# Springs, elastic potential energy, kinetic energy

If a ball with some kinetic energy collides with a spring, the ball doesn't lose its kinetic energy in an instant, right? it loses kinetic energy as the spring gains potential elastic energy. Right?

So now I'm wondering. If I have a spring on the ground, and If I let the block falls from some meteres to collide with the spring on the ground. How can I calculate the maximum compression of the spring ?

I was thinking like this: The block has an Initial potential energy, that it's going to convert to kinetic energy, and at the time that the block collides with the spring the whole kinetic energy would transfer to the spring, so I could calculate all about the spring doing this:

say X is the initial potential energy of the BLOCK. Total Energy= Kinetic energy of the spring + Elastic Potential energy of the spring (=) X= Kinetic energy of the spring + Elastic Potential energy of the spring

But now I'm wondering if it wouldn't be more accurate to say that X= Kinetic energy of the spring + Elastic Potential energy of the spring - Kinetic energy of the ball !!

What do you think?

• We usually take the spring to be massless, so it has no kinetic energy. I think you need to work on clarifying what you are trying to say. – garyp May 26 '16 at 18:07
• I think you have to decide whether it's a ball or a block. If you drop a ball onto a stiff spring, the ball could bounce off without compressing the spring. (Technically that would be an elastic collision.) If you drop a block onto an easily compressed spring, then you're expecting an inelastic collision, i.e. the block stays in contact with the top of the spring. In that case, some of the energy will be converted to heat. So depending on your parameters, the heat loss may or may not be significant, and the kinetic energy of the spring may or may not be significant. – user3386109 May 26 '16 at 18:11
• @user3386109: that is not useful and quite confusing to the OP. Even a stiff spring will compress somewhat. That the cause of its elastic response. We're also assuming a Hookean spring: no heat is involved then. – Gert May 26 '16 at 19:15
• A massless, Hookean spring will convert the falling ball's kinetic energy to spring potential energy, until the ball momentarily stops. The restoring force of the spring will then start accelerating the ball upwards, until the spring's potential energy has been fully converted back to ball kinetic energy. You need to look up potential energy of a Hookean spring. – Gert May 26 '16 at 19:20
• @Gert You don't seem to understand the difference between an elastic response and an elastic/inelastic collision. It's clear from the question that the OP fully understands the theory behind a Hookean spring, and wants to go beyond that. – user3386109 May 26 '16 at 19:32