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Solving for masses in an elastic collision

  • Thread starter mruss
  • Start date
  • #1
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This isn't an actual homework problem, but it feels like it could be.

Homework Statement


Two masses, m1 and m2 are involved in an elastic collision. The initial velocities v1_0 and v2_0 are 1 and -2, respectively. The final velocities v1_1 and v2_1 are -3 and 0, respectively. Solve for m1 and m2.

Homework Equations


Given the collision is elastic, here are the two relevant equations:
1. m1*v1_0 + m2*v2_0 = m1*v1_1 + m2*v2_1
2. 1/2 (m1*v1_0^2 + m2*v2_0^2) = 1/2 (m1*v1_1^2 + m2*v2_1^2)

The Attempt at a Solution


I'm not sure what I'm doing wrong, but when I try to solve these 2 equations with 2 unknowns, I end up getting m1 = m2 = 0. For example, using equation 1 & 2 from above:
1. m1 - 2 * m2 = -3 * m1
→ 4 * m1 = 2 * m2
→ 2 * m1 = m2
2. m1 + 4 * m2 = 9 * m1
→ 4 * m2 = 8 * m1
→ 2 * m1 = m2

At this point, you only really have one equation so you can't solve for two unknowns, but if you do substitute 2 * m1 for m2 in the other equation you get 2 * m1 = 2 * m1 --> 0 = 0.

Any help would be appreciated, thanks.
 

Answers and Replies

  • #2
gneill
Mentor
20,793
2,773
What you've shown is that the ratio of the masses, m1/m2, is 1/2.
 
  • #3
6
0
Yes, I agree that I've done that. What I'm trying to do is solve for 2 masses in an elastic collision. Do you have advice on how to do that?
 
  • #4
1,540
134
This isn't an actual homework problem, but it feels like it could be.

Homework Statement


Two masses, m1 and m2 are involved in an elastic collision. The initial velocities v1_0 and v2_0 are 1 and -2, respectively. The final velocities v1_1 and v2_1 are -3 and 0, respectively. Solve for m1 and m2.

Homework Equations


Given the collision is elastic, here are the two relevant equations:
1. m1*v1_0 + m2*v2_0 = m1*v1_1 + m2*v2_1
2. 1/2 (m1*v1_0^2 + m2*v2_0^2) = 1/2 (m1*v1_1^2 + m2*v2_1^2)

The Attempt at a Solution


I'm not sure what I'm doing wrong, but when I try to solve these 2 equations with 2 unknowns, I end up getting m1 = m2 = 0. For example, using equation 1 & 2 from above:
1. m1 - 2 * m2 = -3 * m1
→ 4 * m1 = 2 * m2
→ 2 * m1 = m2
2. m1 + 4 * m2 = 9 * m1
→ 4 * m2 = 8 * m1
→ 2 * m1 = m2

At this point, you only really have one equation so you can't solve for two unknowns, but if you do substitute 2 * m1 for m2 in the other equation you get 2 * m1 = 2 * m1 --> 0 = 0.

Any help would be appreciated, thanks.
You have calculated m1/m2 =1/2 and as long as the two masses are in the ratio 1:2 say (4,8) (3,6),they all are valid solutions to the problem.

Nevertheless, 2(m1) =2(m1) doesnt mean m1=0 .

Take both the terms on one side,

2m1-2m1 =0 .
m1(2-2) = 0
m1(0) = 0

This means value of m1 is indeterminate :smile:.
 
  • #5
6
0
Thanks Tanya, I appreciate the response. I guess conservation of momentum and conservation of (kinetic) energy are not enough to solve for the masses in an elastic collision.

Do you know what additional information/formulas I would need to actually nail down the two masses, rather than just the relationship between them?

Thanks
 

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