Determine the compression in the spring

[rrosa522]

Homework Statement

A 1.2 kg glider moving at 3.0 m/s right

undergoes an elastic head-on collision with a glider of equal mass moving at 3.0 m/s left . T​

he collision is cushioned by a spring with k=6.0*10^4 N/m. Determine the compression in the spring when the second glider is moving at 1.5m/s. Ans =1.6cm

Homework Equations

same mass therefore..
vf1= Vi2
vf2= Vi1

The Attempt at a Solution

I think I would be able to do this question if could understand it. Is the initial velocity of the second glider 3m/s or 1.5m/s?. I would really appreciate if someone can explain this question to me because I really don't know where to start.​

 

[TSny]

Initially, before the collision, each mass is moving at 3.0 m/s.

 

[Let'sthink]

The equations given refer to the exchanged velocities after the collision wen they are not again in contact with each other. The question has been asked about the state when they are still existing force on each other through the spring. At that instant apply energy and momentum conservation.

 

[rrosa522]

Initially, before the collision, each mass is moving at 3.0 m/s.

My teacher told me that when the masses are identical then vf1= Vi2 and vf2= Vi1, so how is it even possible that vf2=1.5m/s ?

 

[Let'sthink]

Your teacher is right but does that happen in zero time just try to visualize the situation. Both change their momentum over a period of time called collision time. This time cannot be zero why. Why think it over. Suppose collision time is zero what will be the rate of change of momentum?

 

[rrosa522]

Your teacher is right but does that happen in zero time just try to visualize the situation. Both change their momentum over a period of time called collision time. This time cannot be zero why. Why think it over. Suppose collision time is zero what will be the rate of change of momentum?

the momentum of both bodies wouldn't change if collision time was zero

 

[Let'sthink]

It is given in the problem that the velocity of one has changed from 3.0 to 1.5. So what will be the velocity of the other as per conservation of momentum? Where has the KE of both gone?

 

[haruspex]

My teacher told me that when the masses are identical then vf1= Vi2 and vf2= Vi1, so how is it even possible that vf2=1.5m/s ?

That applies when 'final' refers to the completion of the collision process. It is clearly not true during the process. E.g., at some point they must both be instantaneously stationary.