# 0.3 Gravity and mechanical energy  (Page 8/9)

 Page 8 / 9

From this we see that when an object is lifted, like the suitcase in our example, it gains potential energy. As it falls back to the ground, it will lose this potential energy, but gain kinetic energy. We know that energy cannot be created or destroyed, but only changed from one form into another. In our example, the potential energy that the suitcase loses is changed to kinetic energy.

The suitcase will have maximum potential energy at the top of the cupboard and maximum kinetic energy at the bottom of the cupboard. Halfway down it will have half kinetic energy and half potential energy. As it moves down, the potential energy will be converted (changed) into kinetic energy until all the potential energy is gone and only kinetic energy is left. The $19,6\phantom{\rule{2pt}{0ex}}J$ of potential energy at the top will become $19,6\phantom{\rule{2pt}{0ex}}J$ of kinetic energy at the bottom.

During a flood a tree truck of mass $100\phantom{\rule{2pt}{0ex}}\mathrm{kg}$ falls down a waterfall. The waterfall is $5\phantom{\rule{2pt}{0ex}}m$ high. If air resistance is ignored, calculate

1. the potential energy of the tree trunk at the top of the waterfall.
2. the kinetic energy of the tree trunk at the bottom of the waterfall.
3. the magnitude of the velocity of the tree trunk at the bottom of the waterfall.

• The mass of the tree trunk $m=100\phantom{\rule{2pt}{0ex}}\mathrm{kg}$
• The height of the waterfall $h=5\phantom{\rule{2pt}{0ex}}m$ . These are all in SI units so we do not have to convert.
• Potential energy at the top
• Kinetic energy at the bottom
• Velocity at the bottom
1. $\begin{array}{ccc}\hfill PE& =& mgh\hfill \\ \hfill PE& =& \left(100\right)\left(9,8\right)\left(5\right)\hfill \\ \hfill PE& =& 4900\phantom{\rule{3.33333pt}{0ex}}\mathrm{J}\hfill \end{array}$
2. The kinetic energy of the tree trunk at the bottom of the waterfall is equal to the potential energy it had at the top of the waterfall. Therefore $KE=4 900\phantom{\rule{2pt}{0ex}}J$ .

3. To calculate the velocity of the tree trunk we need to use the equation for kinetic energy.

$\begin{array}{ccc}\hfill KE& =& \frac{1}{2}m{v}^{2}\hfill \\ \hfill 4900& =& \frac{1}{2}\left(100\right)\left({v}^{2}\right)\hfill \\ \hfill 98& =& {v}^{2}\hfill \\ \hfill v& =& 9,899...\hfill \\ \hfill v& =& 9,90\phantom{\rule{0.166667em}{0ex}}\mathrm{m}·{\mathrm{s}}^{-1}\mathrm{downwards}\hfill \end{array}$

A $2\phantom{\rule{2pt}{0ex}}\mathrm{kg}$ metal ball is suspended from a rope. If it is released from point $A$ and swings down to the point $B$ (the bottom of its arc):

1. Show that the velocity of the ball is independent of it mass.
2. Calculate the velocity of the ball at point $B$ .

• The mass of the metal ball is $m=2\phantom{\rule{2pt}{0ex}}\mathrm{kg}$
• The change in height going from point $A$ to point $B$ is $h=0,5\phantom{\rule{2pt}{0ex}}m$
• The ball is released from point $A$ so the velocity at point, ${v}_{A}=0\phantom{\rule{2pt}{0ex}}m·s{}^{-1}$ .

All quantities are in SI units.

• Prove that the velocity is independent of mass.
• Find the velocity of the metal ball at point $B$ .
1. As there is no friction, mechanical energy is conserved. Therefore:

$\begin{array}{ccc}\hfill {U}_{A}& =& {U}_{B}\hfill \\ \hfill P{E}_{A}+K{E}_{A}& =& P{E}_{B}+K{E}_{B}\hfill \\ \hfill mg{h}_{A}+\frac{1}{2}m{\left({v}_{A}\right)}^{2}& =& mg{h}_{B}+\frac{1}{2}m{\left({v}_{B}\right)}^{2}\hfill \\ \hfill mg{h}_{A}+0& =& 0+\frac{1}{2}m{\left({v}_{B}\right)}^{2}\hfill \\ \hfill mg{h}_{A}& =& \frac{1}{2}m{\left({v}_{B}\right)}^{2}\hfill \end{array}$

As the mass of the ball $m$ appears on both sides of the equation, it can be eliminated so that the equation becomes:

$g{h}_{A}=\frac{1}{2}{\left({v}_{B}\right)}^{2}$
$2g{h}_{A}={\left({v}_{B}\right)}^{2}$

This proves that the velocity of the ball is independent of its mass. It does not matter what its mass is, it will always have the same velocity when it falls through this height.

2. We can use the equation above, or do the calculation from 'first principles':

$\begin{array}{ccc}\hfill {\left({v}_{B}\right)}^{2}& =& 2g{h}_{A}\hfill \\ \hfill {\left({v}_{B}\right)}^{2}& =& \left(2\right)\left(9.8\right)\left(0,5\right)\hfill \\ \hfill {\left({v}_{B}\right)}^{2}& =& 9,8\hfill \\ \hfill {v}_{B}& =& \sqrt{9,8}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{0.166667em}{0ex}}\mathrm{m}·{\mathrm{s}}^{-1}\hfill \end{array}$

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
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
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
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