# Question 7c363

Oct 31, 2016

The Law of Conservation of Energy is one of the most important Physic's Laws. This law says that energy never is destroyed or created, it just changes from one form of energy to another.

#### Explanation:

Without going into details of the latest theories on the structure of the Universe and in particular theories about space, time and origin of matter, the principle of conservation of energy is a universal law.

This law says that the energy of the universe remains constant. This means that in any physical or chemical process, the total energy of universe remains constant. If a form of energy increases or decreases is always at the expense of other forms of energy decreases or increases, respectively.

A practical example of this would be the case of a body falling from a height. Suppose we are at a height $h$ on the ground and we are holding an object. When it is released, its initial velocity is zero, but due to the gravitational pull of the Earth, will start moving with a constant acceleration of $9.8 m / {s}^{2}$, so that when it reaches the ground will collide against it at a speed $v$ that if we estimate we will see that is v = sqrt {2 · g · h} .

What has happened from the point of view of energy?

When the object was at a height $h$ on the ground with velocity ${v}_{0} = 0$ its gravitational potential energy is U = m · g · h  and its kinetic energy ${E}_{k} = 0$.

We release the object and this is accelerating as it falls. On reaching the floor height is zero, so that the potential energy is now $U = 0$. What happened with the potential energy that was the object before falling? If we calculate the kinetic energy just when the object hits the ground, its value is E_k = 1 // 2 · m cdot v ^ 2 #. If we make the calculations we see that the potential energy loss suffered by the falling body has been transformed into a gain of kinetic energy in the same process.

If $\Delta U = U \left(g r o u n d\right) - U \left(u p\right)$ is the change in potential energy that has taken place in this process, and $\Delta {E}_{k} = {E}_{k} \left(g r o u n d\right) - {E}_{k} \left(u p\right)$ is the corresponding change in energy kinetics, according to the law of conservation of energy has to be that:

$\Delta E = \Delta U + \Delta {E}_{k} = 0 \Rightarrow \Delta U = - \Delta {E}_{k}$ .