Troubleshooting Spring and Masses: How to Solve for Maximum Compression?

[Physics_Boi]

1. Homework Statement

Attached in the picture below.

Homework Equations

Spring energy = 0.5Kx²
Kinetic energy = 0.5mv²

The Attempt at a Solution

I tried setting the equations for spring energy and kinetic energy equal, since I thought the maximum compression would occur when the box had no velocity, and stopped momentarily (in accordance with the Law of the Conservation of Energy)
0.5mv² = 0.5Kx² and when I solved for x, I got v * sqrt(m/K). I don’t know what I am missing, can somebody please help me?[/B]

 

[gneill]

There is no "picture below". I think you need to edit your post.

 

[rude man]

View attachment 236053
Attached in the picture below.

?

 

[Chestermiller]

What can you say about the velocities of the two masses when the spring attains maximum compression. In addition to energy being conserved, what else is conserved?

 

[Physics_Boi]

Oh could I also use conservation of momentum? Does that mean the second block would also have some velocity when the spring is compressed?

 

[Chestermiller]

Oh could I also use conservation of momentum? Does that mean the second block would also have some velocity when the spring is compressed?

Yes and yes

 

[rude man]

Oh could I also use conservation of momentum? Does that mean the second block would also have some velocity when the spring is compressed?

You shouldn't just guess. Why is momentum conserved?

 

[Physics_Boi]

Momentum would be conserved since there wouldn't be any external force acting on the object.

 

[rude man]

Momentum would be conserved since there wouldn't be any external force acting on the object.

Right, but think "the system" instead of the object which consists of the two masses and the spring

 

[Physics_Boi]

Ok thank you for the help! I solved the problem successfully using the conservation of momentum and energy!

 

[rude man]

Ok thank you for the help! I solved the problem successfully using the conservation of momentum and energy!

Congrats!