How Does a Coefficient of Restitution of 1/3 Affect Post-Collision Speeds?

[arpitm08]

Coefficient of Restitution? PLEASE HELP!

Homework Statement

Two balls of equal mass moving with the speed of 3 m/s, collide head on. Find the speed of each after impact if the coefficient of restitution is 1/3.

Homework Equations

e=(v2-v1)/(u1-u2)
v2= velocity after impact of object 2
v1= velocity after impact of object 1
u2= velocity before impact of object 2
u1= velocity before impact of object 1

The Attempt at a Solution

I put the numbers into the equation and it yield 0 over something.
The answer is 1 m/s for both ball, but with that into the equation, it would yield 0/0.
My book doesn't say anything on how to do this problem. Maybe it is as simple as multiplying the velocities by 1/3 to get the answer.
Could someone please help me out?

 

[Doc Al]

direction counts!

Since the balls approach each other, one has a velocity of +3 m/s while the other has a velocity of -3 m/s.

 

[arpitm08]

yes that is true, but i just copied the problem exactly from the book.

 

[Doc Al]

yes that is true, but i just copied the problem exactly from the book.

There's nothing wrong with the problem statement, just with your attempted solution.

I put the numbers into the equation and it yield 0 over something.

That just means you input the wrong numbers. Realize that u and v are velocities, not just speeds.

 

[ajinx999]

Considering
u1 = 3 m/s
u2 = -3 m/s
e = 1/3
e = (v2-v1)/(u1-u2)
→ v2-v1 = 2 m/s
u1+u2=v1+v2
...(conservation of linear momentum)
→ v1+v2 = 0
→ v1 = -v2
Therefore, the speed of each ball after impact is 1 m/s.