Elastic collision between two bodies

AI Thread Summary
In an elastic collision, both momentum and kinetic energy are conserved, which is crucial for solving the problem of a 2.0 kg body colliding with a stationary body. The initial momentum equation is set up as m1v1i + m2v2i = m1v1f + m2v2f, where the first body continues moving at one-fourth its original speed after the collision. The challenge lies in determining the mass of the second body and its final velocity, which are not provided directly. To solve the problem, one can isolate variables in the momentum equation and substitute them into the energy conservation equation. This approach allows for the calculation of the unknown mass without needing the final velocity of the second body.
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Homework Statement


A body of mass 2.0Kg makes an elastic collision with another body at rest and continues to move in the original direction but with one-fourth of its original speed. What is the mass of the other body?

Homework Equations


Because it is an elastic collision I know that Energy and momentum are conserved.

So, m1v1i+ m2v2i = m1v1f+m2v2f

V1f = V2f = Vf

The Attempt at a Solution



I'm not really sure where to go because I'm not given the velocity of the second block after the collision.

2*v1i + 0 = 2*(1/4v1i) + m2v2I'm confused because it states that the original block continues to move in the original direction. Because the blocks don't adhere to each-other or go in opposite directions I'm not sure what to do.
 
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Lets say block A is the 2kg one initially moving and block B is the one initially stationary.
You are not told that the blocks do not stick together.
Even if they do not, it is possible for block B to end up moving faster than block A.

You are not told the mass of block B or it's final velocity, but you can write down two equations which must be true simultaneously. Write them down.
 
lookalike said:

Homework Statement


A body of mass 2.0Kg makes an elastic collision with another body at rest and continues to move in the original direction but with one-fourth of its original speed. What is the mass of the other body?


Homework Equations


Because it is an elastic collision I know that Energy and momentum are conserved.

So, m1v1i+ m2v2i = m1v1f+m2v2f

V1f = V2f = Vf





The Attempt at a Solution



I'm not really sure where to go because I'm not given the velocity of the second block after the collision.

2*v1i + 0 = 2*(1/4v1i) + m2v2





I'm confused because it states that the original block continues to move in the original direction. Because the blocks don't adhere to each-other or go in opposite directions I'm not sure what to do.


Just so you know you're told that it's an perfectly elastic collision so you know that both momentum and kinetic energy is conserved.

So why not just isolate for a variable in one equation plug it into the next equation to get the answer, while cancelling out any unknowns
 

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