# does elastic material have more Kinetic energy?



## kingofjong (Aug 21, 2021)

Hello 

If I were to apply force to elastic material will it have more kinetic energy then non elastic materials?

Thank you


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## Edgy Cheesy Graphite PE (Aug 23, 2021)

Welcome to EB @kingofjong
I must say, the way you asked this question isn't very clear, but I'll do my best to give you an answer.

When you say elastic material, I'm assuming you mean something less stiff like rubber, as compared to something more stiff like steel.
Or do you mean a material that has linear elastic behaving like a metal, as compared to something that has a different behavior like rubber, plastic, composite, etc. I'm going to assume you're taking about the first thing, less stiff vs more stiff.

Kinetic energy is the energy of movement. So only something that is moving has kinetic energy. The formula is KE = 0.5 * mass * velocity squared (KE=0.5*m*v^2).

Again, I'm assuming that you mean an unconstrained material where we're applying a force to change it's movement. As opposed to a material held in place where the force with deform it, not move it. Ok, so we apply a force to give the material kinetic energy, i.e. to accelerate it. The simple (i.e. school) answer is that acceleration is governed by the equation Force = mass * acceleration (F=m*a). Rearranging that to solve for a gives acceleration = Force / mass (a=F/m). So stiffness has nothing to do with it only force and mass. Therefore the amount of elasticity has nothing to do with the amount of kinetic energy.

The above explanation works well for a static force (a force that is constant or slowly applied). If you get into dynamic analysis (like a very short duration impact, or an explosive force, etc) things get more complicated. The full equation of motion is F = m*a + c*v + k*x (force = mass * acceleration + damping * velocity + stiffness * displacement). So some of the force energy goes into deforming the material which does depend on it's stiffness, i.e. it's elasticity. And some of the force energy gets damped out based on the internal velocity of the molecules of the material. In this case, yes the amount of elasticity could have some effect, but it would probably be extremely small difference.

The cutoff where things get more complicated depends on a few different things (natural frequency of the material, duration of the load application, etc) which are more complex than this explanation. But for common materials, unless you're talking about an explosion, a bullet impact, high frequency vibration, etc. Than the simpler explanation is fine.


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