# 18.2 Conservation of energy  (Page 3/3)

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## Potential energy

1. A tennis ball, of mass $120\phantom{\rule{2pt}{0ex}}\mathrm{g}$ , is dropped from a height of $5\phantom{\rule{2pt}{0ex}}\mathrm{m}$ . Ignore air friction.
1. What is the potential energy of the ball when it has fallen $3\phantom{\rule{2pt}{0ex}}\mathrm{m}$ ?
2. What is the velocity of the ball when it hits the ground?
2. A bullet, mass $50\phantom{\rule{2pt}{0ex}}\mathrm{g}$ , is shot vertically up in the air with a muzzle velocity of $200\phantom{\rule{2pt}{0ex}}\mathrm{m}·\mathrm{s}{}^{-1}$ . Use the Principle of Conservation of Mechanical Energy to determine the height that the bullet will reach. Ignore air friction.
3. A skier, mass $50\phantom{\rule{2pt}{0ex}}\mathrm{kg}$ , is at the top of a $6,4\phantom{\rule{2pt}{0ex}}\mathrm{m}$ ski slope.
1. Determine the maximum velocity that she can reach when she skies to the bottom of the slope.
2. Do you think that she will reach this velocity? Why/Why not?
4. A pendulum bob of mass $1,5\phantom{\rule{2pt}{0ex}}\mathrm{kg}$ , swings from a height A to the bottom of its arc at B. The velocity of the bob at B is $4\phantom{\rule{2pt}{0ex}}\mathrm{m}·\mathrm{s}{}^{-1}$ . Calculate the height A from which the bob was released. Ignore the effects of air friction.
5. Prove that the velocity of an object, in free fall, in a closed system, is independent of its mass.

## Summary

• The potential energy of an object is the energy the object has due to his position above a reference point.
• The kinetic energy of an object is the energy the object has due to its motion.
• Mechanical energy of an object is the sum of the potential energy and kinetic energy of the object.
• The unit for energy is the joule (J).
• The Law of Conservation of Energy states that energy cannot be created or destroyed, but can only be changed from one form into another.
• The Law of Conservation of Mechanical Energy states that the total mechanical energy of an isolated system remains constant.
• The table below summarises the most important equations:
 Potential Energy ${E}_{P}=mgh$ Kinetic Energy ${E}_{K}=\frac{1}{2}m{v}^{2}$ Mechanical Energy ${E}_{M}={E}_{K}+{E}_{P}$

## End of chapter exercises: gravity and mechanical energy

1. Give one word/term for the following descriptions.
1. The force with which the Earth attracts a body.
2. The unit for energy.
3. The movement of a body in the Earth's gravitational field when no other forces act on it.
4. The sum of the potential and kinetic energy of a body.
5. The amount of matter an object is made up of.
2. Consider the situation where an apple falls from a tree. Indicate whether the following statements regarding this situation are TRUE or FALSE. Write only 'true' or 'false'. If the statement is false, write down the correct statement.
1. The potential energy of the apple is a maximum when the apple lands on the ground.
2. The kinetic energy remains constant throughout the motion.
3. To calculate the potential energy of the apple we need the mass of the apple and the height of the tree.
4. The mechanical energy is a maximum only at the beginning of the motion.
5. The apple falls at an acceleration of $9,8\phantom{\rule{2pt}{0ex}}\mathrm{m}·\mathrm{s}{}^{-2}$ .
3. A man fires a rock out of a slingshot directly upward. The rock has an initial velocity of $15\phantom{\rule{2pt}{0ex}}\mathrm{m}·\mathrm{s}{}^{-1}$ .
1. What is the maximum height that the rock will reach?
2. Draw graphs to show how the potential energy, kinetic energy and mechanical energy of the rock changes as it moves to its highest point.
4. A metal ball of mass $200\phantom{\rule{2pt}{0ex}}\mathrm{g}$ is tied to a light string to make a pendulum. The ball is pulled to the side to a height (A), $10\phantom{\rule{2pt}{0ex}}\mathrm{cm}$ above the lowest point of the swing (B). Air friction and the mass of the string can be ignored. The ball is let go to swing freely.
1. Calculate the potential energy of the ball at point A.
2. Calculate the kinetic energy of the ball at point B.
3. What is the maximum velocity that the ball will reach during its motion?
5. A truck of mass $1,2\phantom{\rule{2pt}{0ex}}\mathrm{tons}$ is parked at the top of a hill, $150\phantom{\rule{2pt}{0ex}}\mathrm{m}$ high. The truck driver lets the truck run freely down the hill to the bottom.
1. What is the maximum velocity that the truck can achieve at the bottom of the hill?
2. Will the truck achieve this velocity? Why/why not?
6. A stone is dropped from a window, $6\phantom{\rule{2pt}{0ex}}\mathrm{m}$ above the ground. The mass of the stone is $25\phantom{\rule{2pt}{0ex}}\mathrm{g}$ . Use the Principle of Conservation of Energy to determine the speed with which the stone strikes the ground.

anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
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 to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
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
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
how did you get the value of 2000N.What calculations are needed to arrive at it
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Berger describes sociologists as concerned with
The fundamental frequency of a sonometer wire streached by a load of relative density 's'are n¹ and n² when the load is in air and completly immersed in water respectively then the lation n²/na is
Properties of longitudinal waves