Work involving motion of object on inlined plane with force of a spring

[Violagirl]

Homework Statement

1) Draw a picture of the situation at three different times: one where the cart is
traveling down the track, one where the cart is at maximum extension, and one
where the cart is traveling back up the track. Label all relevant quantities on the
diagram for each time.

2) Define the system of interest so that you can use gravitational potential energy,
spring potential energy, and kinetic energy. Write the energy conservation equation
for the system that relates its initial energy to its energy at any point during its
motion.

Homework Equations

For a spring: F=-kx
W=mas=F*s
k=1/2mv²
μ=-mg(h-h₀)
E = E₀+W_a

The Attempt at a Solution

This is for my prelab homework.

For the first question, I drew out the three situations. For situation one, the relevant forces are the normal force and gravitational forces.

For situation two, when the cart reaches a maximum acceleration, the normal and gravitational forces still apply along with the force of the spring, kx in the opposite direction.

For the situation three when the cart moves backwards, the acceleration is in the opposite direction, and the forces of the spring, normal force, and gravitational forces all apply.

Question two is where I am stuck. In selecting a situation where an equation can be set up to represent each force, I am thinking that situation three would apply? I'm just having some confusion in setting it up. Here's what I am thinking:

K+μ=K₀+E₀+W_a

F_x: 1/2mv²-mg(h-h₀)=1/2m₀v²-mg(h-h₀)-kx+N cos θ

F_y: W=ma_ys=0;
N sinθ-mg(h-h₀)=0

My thanks and appreciation goes out to anyone that looks and checks this for me, I've been having a hard time with it.

 

[Violagirl]

Just wanted to bump this up as I'm still unsure. Thanks everyone!

 

[haruspex]

Homework Statement

1) Draw a picture of the situation at three different times: one where the cart is
traveling down the track, one where the cart is at maximum extension, and one
where the cart is traveling back up the track. Label all relevant quantities on the
diagram for each time.

Seems like there is some earlier description missing. Is the initial state with the spring at zero extension?

Homework Equations

For a spring: F=-kx
W=mas=F*s
k=1/2mv²
μ=-mg(h-h₀)
E = E₀+W_a

These are not all self-explanatory. Please define the variables.

For the situation three when the cart moves backwards, the acceleration is in the opposite direction, and the forces of the spring, normal force, and gravitational forces all apply.

The movement is in the opposite direction, but how about the acceleration?

Question two is where I am stuck. In selecting a situation where an equation can be set up to represent each force, I am thinking that situation three would apply?

One or three will do - they're both generic situations.
Your equations cannot be right because they mix energy and force.
After defining your variables properly, write down the expressions for:
- energy in the spring
- kinetic energy of the cart
- potential energy of the cart