<< Chapter < Page Chapter >> Page >

Types of collisions

Two types of collisions are of interest:

  • elastic collisions
  • inelastic collisions

In both types of collision, total momentum is always conserved. Kinetic energy is conserved for elastic collisions, but not for inelastic collisions.

Elastic collisions

Elastic Collisions

An elastic collision is a collision where total momentum and total kinetic energy are both conserved.

This means that in an elastic collision the total momentum and the total kinetic energy before the collision is the same as after the collision. For these kinds of collisions, the kinetic energy is not changed into another type of energy.

Before the collision

[link] shows two balls rolling toward each other, about to collide:

Two balls before they collide.

Before the balls collide, the total momentum of the system is equal to all the individual momenta added together. Ball 1 has a momentum which we call p i 1 and ball 2 has a momentum which we call p i 2 , it means the total momentum before the collision is:

p i = p i 1 + p i 2

We calculate the total kinetic energy of the system in the same way. Ball 1 has a kinetic energy which we call K E i 1 and the ball 2 has a kinetic energy which we call KE i 2 , it means that the total kinetic energy before the collision is:

K E i = K E i 1 + K E i 2

After the collision

[link] shows two balls after they have collided:

Two balls after they collide.

After the balls collide and bounce off each other, they have new momenta and new kinetic energies. Like before, the total momentum of the system is equal to all the individual momenta added together. Ball 1 now has a momentum which we call p f 1 and ball 2 now has a momentum which we call p f 2 , it means the total momentum after the collision is

p f = p f 1 + p f 2

Ball 1 now has a kinetic energy which we call K E f 1 and ball 2 now has a kinetic energy which we call K E f 2 , it means that the total kinetic energy after the collision is:

K E f = K E f 1 + K E f 2

Since this is an elastic collision, the total momentum before the collision equals the total momentum after the collision and the total kinetic energy before the collision equals the total kinetic energy after the collision. Therefore:

Initial Final p i = p f p i 1 + p i 2 = p f 1 + p f 2 and K E i = K E f K E i 1 + K E i 2 = K E f 1 + K E f 2

Consider a collision between two pool balls. Ball 1 is at rest and ball 2 is moving towards it with a speed of 2 m · s - 1 . The mass of each ball is 0.3 kg. After the balls collide elastically , ball 2 comes to an immediate stop and ball 1 moves off. What is the final velocity of ball 1?

  1. We are given:

    • mass of ball 1, m 1 = 0.3 kg
    • mass of ball 2, m 2 = 0.3 kg
    • initial velocity of ball 1, v i 1 = 0 m · s - 1
    • initial velocity of ball 2, v i 2 = 2 m · s - 1
    • final velocity of ball 2, v f 2 = 0 m · s - 1
    • the collision is elastic

    All quantities are in SI units. We are required to determine the final velocity of ball 1, v f 1 . Since the collision is elastic, we know that

    • momentum is conserved, m 1 v i 1 + m 2 v i 2 = m 1 v f 1 + m 2 v f 2
    • energy is conserved, 1 2 ( m 1 v i 1 2 + m 2 v i 2 2 ) = 1 2 ( m 1 v f 1 2 + m 2 v f 2 2 )
  2. Choose to the right as positive.

  3. Momentum is conserved. Therefore:

    p i = p f m 1 v i 1 + m 2 v i 2 = m 1 v f 1 + m 2 v f 2 ( 0 , 3 ) ( 0 ) + ( 0 , 3 ) ( 2 ) = ( 0 , 3 ) v f 1 + 0 v f 1 = 2 m · s - 1
  4. The final velocity of ball 1 is 2 m · s - 1 to the right.

Got questions? Get instant answers now!

Questions & Answers

Is the normal force always 0
Mpilo Reply
define the term rate of reaction in word
David Reply
I think it a chemical process in which substance act mutually on each other.
Sphesihle
how many bones are in the human body?
Asali
what is wave lengh
mama Reply
is the de broglie wavelength of the particle
Hope
calcium and magnesium, which one can displace aluminum from its compound?
Markia Reply
how is aluminum ion formed?
Dickens
molecules with the same molecular formula but different chain
Malaza Reply
what will be the answer
.angel
chain isomer
Anele
what does the newton's law says?
there are 3 newtons laws which are newton's law of universal gravitation, law of cooling, law of motion
Imagine
Did the feather or leaf hit the ground first?
Shaloom Reply
leaf
Pradip
2 to 30 minut long distance race 20 km what's the avarage speed for the race
Jamilla Reply
what is meaning of covalent bonds
Lungani Reply
bonds that exists between non metal atoms. each atom contribute electron(s) which will form a bond joining the two atoms. electrons in the bond now belongs to both atoms
Matome
how do we name haloalkanes
Thobeka Reply
how do we name haloalkanes
lesedi
what are examples of haloalkanes
Mpho
haloalkanes are compounds that consist of the halogen group chlorine bromine flourine and so on like 2-bromobutan
Samkele
give an example of calculating work
Nwabisa Reply
what is chain Isomer?
Christian Reply
chain isomer ar compounds with the same molecular formular but different chain length
Samkele
Where does the functional group of ketone in carbons belong
Keletso Reply
alkane
Isamkele
how can I find the structural formulae and IUPAC names of hexane?
Matshidiso Reply
@Matshidiso identify your compound which is an alkane..the general formula for alkane is CnH2n+2... hex-6 substitute n with 6 implying that you'll have 6 carbons and 14 Hydrogens then you can draw your structural formula *NB* every carbon has to have 4 bonds
Kgabo
what are disadvantages of primary cells and advantage of secondary cells?
Thabang Reply

Get the best Siyavula textbooks: gr... course in your pocket!





Source:  OpenStax, Siyavula textbooks: grade 12 physical science. OpenStax CNX. Aug 03, 2011 Download for free at http://cnx.org/content/col11244/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Siyavula textbooks: grade 12 physical science' conversation and receive update notifications?

Ask