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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

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
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I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
I'm not sure why it wrote it the other way
I got X =-6
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
Idrissa Reply
im all ears I need to learn
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what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
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a perfect square v²+2v+_
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algebra 2 Inequalities:If equation 2 = 0 it is an open set?
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or infinite solutions?
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
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Kristine 2*2*2=8
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Differences Between Laspeyres and Paasche Indices
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No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
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J, combine like terms 7x-4y
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how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
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Damian Reply
types of nano material
abeetha Reply
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Ramkumar Reply
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Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
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good afternoon madam
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what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
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silver nanoparticles could handle the job?
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Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele 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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