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K E = 1 2 m v 2

Consider the 1 kg suitcase on the cupboard that was discussed earlier. When the suitcase falls, it will gain velocity (fall faster), until it reaches the ground with a maximum velocity. The suitcase will not have any kinetic energy when it is on top of the cupboard because it is not moving. Once it starts to fall it will gain kinetic energy, because it gains velocity. Its kinetic energy will increase until it is a maximum when the suitcase reaches the ground.

A 1 kg brick falls off a 4 m high roof. It reaches the ground with a velocity of 8,85 m · s - 1 . What is the kinetic energy of the brick when it starts to fall and when it reaches the ground?

    • The mass of the rock m = 1 kg
    • The velocity of the rock at the bottom v bottom = 8,85 m · s - 1

    These are both in the correct units so we do not have to worry about unit conversions.

  1. We are asked to find the kinetic energy of the brick at the top and the bottom. From the definition we know that to work out K E , we need to know the mass and the velocity of the object and we are given both of these values.

  2. Since the brick is not moving at the top, its kinetic energy is zero.

  3. K E = 1 2 m v 2 = 1 2 ( 1 kg ) ( 8 , 85 m · s - 1 ) 2 = 39 , 2 J

Checking units

According to the equation for kinetic energy, the unit should be kg · m 2 · s - 2 . We can prove that this unit is equal to the joule, the unit for energy.

( kg ) ( m · s - 1 ) 2 = ( kg · m · s - 2 ) · m = N · m ( because Force ( N ) = mass ( kg ) × acceleration ( m · s - 2 ) ) = J ( Work ( J ) = Force ( N ) × distance ( m ) )

We can do the same to prove that the unit for potential energy is equal to the joule:

( kg ) ( m · s - 2 ) ( m ) = N · m = J

A bullet, having a mass of 150 g , is shot with a muzzle velocity of 960 m · s - 1 . Calculate its kinetic energy.

    • We are given the mass of the bullet m = 150 g . This is not the unit we want mass to be in. We need to convert to kg.
      Mass in grams ÷ 1000 = Mass in kg 150 g ÷ 1000 = 0 , 150 kg
    • We are given the initial velocity with which the bullet leaves the barrel, called the muzzle velocity, and it is v = 960 m · s - 1 .
    • We are asked to find the kinetic energy.
  1. We just substitute the mass and velocity (which are known) into the equation for kinetic energy:

    K E = 1 2 m v 2 = 1 2 ( 0 , 150 ) ( 960 ) 2 = 69 120 J

Kinetic energy

  1. Describe the relationship between an object's kinetic energy and its:
    1. mass and
    2. velocity
  2. A stone with a mass of 100 g is thrown up into the air. It has an initial velocity of 3 m · s - 1 . Calculate its kinetic energy
    1. as it leaves the thrower's hand.
    2. when it reaches its turning point.
  3. A car with a mass of 700 kg is travelling at a constant velocity of 100 km · hr - 1 . Calculate the kinetic energy of the car.

Mechanical energy

Mechanical energy is the sum of the gravitational potential energy and the kinetic energy.

Mechanical energy, U , is simply the sum of gravitational potential energy ( P E ) and the kinetic energy ( K E ). Mechanical energy is defined as:

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Maths test. OpenStax CNX. Feb 09, 2011 Download for free at http://cnx.org/content/col11236/1.2
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