What is the Velocity of the Spring After Compression?

[Chantry09]

Homework Statement

http://img521.imageshack.us/img521/4360/physicsjg1.jpg

Homework Equations

Elastic Energy = 0.5 x k x X²
Kinetic Energy = 0.5 x m x V²

The Attempt at a Solution

At 1m i worked out there is 1.922J of energy (0.5 x 10 x 0.62²) stored in the spring. Since no energy is lost and initially the spring has no energy i assume it must be:

Initial Kinetic Energy = Final Elastic Energy
Initial Kientic Energy = 1.922J
0.5 x m x V² = 1.922
0.5 x 10 x V² = 1.922
5 x V² = 1.922
V² = 0.384
V = 0.634 m/s

The answer however should be 0.876 m /s. Can someone please help me see where i have gone wrong?

James

 

[Doc Al]

For one thing, they are asking for the speed of the slider immediately after the collision. The spring hasn't stretched yet. (I assume that there are other parts to this question?)

Analyze the collision. Energy is not conserved during the collision; you are told that it's a partially inelastic collision. But what is conserved?

 

[Chantry09]

Momentum?

Im not told the speed of A so i can't work out the speed of B as a result of the collision. Therefore I've been using the rules of energy conservation. Initial kientic energy of B = Final elastic energy in spring?

 

[Doc Al]

typo!

Forget what I said in my last post. (I've got to learn to read more carefully. )

Your energy method is perfectly correct. But there is a typo in the problem. Note that on the diagram the spring constant is given as k = 20 N/m. Use that value and you'll get the required answer.

Sorry about that!

 

[Chantry09]

Ah i didnt spot that error on the sheet, i guess i should learn to read more carefully too!

Thank you.