Find inequality for coefficient of restituition

  • #1
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Homework Statement


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.

Homework Equations


v2 - v1/u1 - u2 =e

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?
 

Answers and Replies

  • #2
haruspex
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You have not used the constraint that after collision they move in opposite directions. What inequality does that give you?
 
  • #3
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Is it v2 - v1 ≥ 8?
 
  • #5
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No. Which way will the heavier mass move?
The heavier one will move to the right and take a positive velocity.
 
  • #6
haruspex
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The heavier one will move to the right and take a positive velocity.
So what does that tell you about how the light mass moves off?
 
  • #7
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So what does that tell you about how the light mass moves off?
The light mass moves in the opposite direction with a negative velocity
 
  • #8
haruspex
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The light mass moves in the opposite direction with a negative velocity
So write that as an inequality.
 
  • #9
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So write that as an inequality.
I don't know....is the velocity of the lighter ball greater than velocity of heavier ball?
So v1 - v2≥ 0?
 
  • #10
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I don't know....is the velocity of the lighter ball greater than velocity of heavier ball?
So v1 - v2≥ 0?
And less than 8?
 
  • #12
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Just write this statement

as an inequality.
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
haruspex
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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.
The statement I've asked you to write as an inequality does not mention v2, so it will not feature in the inequality.
 
  • #14
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The statement I've asked you to write as an inequality does not mention v2, so it will not feature in the inequality.
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
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The statement I've asked you to write as an inequality does not mention v2, so it will not feature in the inequality.
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
haruspex
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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?
If you are told x is negative, how would you write that as an inequality?
 
  • #17
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If you are told x is negative, how would you write that as an inequality?
So it's -v1 ≥ -8 which gives v1 ≥ 8?
 
  • #18
haruspex
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So it's -v1 ≥ -8 which gives v1 ≥ 8?
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
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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?
n< 0
 
  • #21
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Right. So apply that to v1 and see where it leads.
By substituting v1>0, into the equation from conservation of momentum, I get v2>2. Therefore, v2 -v1>2. Using this in coefficient of restitution equation yields e> 1/4
 
  • #22
haruspex
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By substituting v1>0, into the equation from conservation of momentum, I get v2>2. Therefore, v2 -v1>2. Using this in coefficient of restitution equation yields e> 1/4
I assume you meant v1<0, but that answer looks right.
 

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