Solving for masses in an elastic collision

In summary: Again, to summarize, the conversation is about an elastic collision problem involving two masses (m1 and m2) and their initial and final velocities. The relevant equations for this problem are given, but the attempt at solving for the masses using these equations results in an indeterminate solution. The expert suggests that there may be additional information or formulas needed to solve for the masses accurately.
  • #1
mruss
6
0
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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  • #2
What you've shown is that the ratio of the masses, m1/m2, is 1/2.
 
  • #3
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
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:.
 
  • #5
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
 

What is an elastic collision?

An elastic collision is a type of collision between two objects where there is no loss of kinetic energy. This means that the total kinetic energy before the collision is equal to the total kinetic energy after the collision.

How do you solve for masses in an elastic collision?

To solve for masses in an elastic collision, you can use the conservation of momentum and conservation of kinetic energy equations. These equations allow you to set the initial and final momentum and kinetic energy equal to each other and solve for the unknown masses.

What are the key concepts to understand when solving for masses in an elastic collision?

The key concepts to understand when solving for masses in an elastic collision are conservation of momentum, conservation of kinetic energy, and the concept of an elastic collision. It is also important to understand the difference between elastic and inelastic collisions, as the equations and solutions will differ between the two types of collisions.

What are some common mistakes when solving for masses in an elastic collision?

Some common mistakes when solving for masses in an elastic collision include not properly setting up the conservation of momentum and conservation of kinetic energy equations, not considering the direction of the velocities, and using the wrong equations for elastic collisions. It is important to carefully review the equations and ensure all variables are accounted for before solving.

What are some real-world applications of solving for masses in an elastic collision?

Solving for masses in an elastic collision is important in understanding and predicting the behavior of objects in collisions, such as in sports like billiards or in car crashes. It is also crucial in the design and testing of safety equipment, such as airbags, to ensure they can effectively absorb and dissipate the energy from collisions.

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