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.

 

[astrokreng]

The net force equation for a falling elastic object during a collision can be expressed as follows:

Fnet = N - W - kx

Where N is the normal force from the ground, W is the weight of the object, and kx is the force exerted by the spring as it compresses.

To answer your question about when N = W + kx, this would occur at the point of maximum compression, when the spring is fully compressed and the object is at rest. At this point, the net force on the object would be zero, as it is in equilibrium. However, this is only a brief moment in time and the object will quickly start to move again due to the force of the spring pushing it back up.

In terms of the impossibility of equilibrium, it is important to remember that equilibrium is a state of balance, not necessarily a state of rest. In this situation, the object may be at rest momentarily, but it is still in a state of equilibrium because the forces acting on it are balanced. As soon as the forces become unbalanced again, the object will start to move.

I hope this helps to clarify the net force equation for a falling elastic object during a collision. It is a complex situation, and it is important to consider all of the forces at play in order to fully understand the motion of the object.