Solving for masses in an elastic collision

AI Thread Summary
In the discussion about solving for masses in an elastic collision, the initial and final velocities of two masses, m1 and m2, are provided. The participant attempts to use conservation of momentum and kinetic energy equations but ends up with an indeterminate solution, finding that m1 and m2 must maintain a ratio of 1:2. They realize that while the equations yield a relationship between the masses, additional information is needed to determine their exact values. The conversation highlights the limitations of using just conservation laws for solving mass problems in elastic collisions. Further details or constraints are necessary to uniquely identify the masses involved.
mruss
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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.
 
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What you've shown is that the ratio of the masses, m1/m2, is 1/2.
 
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?
 
mruss said:
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) doesn't 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:.
 
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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