# Explain how it is possible for a ball to have kinetic and potential energy at the time?

Jun 4, 2017

It is possible.

#### Explanation:

There are many different types of energy we can talk about but in this particular example, I will give you the example of mechanical energy.

Take gravitational potential energy (PE), for example. This type of energy is the energy of an object due to some given height with respect to some reference level like on top of a hill or rooftop. Kinetic energy KE is the energy associated with the object due to its speed or motion like when you throw a ball or slide a box across a floor. The formulae are given below.

$\textcolor{w h i t e}{- - - - - -} P E = m g h \textcolor{w h i t e}{- - - -} K E = \frac{1}{2} m {v}^{2}$

So let's say you climbed on top of a tree in your backyard and decided you wanted to drop some acorns down at people. We will assume there is no air resistance (we live in some vacuum world) and remembering that the total mechanical energy of the system is constant

$- - - - - - - - - - - - - - - - - - - - -$

$\underline{\textcolor{b l u e}{\text{Moment you first drop the acorn}}}$

• The moment you drop the acorn, its initial speed is given to be $0 \frac{m}{s}$. What does this mean? This means the acorn does not have any KE at the moment since it has no speed. It does, however, have some height with respect to the ground level. This means it has potential energy. So, all the mechanical energy is due to its PE only, and nothing else.

$\textcolor{w h i t e}{- - - -}$

$\underline{\textcolor{\mathmr{and} a n \ge}{\text{The halfway point of the fall}}}$

• Now let's say you have already dropped the acorn at want to observe what happens at the mid point of the fall. Here, it still has some height, albeit a smaller one than when it was at the top of the tree, and it possesses some speed. Both its PE and KE will be half of the total mechanical energy of the acorn.

$\textcolor{w h i t e}{- - - -}$

$\underline{\textcolor{m a \ge n t a}{\text{Moment right before impact}}}$

• Lastly, right before impact, the acorn will achieve its greatest speed and its relative height will be $\text{0 m}$. Meaning, its mechanical energy at this point is all due to its KE only and nothing else.
Jun 4, 2017

.

#### Explanation:

There are numerous situations but I will explain the most common example.

A boy is holding a ball on top of a building of height. At this point, the ball possess gravitational potential energy and no kinetic energy as it is stationary.

He drops the ball down the building. During the duration of the fall, the ball's gravitational potential energy is converted to kinetic energy.

• Gravitational energy is given by mass x gravitational acceleration x height of ball relative to ground.

Thus, as the ball's height above ground decreases as it falls down, it loses GPE.

• Due to the Law of Conservation of Energy, the total energy of the ball remains unchanged. Thus, the loss in GPE has to be converted to another form of energy.

• The ball gains kinetic energy as it's velocity increases due to gravitational acceleration. (The ball also gains heat energy due to air friction, but shouldn't be too significant.)

Throughout the period of the fall, the ball possesses both GPE and KE.

When the ball is just about to land on the ground, it possesses no GPE and maximum KE.