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By the end of this section, you will be able to:
  • Identify the type of collision
  • Correctly label a collision as elastic or inelastic
  • Use kinetic energy along with momentum and impulse to analyze a collision

Although momentum is conserved in all interactions, not all interactions (collisions or explosions) are the same. The possibilities include:

  • A single object can explode into multiple objects (one-to-many).
  • Multiple objects can collide and stick together, forming a single object (many-to-one).
  • Multiple objects can collide and bounce off of each other, remaining as multiple objects (many-to-many). If they do bounce off each other, then they may recoil at the same speeds with which they approached each other before the collision, or they may move off more slowly.

It’s useful, therefore, to categorize different types of interactions, according to how the interacting objects move before and after the interaction.

One-to-many

The first possibility is that a single object may break apart into two or more pieces. An example of this is a firecracker, or a bow and arrow, or a rocket rising through the air toward space. These can be difficult to analyze if the number of fragments after the collision is more than about three or four; but nevertheless, the total momentum of the system before and after the explosion is identical.

Note that if the object is initially motionless, then the system (which is just the object) has no momentum and no kinetic energy. After the explosion, the net momentum of all the pieces of the object must sum to zero (since the momentum of this closed system cannot change). However, the system will have a great deal of kinetic energy after the explosion, although it had none before. Thus, we see that, although the momentum of the system is conserved in an explosion, the kinetic energy of the system most definitely is not; it increases. This interaction—one object becoming many, with an increase of kinetic energy of the system—is called an explosion    .

Where does the energy come from? Does conservation of energy still hold? Yes; some form of potential energy is converted to kinetic energy. In the case of gunpowder burning and pushing out a bullet, chemical potential energy is converted to kinetic energy of the bullet, and of the recoiling gun. For a bow and arrow, it is elastic potential energy in the bowstring.

Many-to-one

The second possibility is the reverse: that two or more objects collide with each other and stick together, thus (after the collision) forming one single composite object. The total mass of this composite object is the sum of the masses of the original objects, and the new single object moves with a velocity dictated by the conservation of momentum. However, it turns out again that, although the total momentum of the system of objects remains constant, the kinetic energy doesn’t; but this time, the kinetic energy decreases. This type of collision is called inelastic    .

In the extreme case, multiple objects collide, stick together, and remain motionless after the collision. Since the objects are all motionless after the collision, the final kinetic energy is also zero; the loss of kinetic energy is a maximum. Such a collision is said to be perfectly inelastic    .

Questions & Answers

Olympus Mons on Mars is the largest volcano in the solar system, at a height of 25 km and with a radius of 312 km. If you are standing on the summit, with what initial velocity would you have to fire a projectile from a cannon horizontally to clear the volcano and land on the surface of Mars? Note that Mars has an acceleration of gravity of 3.7 m/s2 .
Eloisa Reply
पृथवी को इसके अक्ष पर कितने कोणीय चाल से घूमाऐ कि भूमधय पे आदमी का भार इसके वासतविक भार से 3/5अधिक हो
Vasudev Reply
best
Murari
At a post office, a parcel that is a 20.0-kg box slides down a ramp inclined at 30.0° 30.0° with the horizontal. The coefficient of kinetic friction between the box and plane is 0.0300. (a) Find the acceleration of the box. (b) Find the velocity of the box as it reaches the end of the plane, if the length of the plane is 2 m and the box starts at rest.
Kaitlin Reply
As an IT student must I take physics seriously?
Akaare Reply
yh
Bernice
hii
Raja
IT came from physics and maths so I don't see why you wouldn't
Brad
conditions for pure rolling
Md
the time period of jupiter is 11.6 yrs. how far is jupiter from the sun. distance of earth from rhe sun is 1.5*10 to the power 11 meter.
Abu Reply
lists 5 drawing instruments and their uses
Micahlolo Reply
that is a question you can find on Google, anyway of top of my head, compass, ruler, protractor, try square, triangles.
Rongfang
A force F is needed to break a copper wire having radius R. The force needed to break a copper wire of radius 2R will be
Lalit Reply
2F
Jacob
it will be doubled
kelvin
double
Devesh
The difference between vector and scaler quantity
Yakubu Reply
vector has both magnitude & direction but scalar has only magnitude
Manash
my marunong ba dto mag prove ng geometry
ron
how do I find resultant of four forces at a point
Inusah
use the socatoa rule
kingsley
draw force diagram, then work out the direction of force.
Rongfang
In a closed system of forces... Summation of forces in any direction or plane is zero... Resolve if there is a need to then add forces in a particular plane or direction.. Say the x direction... Equate it tk zero
Jacob
define moment of inertia
Manoj Reply
it is the tendency for a body to continue in motion if is or continue to be at rest if it is.
prince
what is Euler s theorem
Manoj Reply
what is thermocouple?
Manoj Reply
joining of two wire of different material forming two junctions. If one is hot and another is cold the it will produce emf...
Badri
joining of two metal of different materials to form a junction in one is hot & another is cold
Manash
define dimensional analysis
Dennis Reply
mathematical derivation?
Hira
explain what Newtonian mechanics is.
Elizabeth Reply
a system of mechanics based of Newton laws motion this is easy difenation of mean...
Arzoodan
what is the meaning of single term,mechanics?
jyotirmayee
mechanics is the science related to the behavior of physical bodies when some external force is applied to them
Lalita
SO ASK What is Newtonian mechanics in physics? Newtonian physics, also calledNewtonian or classical mechanics, is the description of mechanical events—those that involve forces acting on matter—using the laws of motion and gravitation formulated in the late seventeenth century by English physicist
Suleiman
can any one send me the best reference book for physics?
Prema
concept of physics by HC verma, Fundamentals of Physics, university of physics
Bhaskar
tq u.
Prema
these are the best physics books one can fond both theory and applications.
Bhaskar
can any one suggest best book for maths with lot of Tricks?
Vivek
what is the water height in barometer?
SUNEELL
13.5*76 cm. because Mercury is 13.5 times dense than Mercury
LOVE
water is 13.5 times dense than the Mercury
LOVE
plz tell me frnds the best reference book for physics along with the names of authors.
Prema
i recomended the reference book for physics from library University of Dublin or library Trinity college
Arzoodan
A little help here... . 1. Newton's laws of Motion, are they applicable to motions of all speeds? 2.state the speeds which are applicable to Newtons laws of Motion
Derek
mechanics which follows Newtons law
Manash
The definition of axial and polar vector .
Arpita
polar vector which have a starting point or pt. of applications is,force,displacement
jyotirmayee
axial vector represent rotational effect and act along the axis of rotation b
jyotirmayee
prove Newton's first law of motion
prince
Hello frnds what is physics in general?
Ngeh
A block of mass m is attached to a spring with spring constant k and free to slide along a horizontal frictionless surface. At t=0, the block spring system is stretched on amount x>0 from the equilibrium position and is released from rest Vx = 0 What is the period of oscillation of the block? What
Ella
What is the velocity of the block when it first comes back to the equilibrium position?
Ella
explain the rule of free body diagram
Mithu Reply
The polar coordinates of a point are 4π/3 and 5.50m. What are its Cartesian coordinates?
Tiam Reply
Practice Key Terms 4

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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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