How Does a Mass and Spring System Behave on an Inclined Plane?

[besenji]

Homework Statement

A spring (80 N/m) has an equilibrium length of 1.00 m. The spring is compressed to a length of 0.50 m and a mass of 2.2 kg is placed at its free end on a frictionless slope which makes an angle of 41 degrees with respect to the horizontal. The spring is then released. (Intro 1 figure)


If the mass is not attached to the spring, how far up the slope will the mass move before coming to rest?

If the mass is attached to the spring, how far up the slope will the mass move before coming to rest?

Now the incline has a coefficient of kinetic friction uk. If the block, attached to the spring, is observed to stop just as it reaches the spring's equilibrium position, what is the coefficient of friction uk?

1/2mv^2+mgh=1/2mv^2+mgh
1/2kx^2

This problem has been giving me a ton of trouble.

I am sure that it involves the conservation of energy theorm, ad the spring constant.

I just need help with he correct equations to be set in the right direction.

 

[alphysicist]

Homework Statement

A spring (80 N/m) has an equilibrium length of 1.00 m. The spring is compressed to a length of 0.50 m and a mass of 2.2 kg is placed at its free end on a frictionless slope which makes an angle of 41 degrees with respect to the horizontal. The spring is then released. (Intro 1 figure)


If the mass is not attached to the spring, how far up the slope will the mass move before coming to rest?

If the mass is attached to the spring, how far up the slope will the mass move before coming to rest?

Now the incline has a coefficient of kinetic friction uk. If the block, attached to the spring, is observed to stop just as it reaches the spring's equilibrium position, what is the coefficient of friction uk?

1/2mv^2+mgh=1/2mv^2+mgh

This energy equation (for conservation of energy) does not have the spring potential energy in it. It's just an extra term for each side:

1/2mv^2+mgh + 1/2 k x^2=1/2mv^2+mgh + 1/2 k x^2

where the terms on the left are for the initial point, and the terms on the right are for the final point. When you apply this equation to the first question, what does this equation become? What do you get as the answer?


(For the third question, energy is not conserved. How will the equation change for that?)