# 0.3 Gravity and mechanical energy  (Page 7/9)

 Page 7 / 9
$U=PE+KE$
$\begin{array}{ccc}\hfill U& =& PE+KE\hfill \\ \hfill U& =& mgh+\frac{1}{2}m{v}^{2}\hfill \end{array}$

## Conservation of mechanical energy

The Law of Conservation of Energy states:

Energy cannot be created or destroyed, but is merely changed from one form into another.

Conservation of Energy

The Law of Conservation of Energy: Energy cannot be created or destroyed, but is merely changed from one form into another.

So far we have looked at two types of energy: gravitational potential energy and kinetic energy. The sum of the gravitational potential energy and kinetic energy is called the mechanical energy. In a closed system, one where there are no external forces acting, the mechanical energy will remain constant. In other words, it will not change (become more or less). This is called the Law of Conservation of Mechanical Energy and it states:

The total amount of mechanical energy in a closed system remains constant.

Conservation of Mechanical Energy

Law of Conservation of Mechanical Energy: The total amount of mechanical energy in a closed system remains constant.

This means that potential energy can become kinetic energy, or vise versa, but energy cannot 'dissappear'. The mechanical energy of an object moving in the Earth's gravitational field (or accelerating as a result of gravity) is constant or conserved, unless external forces, like air resistance, acts on the object.

We can now use the conservation of mechanical energy to calculate the velocity of a body in freefall and show that the velocity is independent of mass.

Show by using the law of conservation of energy that the velocity of a body in free fall is independent of its mass.

In problems involving the use of conservation of energy, the path taken by the object can be ignored. The only important quantities are the object's velocity (which gives its kinetic energy) and height above the reference point (which gives its gravitational potential energy).
In the absence of friction, mechanical energy is conserved and
${U}_{\mathrm{before}}={U}_{\mathrm{after}}$

In the presence of friction, mechanical energy is not conserved. The mechanical energy lost is equal to the work done against friction.

$\Delta U={U}_{\mathrm{before}}-{U}_{\mathrm{after}}=\mathrm{work}\mathrm{done}\mathrm{against}\mathrm{friction}$

In general, mechanical energy is conserved in the absence of external forces. Examples of external forces are: applied forces, frictional forces and air resistance.

In the presence of internal forces like the force due to gravity or the force in a spring, mechanical energy is conserved.

The following simulation covers the law of conservation of energy.
run demo

## Using the law of conservation of energy

Mechanical energy is conserved (in the absence of friction). Therefore we can say that the sum of the $PE$ and the $KE$ anywhere during the motion must be equal to the sum of the $PE$ and the $KE$ anywhere else in the motion.

We can now apply this to the example of the suitcase on the cupboard. Consider the mechanical energy of the suitcase at the top and at the bottom. We can say:

$\begin{array}{ccc}\hfill {U}_{top}& =& {U}_{bottom}\hfill \\ \hfill P{E}_{top}+K{E}_{top}& =& P{E}_{bottom}+K{E}_{bottom}\hfill \\ \hfill mgh+\frac{1}{2}m{v}^{2}& =& mgh+\frac{1}{2}m{v}^{2}\hfill \\ \hfill \left(1\right)\left(9,8\right)\left(2\right)+0& =& 0+\frac{1}{2}\left(1\right)\left({v}^{2}\right)\hfill \\ \hfill 19,6\phantom{\rule{3.33333pt}{0ex}}\mathrm{J}& =& \frac{1}{2}{v}^{2}\hfill \\ \hfill 39,2& =& {v}^{2}\hfill \\ \hfill v& =& 6,26\phantom{\rule{0.166667em}{0ex}}\mathrm{m}·{\mathrm{s}}^{-1}\hfill \end{array}$

The suitcase will strike the ground with a velocity of $6,26\phantom{\rule{2pt}{0ex}}m·s{}^{-1}$ .

what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how did you get the value of 2000N.What calculations are needed to arrive at it
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