Is There a Conservation Equation for Spring Forces and Potential Energy?

[pb23me]

Homework Statement

I just have a question about the force of a spring. Since the force of a spring force is a conservative force, is there a conservation equation for springs? Also, when a mass is put on a spring and it streches out fully, at this point velocity is zero and potential energy is at its max. What can i set potential energy equal to at this point?

Homework Equations

The Attempt at a Solution

 

[PhanthomJay]

Homework Statement

I just have a question about the force of a spring. Since the force of a spring force is a conservative force, is there a conservation equation for springs?

yes, it is similar to the conservation of energy equation with the added terms of the spring's potential energy

Also, when a mass is put on a spring and its streches out fully, at this point velocity is zero and potential energy is at its max. What can i set potential energy equal to at this point?

Use the conservation of energy equation! What is the potential energy of a spring?

 

[pb23me]

ok so would it be kx_i²+mv_i²=kx_f²+mv_f²

 

[PhanthomJay]

ok so would it be kx_i²+mv_i²=kx_f²+mv_f²

Yes, if the the spring was horizontal and no other forces (like friction) acting..If the spirng was hanging vertical and the mass released, you'd have to include the gravitational potential energy change also. (It's a good idea to not drop the '1/2' term, even though it cancels out in this first example).

 

[pb23me]

ok so if it were hanging vertically it would be mgy_i+1/2mv_i²+1/2kx_i²=mgy_f+1/2mv_f²+1/2kx_f²?

 

[PhanthomJay]

ok so if it were hanging vertically it would be mgy_i+1/2mv_i²+1/2kx_i²=mgy_f+1/2mv_f²+1/2kx_f²?

yes, indeed.

 

[pb23me]

awsome maybe you could take a look at my other prob entitled simple harmonic motion haha