Question

Elias stretches a rubber band and let's it go. The rubber band flies across the room. Elias says this demonstrates the transformation of kinetic energy to elastic potential energy. Is Elias correct? Explain.

Answer 1

Answer:

This is not correct, actually it shows the transformation of elastic potential energy into kinetic energy.

Explanation:

We will explain this with and example and some numerical values to demostrate this energy transformation.

The elastic band has a behavior similar to a spring which is compressed and when released it transforms its energy from elastic to kinetic, we're going to choose a system which consists of a body 1 [kg], which is compressed against a spring with a constant of 20[kN/m], the maximum point where it is compressed is taken as the reference point where the energy potential is zero. When the package is released determine the maximum height the package reaches when released. The spring has been compressed 50 [mm].

In the attached image we can see a sketch of the mass and the spring, and the conditions of the block at maximum height.

The energy when we compress the spring will be:

$U_{1-2} =\frac{1}{2} *k*dx\\where\\k=spring constant [kN/m]\\dx=spring change [m]$

The energy when the block is in the highest position will be defined only by the potential energy with respect to the reference point. In this point the velocity is zero.

$U_{1-2} =\frac{1}{2} *(20000)*(50*10^-3)\\U_{1-2}= 500[J]\\Elastic energy = potential energy\\U_{1-2}=Ep\\Ep=m*g*h\\500 = 1*9.81*h\\h= 50 [m]$

We can see that the mass goes 50 [m] in the vertical direction, as a result of the transformation of elasticity energy into potential.