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v 2 = m 1 m 2 v 1 sin θ 1 sin θ 2

Entering known values into this equation gives

v 2 = 0 . 250 kg 0 . 400 kg 1 . 50 m/s 0 . 7071 0 . 7485 . size 12{ { {v}} sup { ' } rSub { size 8{2} } = - left ( { {0 "." "250"" kg"} over {0 "." "400"" kg"} } right ) left (1 "." "50"" m/s" right ) left ( { {0 "." "7071"} over { - 0 "." "7485"} } right ) "." } {}

Thus,

v 2 = 0 . 886 m/s . size 12{ { {v}} sup { ' } rSub { size 8{2} } =0 "." "886"" m/s"} {}

Discussion

It is instructive to calculate the internal kinetic energy of this two-object system before and after the collision. (This calculation is left as an end-of-chapter problem.) If you do this calculation, you will find that the internal kinetic energy is less after the collision, and so the collision is inelastic. This type of result makes a physicist want to explore the system further.

A purple ball of mass m1 and velocity v one moves in the right direction into a dark room. It collides with an object of mass m two of value zero point four zero milligrams which was initially at rest and then leaves the dark room from the top right hand side making an angle of forty-five degrees with the horizontal and at velocity v one prime. The net external force on the system is zero. The momentum before and after collision remains the same. The velocity v two prime of the mass m two and the angle theta two it would make with the horizontal after collision not given.
A collision taking place in a dark room is explored in [link] . The incoming object m 1 size 12{m rSub { size 8{1} } } {} is scattered by an initially stationary object. Only the stationary object’s mass m 2 size 12{m rSub { size 8{2} } } {} is known. By measuring the angle and speed at which m 1 size 12{m rSub { size 8{1} } } {} emerges from the room, it is possible to calculate the magnitude and direction of the initially stationary object’s velocity after the collision.

Elastic collisions of two objects with equal mass

Some interesting situations arise when the two colliding objects have equal mass and the collision is elastic. This situation is nearly the case with colliding billiard balls, and precisely the case with some subatomic particle collisions. We can thus get a mental image of a collision of subatomic particles by thinking about billiards (or pool). (Refer to [link] for masses and angles.) First, an elastic collision conserves internal kinetic energy. Again, let us assume object 2 m 2 size 12{ left (m rSub { size 8{2} } right )} {} is initially at rest. Then, the internal kinetic energy before and after the collision of two objects that have equal masses is

1 2 mv 1 2 = 1 2 mv 1 2 + 1 2 mv 2 2 .

Because the masses are equal, m 1 = m 2 = m size 12{m rSub { size 8{1} } =m rSub { size 8{2} } =m} {} . Algebraic manipulation (left to the reader) of conservation of momentum in the x size 12{x} {} - and y size 12{y} {} -directions can show that

1 2 mv 1 2 = 1 2 mv 1 2 + 1 2 mv 2 2 + mv 1 v 2 cos θ 1 θ 2 .

(Remember that θ 2 size 12{θ rSub { size 8{2} } } {} is negative here.) The two preceding equations can both be true only if

m v 1 v 2 cos θ 1 θ 2 = 0 .

There are three ways that this term can be zero. They are

  • v 1 = 0 : head-on collision; incoming ball stops
  • v 2 = 0 : no collision; incoming ball continues unaffected
  • cos ( θ 1 θ 2 ) = 0 : angle of separation ( θ 1 θ 2 ) is 90º after the collision

All three of these ways are familiar occurrences in billiards and pool, although most of us try to avoid the second. If you play enough pool, you will notice that the angle between the balls is very close to 90º size 12{"90"°} {} after the collision, although it will vary from this value if a great deal of spin is placed on the ball. (Large spin carries in extra energy and a quantity called angular momentum , which must also be conserved.) The assumption that the scattering of billiard balls is elastic is reasonable based on the correctness of the three results it produces. This assumption also implies that, to a good approximation, momentum is conserved for the two-ball system in billiards and pool. The problems below explore these and other characteristics of two-dimensional collisions.

Connections to nuclear and particle physics

Two-dimensional collision experiments have revealed much of what we know about subatomic particles, as we shall see in Medical Applications of Nuclear Physics and Particle Physics . Ernest Rutherford, for example, discovered the nature of the atomic nucleus from such experiments.

