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By the end of this section, you will be able to:
  • Calculate the kinetic energy of a particle given its mass and its velocity or momentum
  • Evaluate the kinetic energy of a body, relative to different frames of reference

It’s plausible to suppose that the greater the velocity of a body, the greater effect it could have on other bodies. This does not depend on the direction of the velocity, only its magnitude. At the end of the seventeenth century, a quantity was introduced into mechanics to explain collisions between two perfectly elastic bodies, in which one body makes a head-on collision with an identical body at rest. The first body stops, and the second body moves off with the initial velocity of the first body. (If you have ever played billiards or croquet, or seen a model of Newton’s Cradle, you have observed this type of collision.) The idea behind this quantity was related to the forces acting on a body and was referred to as “the energy of motion.” Later on, during the eighteenth century, the name kinetic energy    was given to energy of motion.

With this history in mind, we can now state the classical definition of kinetic energy. Note that when we say “classical,” we mean non-relativistic, that is, at speeds much less that the speed of light. At speeds comparable to the speed of light, the special theory of relativity requires a different expression for the kinetic energy of a particle, as discussed in Relativity .

Since objects (or systems) of interest vary in complexity, we first define the kinetic energy of a particle with mass m .

Kinetic energy

The kinetic energy of a particle is one-half the product of the particle’s mass m and the square of its speed v :

K = 1 2 m v 2 .

We then extend this definition to any system of particles by adding up the kinetic energies of all the constituent particles:

K = 1 2 m v 2 .

Note that just as we can express Newton’s second law in terms of either the rate of change of momentum or mass times the rate of change of velocity, so the kinetic energy of a particle can be expressed in terms of its mass and momentum ( p = m v ) , instead of its mass and velocity. Since v = p / m , we see that

K = 1 2 m ( p m ) 2 = p 2 2 m

also expresses the kinetic energy of a single particle. Sometimes, this expression is more convenient to use than [link] .

The units of kinetic energy are mass times the square of speed, or kg · m 2 /s 2 . But the units of force are mass times acceleration, kg · m/s 2 , so the units of kinetic energy are also the units of force times distance, which are the units of work, or joules. You will see in the next section that work and kinetic energy have the same units, because they are different forms of the same, more general, physical property.

Kinetic energy of an object

(a) What is the kinetic energy of an 80-kg athlete, running at 10 m/s? (b) The Chicxulub crater in Yucatan, one of the largest existing impact craters on Earth, is thought to have been created by an asteroid, traveling at
22 km/s and releasing 4.2 × 10 23 J of kinetic energy upon impact. What was its mass? (c) In nuclear reactors, thermal neutrons, traveling at about 2.2 km/s, play an important role. What is the kinetic energy of such a particle?

Strategy

To answer these questions, you can use the definition of kinetic energy in [link] . You also have to look up the mass of a neutron.

Solution

Don’t forget to convert km into m to do these calculations, although, to save space, we omitted showing these conversions.

  1. K = 1 2 ( 80 kg ) ( 10 m/s ) 2 = 4.0 kJ .
  2. m = 2 K / v 2 = 2 ( 4.2 × 10 23 J ) / ( 22 km/s ) 2 = 1.7 × 10 15 kg .
  3. K = 1 2 ( 1.68 × 10 −27 kg ) ( 2.2 km/s ) 2 = 4.1 × 10 −21 J .

Significance

In this example, we used the way mass and speed are related to kinetic energy, and we encountered a very wide range of values for the kinetic energies. Different units are commonly used for such very large and very small values. The energy of the impactor in part (b) can be compared to the explosive yield of TNT and nuclear explosions, 1 megaton = 4.18 × 10 15 J . The Chicxulub asteroid’s kinetic energy was about a hundred million megatons. At the other extreme, the energy of subatomic particle is expressed in electron-volts, 1 eV = 1.6 × 10 −19 J . The thermal neutron in part (c) has a kinetic energy of about one fortieth of an electron-volt.

