How Do You Determine the Mass of the Second Object in an Elastic Collision?

[katrvu]

An object with mass 3.6 kg is moving in the positive x direction when it strikea second object head-on. THe collision is elastic and afterwards both objects are moving in the positive x direction. If the final speed of the second object is equal to 8 times the final speed of the first object, what is the mass of the second object?

answer should be 2.62 kg. anyone knows how to solve it?

Thank you so much

 

[aniketp]

how did you try to approach the problem?

 

[katrvu]

well, it says it's elastic collision. so I came up with the following conservations:
let x direction be positive
1. from conservation of momentum
mv1-mv2=mv1f+mv2f
mv1-mv2=mv1f+m8v1f

2. from conservation of energy
1/2mv1^2+1/2mv2^2=1/2mv1f^2+1/2mv2f^2
mv1^2+mv2^2=mv1f^2+m64v1f^2

but there are so many unknows.. donno where to go from here

 

[aniketp]

It would be wiser to use the co-effecient of restitution here. The energy equation gets tedious. ;)

 

[Bob S]

Is the second object at rest when it is struck by the first object? What quantity has to be conserved in the described collision? What additional quantity is conserved if the collision is elastic (no energy dissipation)?

Next, let's do a thought experiment: Suppose the mass of the second object were the same as the first, what would the results of the collision be? Based on this result, and the description of of the unknown collision, is the mass of the second object more or less than the first?

 

[katrvu]

Is the second object at rest when it is struck by the first object? What quantity has to be conserved in the described collision? What additional quantity is conserved if the collision is elastic (no energy dissipation)?

Next, let's do a thought experiment: Suppose the mass of the second object were the same as the first, what would the results of the collision be? Based on this result, and the description of of the unknown collision, is the mass of the second object more or less than the first?

based on the question the 2nd object must be less because it's final speed is much faster, this is because of impulse I believe. The question doesn't say 2nd object is at rest, so 2nd object should have initial speed and collide head on. any suggestions?
thanks

 

[katrvu]

any idea?