# Find inequality for coefficient of restituition

1. Jul 7, 2015

### toforfiltum

1. The problem statement, all variables and given/known data
A small smooth sphere of mass 3 kg moving on a smooth horizontal plane with speed 8 ms-1 collides directly with a sphere of mass 12 kg which is at rest. Given that the spheres move in opposite directions after the collision, obtain the inequality satisfied by e.

2. Relevant equations
v2 - v1/u1 - u2 =e

3. The attempt at a solution
To be honest, I'm totally lost. I know that v2-v1= 8e, and 0≤e≤1. Also, using principle of conservation of momentum, I know that v1 + 4v2=8. I don't know how to solve this because I only have two equations for 3 unknowns. Any hints?

2. Jul 7, 2015

### haruspex

You have not used the constraint that after collision they move in opposite directions. What inequality does that give you?

3. Jul 7, 2015

### toforfiltum

Is it v2 - v1 ≥ 8?

4. Jul 7, 2015

### haruspex

No. Which way will the heavier mass move?

5. Jul 7, 2015

### toforfiltum

The heavier one will move to the right and take a positive velocity.

6. Jul 7, 2015

### haruspex

So what does that tell you about how the light mass moves off?

7. Jul 7, 2015

### toforfiltum

The light mass moves in the opposite direction with a negative velocity

8. Jul 7, 2015

### haruspex

So write that as an inequality.

9. Jul 7, 2015

### toforfiltum

I don't know....is the velocity of the lighter ball greater than velocity of heavier ball?
So v1 - v2≥ 0?

10. Jul 7, 2015

### toforfiltum

And less than 8?

11. Jul 7, 2015

### haruspex

Just write this statement
as an inequality.

12. Jul 7, 2015

### toforfiltum

Haha I'm feeling hopeless here. Please forgive my slowness. Is it -v1-v2≤8? I've tried this question for a long time...and I just can't get it.

13. Jul 7, 2015

### haruspex

The statement I've asked you to write as an inequality does not mention v2, so it will not feature in the inequality.

14. Jul 7, 2015

### toforfiltum

Ok, I have made some headway, but in the right direction or not I'm not sure. So v1≤8. And if so, using the equation from conservation of momentum, I'll get v2≥4. Is it right?

15. Jul 7, 2015

### toforfiltum

Ok, I have made some headway, but in the right direction or not. I'm not sure. So v1≤8. And if so, using the equation from conservation of momentum, I'll get v2≥4. Is it right?

16. Jul 7, 2015

### haruspex

If you are told x is negative, how would you write that as an inequality?

17. Jul 7, 2015

### toforfiltum

So it's -v1 ≥ -8 which gives v1 ≥ 8?

18. Jul 7, 2015

### haruspex

Forget 8, forget about this whole problem for the moment. If you are told that some number x is negative, how do you express that statement as an inequality?

19. Jul 7, 2015

### toforfiltum

n< 0

20. Jul 7, 2015

### haruspex

Right. So apply that to v1 and see where it leads.