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Questions & Answers

Specific heat capacity .....what is the formulae for solving the SHC of a substance in respect to its container
E-vibes Reply
Heat ÷ (change in temperature x Mass)
akshay
what is symbol of nano
Iqra Reply
what is the symbol of nano
Iqra
n
Grant
n
Irtza
using dimensional analysis find the unit of gravitation constant G in F=G m1 m2/r
John Reply
Newton meter per kg square
Irtza
meter squre par second and kg swaure
Irtza
what are the possible sources of error in coefficient of static and dynamic friction and there precautions
GRACE
what is Bohr
Shcorah Reply
He is a physicist who formulated the atomic model of an Atom
Lily
And made 3 postulates
Lily
Check university physics vol 3 > Nuclear physics
Lily
Bohr model
kami
what is mean by Doppler effect
RAMANJI Reply
Good
Ahmad
increase or decrease in the frequency of sound and light.
Jhon
good
Eng
is it?
Vinayaka
actually it is apparent change in the frequency of light or sound as object move towards or away.
Vinayaka
state the basic assumption of kinetic theory of gases
FELIX Reply
state the characteristics of gases that differentiate them from solids
FELIX
identify the magnitude and direction a vector quantity
Alvean Reply
Identify work done on an inclined plane given at angle to the horizontal
DOLLY
formula for Velocity
Honey_and Reply
what is the value of x 6yx7y
Elijah Reply
what is the formula for frictional force
bassey Reply
I believe, correct me if I am wrong, but Ffr=Fn*mu
Grant
frictional force ,mathematically Fforce (Ffr) =K∆R where by K stands for coefficient of friction ,R stands for normal force/reaction NB: R = mass of a body ( m) x Acc.due gravity (g) The formula will hold the meaning if and only if the body is relatively moving with zero angle (∅ = 0°C)
Boay
What is concept associated with linear motion
Adeoye Reply
what causes friction?
Elijah
uneven surfaces cause friction Elijah
Shii
rough surfacea
Grant
what will happen to vapor pressure when you add solute to a solution?
shane Reply
how is freezing point depression different from boiling point elevation?
shane
how is the osmotic pressure affect the blood serum?
shane
what is the example of colligative properties that seen in everyday living?
shane
freezing point depression deals with the particles in the matter(liquid) loosing energy.....while boiling elevation is the particles of the matter(liquid)gaining energy
E-vibes
What is motion
Adeoye Reply
moving place to place
Addis
change position with respect to surrounding
Muhammad
to which
Addis
to where ?
Addis
the phenomenon of an object to changes its position with respect to the reference point with passage of time then it is called as motion
Shubham
it's just a change in position
festus
reference point -it is a fixed point respect to which can say that a object is at rest or motion
Shubham
yes
Shubham
A change in position
Lily
change in position depending on time
bassey
a change in the position of a body
E-vibes
Is there any calculation for line integral in scalar feild?
Sadia Reply
what is thrust
Aarti Reply
when an object is immersed in liquid, it experiences an upward force which is called as upthrust.
Phanindra
@Phanindra Thapa No, that is buoyancy that you're talking about...
Shii
thrust is simply a push
Shii
it is a force that is exerted by liquid.
Phanindra
what is the difference between upthrust and buoyancy?
misbah
The force exerted by a liquid is called buoyancy. not thrust. there are many different types of thrust and I think you should Google it instead of asking here.
Sharath
hey Kumar, don't discourage somebody like that. I think this conversation is all about discussion...remember that the more we discuss the more we know...
festus
thrust is an upward force acting on an object immersed in a liquid.
festus
uptrust and buoyancy are the same
akanbi
the question isn't asking about up thrust. he simply asked what is thrust
Shii
a Thrust is simply a push
Shii
the perpendicular force applied on the body
Shubham
thrust is a force of depression while
bassey
what is friction?
MFON
while upthrust is a force that act on a body when it is fully or partially submerged in a liquid
bassey
mathematically upthrust (u) = Real weight (wr) - Apparent weight (wa) u = wr- wa.
Boay
friction is a force which opposes relative motion.
Boay
Practice Key Terms 1

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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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