# Hard to imagine spring-mass problem

A mass moving with some initial speed hits a very very long NOT massless spring. Friction is ignored.
Will all of the kinetic energy that the mass had become the springs potential energy? And when the spring itself would start to move?
To me it smells like a nonelastic collision where all the kinetic energy is transfered to some other energy(in this case to the springs potential energy).
And what would happen after the mass stops?

A very confusing situation this is...

Wait, so what exactly are they asking of you? I mean, usually the physics classes ask for something like, "What is the potential energy of the [insert object here]," right? My advice so far is to write down the givens. Then you can use the physics principles to rule out the irrelevant material and finish the problem using the equations of classical mechanics. Although, depending on whether or not the problem is asking for a certain value, I could be giving you the completely wrong approach. Why don't you just type it all out word-for-word?

It is given that the initial speed is (v), the objects mass is M, the springs constant is (k), and the springs mass per unit length is (a). And you have to derive an equation how speed changes through time.

I just want some thoughts about whats going to happen.

You can model it a few different ways. For example, you could divide the spring into several smaller masses connected by ideal massless springs with spring constants of k. The free body diagram would take the acceleration of the spring masses into account along with the force of the object.

A characteristic of massive springs is the ability to support waves. The particle striking will generate waves in the spring (unless it is traveling faster than the speed of sound in the spring), which carry both potential and kinetic energy. This is what you will find if you follow timthereaper's procedure.

If you want to ignore the waves, for example, you actually have a long massless spring attached to a mass at the end, then the particle will impart some center of mass motion into the spring by conservation of momentum, and therefore impart kinetic energy.

It all depends on what you mean by a massive spring.

I believe it wouold generate a longitudinal wave. What would describe the generated waves and be helpfull for solving these problems?