Impulse and Net Force Equations

[lehel]

I have a problem in trying to express a net force equation for a falling elastic object when collision ensues.

For instance, you drop a spring with a spring coefficient k. the spring compresses a distance x after a time t for a maximum time of tf and distance xf. the spring has a weight W. during the collision, the ground creates a normal force N which is the result of impulse.

thus, calling the direction upward the positive y-axis, the net force on y = N - W - kx. My question is, what does the net force along y equal? Actually, my real question is if there is a point where N = W + kx. But even if at a certain point there is no total accerlation, you would have an equilibrium equation would you not? Isn't that impossible because if the spring was in equilibrium for even a fraction of time dt, wouldn't it stay at rest?

 

[benabean]

You are better attempting this question with the work-energy theorem. Because the force of spring changes over time, integration will be needed.

The maths is the easy part, visualizing the problem is were the work is.