Solving Momentum & Energy Homework Problem

[Veronica_Oles]

Homework Statement

Okay there is 2 boxes. One mass has a spring attached to it. They undergo a collision. The spring then has a constant of 600N/m.
M 1 = 1kg Vi1 = 4m/s Vf1 = 3m/s
M 2 = 2.10kg Vi2 = 2.50m/s
Determine Vf of M 2 and x value on impact.

2. Homework Equations

The Attempt at a Solution

I am just wondering if my method is correct for solving these questions.

First I would use the formula:
m1vi1 + m2vi2 = m1vf1 + m2vf2 to find the final velocity of m2.

Determining the X value is where I struggle. I know it's energy conservation but I'm not sure how to set it up.

I did Ee = Ekf + Ekf

I used my 2 final velocities in the equation due to the fact the question asked what was the X value impact.

Is this the correct way to solve this problem??

 

[kuruman]

Exactly what does the x value represent?

 

[Veronica_Oles]

Exactly what does the x value represent?

The displacement.. How much spring stretches or compresses from equilibrium.

 

[kuruman]

Since it's a collision, it must be compression and I would assume maximum compression. What is the relative velocity of the two masses at maximum compression?

 

[Veronica_Oles]

Since it's a collision, it must be compression and I would assume maximum compression. What is the relative velocity of the two masses at maximum compression?

I calculated that vf2 is 2.98 m/s.

 

[kuruman]

I calculated that vf2 is 2.98 m/s.

That's the final velocity of mass 2. I asked you for the relative velocity between the two masses when the spring is at maximum compression. Can you imagine what it could be?

 

[Veronica_Oles]

That's the final velocity of mass 2. I asked you for the relative velocity between the two masses when the spring is at maximum compression. Can you imagine what it could be?

Relative velocity: Vf1-Vf2 = 3.0-2.98 = 0.02??

 

[haruspex]

Vi1 = 4m/s Vf1 = 3m/s

Same direction or opposite directions?

 

[kuruman]

Relative velocity: Vf1-Vf2 = 3.0-2.98 = 0.02??

Just think. Maximum compression means that the spring is not being compressed any more instantaneously. At that instant (never mind what happens later): (1) can the two masses be moving relative to each other? (2) What is their total kinetic energy? (3) What is the potential energy stored in the spring?

 

[Veronica_Oles]

Same direction or opposite directions?

Pretty sure question did not give directions, it was just assumed one was going towards each other, then after collision away from each other.