General Rule for Spring Compression?

[FrenchAtticus]

Homework Statement

A block of mass m slides on a horizontal frictionless table with an initial speed. It then compresses a spring of force constant k and is brought to rest. How much is the spring compressed x from it's natural length.

Homework Equations

??

 

[mgb_phys]

Conservation of energy.
Whats the energy of a moving block
Whats the energy of a compressed spring

 

[FrenchAtticus]

Conservation of energy is mgh1 + 1/2mv1^2 = mgh2 + 1/2mv2^2

energy of a moving block is 1/2mv^2

energy of a compressed spring is potential?

How do I apply these to find how much the spring will compress.

 

[mgb_phys]

Conservation of energy is mgh1 + 1/2mv1^2 = mgh2 + 1/2mv2^2

No this is only for a falling object mgh2 = gravitational potential energy.

energy of a compressed spring is potential?

Whats the equation for the energy in a compressed spring?

 

[FrenchAtticus]

energy in a compressed spring is F = -Kx

and is conservation of energy m1v1 = m2v2?

 

[mgb_phys]

No that's momentum.
Spring energy = 1/2 k x^2
Kinetic energy = 1/2 m v ^2

For conservation of energy you have the ke of the block at the start and the spring energy at the end. So the ke just equals the spring energy.