# 0.1 Gravity and mechanical energy

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## Introduction

All objects have energy. The word energy comes from the Greek word energeia ( $έ\nu έ\rho \gamma \epsilon \iota \alpha$ ), meaning activity or operation. Energy is closely linked to mass and cannot be created or destroyed. In this chapter we will consider potential and kinetic energy.

## Potential energy

The potential energy of an object is generally defined as the energy an object has because of its position relative to other objects that it interacts with. There are different kinds of potential energy such as gravitional potential energy, chemical potential energy, electrical potential energy, to name a few. In this section we will be looking at gravitational potential energy.

Potential energy

Potential energy is the energy an object has due to its position or state.

Gravitational potential energy is the energy of an object due to its position above the surface of the Earth. The symbol ${E}_{P}$ is used to refer to gravitational potential energy. You will often find that the words potential energy are used where gravitational potential energy is meant. We can define potential energy (or gravitational potential energy, if you like) as:

${E}_{P}=mgh$

where ${E}_{P}$ = potential energy measured in joules (J)

m = mass of the object (measured in kg)

g = gravitational acceleration ( $9,8\phantom{\rule{2pt}{0ex}}\mathrm{m}·\mathrm{s}{}^{-2}$ )

h = perpendicular height from the reference point (measured in m)

You may sometimes see potential energy written as $\mathrm{PE}$ . We will not use this notation in this book, but you may see it in other books.

A suitcase, with a mass of $1\phantom{\rule{2pt}{0ex}}\mathrm{kg}$ , is placed at the top of a $2\phantom{\rule{2pt}{0ex}}\mathrm{m}$ high cupboard. By lifting the suitcase against the force of gravity, we give the suitcase potential energy. This potential energy can be calculated using [link] .

If the suitcase falls off the cupboard, it will lose its potential energy. Halfway down the cupboard, the suitcase will have lost half its potential energy and will have only $9,8\phantom{\rule{2pt}{0ex}}\mathrm{J}$ left. At the bottom of the cupboard the suitcase will have lost all it's potential energy and it's potential energy will be equal to zero.

Objects have maximum potential energy at a maximum height and will lose their potential energy as they fall.

A brick with a mass of $1\phantom{\rule{2pt}{0ex}}\mathrm{kg}$ is lifted to the top of a $4\phantom{\rule{2pt}{0ex}}m$ high roof. It slips off the roof and falls to the ground. Calculate the potential energy of the brick at the top of the roof and on the ground once it has fallen.

• The mass of the brick is $m=1\phantom{\rule{2pt}{0ex}}\mathrm{kg}$
• The height lifted is $h=4\phantom{\rule{2pt}{0ex}}\mathrm{m}$

All quantities are in SI units.

• We are asked to find the gain in potential energy of the brick as it is lifted onto the roof.
• We also need to calculate the potential energy once the brick is on the ground again.
1. Since the block is being lifted we are dealing with gravitational potential energy. To work out ${E}_{P}$ , we need to know the mass of the object and the height lifted. As both of these are given, we just substitute them into the equation for ${E}_{P}$ .

2. $\begin{array}{ccc}\hfill {E}_{P}& =& mgh\hfill \\ & =& \left(1\right)\left(9,8\right)\left(4\right)\hfill \\ & =& 39,2\phantom{\rule{0.166667em}{0ex}}\mathrm{J}\hfill \end{array}$

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nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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Daniel
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Abigail
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Anassong
Do somebody tell me a best nano engineering book for beginners?
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are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
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Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
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CYNTHIA
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Harper
Do you know which machine is used to that process?
s.
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for screen printed electrodes ?
SUYASH
What is lattice structure?
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Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
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Cied
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Cied
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I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
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Porter
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Yasmin
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Cesar
I'm interested in nanotube
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how to synthesize TiO2 nanoparticles by chemical methods
Zubear
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