, and set u<0

Kerwin

By Nikhil Shah (P3372) on Wednesday, November 29, 2000 - 06:57 pm:

I approached in the same manner, and ended up with e>1/4.

Is that correct?

By Anonymous on Wednesday, November 29, 2000 - 07:14 pm:

Kerwin,

I got those two equations.
But was unsure of what to do with it.
Therefore 3 variables.

By Kerwin Hui (Kwkh2) on Wednesday, November 29, 2000 - 09:19 pm:

8=u+4v, 8e=v-u

Eliminate v (and thus obtaining u in terms of e), and set u<0 will give you the inequality you need.

Kerwin

By Anonymous on Thursday, November 30, 2000 - 10:02 am:

OK thanks, I get that, but I'm not sure why you set u<0?

By Kerwin Hui (Kwkh2) on Thursday, November 30, 2000 - 11:52 am:

Obviously v is positive, so we need u to be negative for the spheres moving in opposite direction.

Kerwin

By Kerwin Hui (Kwkh2) on Thursday, November 30, 2000 - 11:53 am:

By the way, Nikhil, don't forget that e is not greater than 1 in reality...

By Anonymous on Thursday, November 30, 2000 - 12:54 pm:

Oh I now see. Thanks!