Questions & Answers

what are the factors effecting demand sedule
Kalimu Reply
we should talk about more important topics, you can search it on Google n u will find your answer we should try to focus on how we can improve our society using economics
shubham
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hon
ways of improving human capital
kelly Reply
what is human capital
kelly
Capital can be defined as man made assets use in production .
Abdulai
What is the differences between central Bank And Commercial Bank ?. 2 for each
Abdulai
Two types of bank clearing house.
Abdulai
what are the most durable assets of a bank
Ngongang
What is Opportunity Cost?
Cephas Reply
may be defined as expression of cost in terms of forgone alternative.
Abdulai
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Saniya Reply
You ask questions on any topics you find difficult.
Favour
What is opportunity cost?
Cephas
is price elasticity of demand the same as elasticity of demand
Favour Reply
not really
Victoria
hi
Gh
hello
Bhartendu
i hope everyone be ok
Gh
No
Hassan
please explain
Favour
No
William
explanations please
cleophas
price elasticity of demand is the reaction of customers /demand to price changes(increase or decrease) elasticity of demand is the reaction of prices brought about by the change in demand
Victoria
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Favour
state the laws of demand and supply
William
dd: when price rises demand decreases whereas when price reduces dd rises ss: when ss rises the price rises and when ss decreases price also reduces. There is a positive relationship
Dhoonah
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Victoria
Draw a demand curve graph
William
though price elasticity and elasticity are used interchangeably, the demand can respond to income changes and prices of related goods as well.
Gurpalak
explain the difference between merit goods and public goods and show why it is possible for profit to be made in the supply of one of these types of good but not the other
Kavishek
Public goods are defined as products where, for any given output, consumption by additional consumers does not reduce the quantity consumed by existing consumers. Merit goods are, for example, education and to some extent the health-care. They are provided by state as "good for you".
ahmed
The ladies are doing much better than the men
Blacks
what happens when there is a shift in demand curve?
Favour
What is Specialization ? Explain in detail
Muhammad
any one ?
Muhammad
specialisation is a method of production whereby an entity focuses on the production of a limited scope of goods to gain a greater degree of efficiency.
Favour
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Muhammad
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Onome
yah
Abdulai
No. price elasticity of demand refers to the manna in which price of good demanded fluctuate mean while elasticity of demand explains the way consumer change in their willingness as they plan or purchase a good
Ngongang
diffirence between demand and supply
Bonny
what is economic
Seray Reply
It is a social science which studies human behavior as a relationship between ends and scarce which have alternative uses
Obeng
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Demba Reply
is the wages measured in money as distinct from actual purchasing power
Favour
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Azeez Reply
this is a curve that slop downward from left to rich
Obeng
yes
Basanta
different between capital and wealth
Samuel Reply
Wealth refers to the amount of asset you have, while, capital is the amount of cash money you have with you now and willing to invest in any business.
Favour
What is scale of reference?
Finda Reply
What is monopoly?
Finda
It is the control of market by single seller or producer
Mayen
the exclusive possession or control of the supply or trade in a commodity or services
Brains
what is scarcity
Bonny Reply
scarcity means that the resources which we can produce goods and services relatives to wants for them.
Bonny
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Sophia Reply
demand means that's good demand according to your needs is called demand
Bonny
needs of people ar called demand
Francis
what's the difference between opportunity cost and production possibility curve?
Francis
apportunity cost means a goods which can be replace by other goods without any ease of saticfaction
Bonny
different between capital and wealth
Samuel
apportunity cost means the profit lose when one alternative is selected over other
Bonny
what is economocs
Bonny Reply
Economics is a science which studies human behaviour as a relationship between ends and scarce means which have alternative uses.
Abubakari
It deals with making choices in the face of scarcity
Abu
what is perfect complements?
Bilal Reply
explain the return to scale with the help of mathematical expression
Bilal
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Bonny
difference between fixed policy and monetary policies
Doris Reply
Difference between extinct and extici spicies
Amanpreet Reply
While the American heart association suggests that meditation might be used in conjunction with more traditional treatments as a way to manage hypertension
Beverly Reply
in a comparison of the stages of meiosis to the stage of mitosis, which stages are unique to meiosis and which stages have the same event in botg meiosis and mitosis
Leah Reply
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Source:  OpenStax, Introduction to applied math and physics. OpenStax CNX. Oct 04, 2012 Download for free at http://cnx.org/content/col11426/1.3
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