6.2 Types of collisions (Page 65/4)

Siyavula textbooks: grade 12 Page 1 / 4

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:

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:

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:

\begin{matrix} 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} \end{matrix}

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 $\cdot$ 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?

Determine how to approach the problem
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 $\cdot$ s $^{- 1}$
- initial velocity of ball 2, $v_{i 2}$ = 2 m $\cdot$ s $^{- 1}$
- final velocity of ball 2, $v_{f 2}$ = 0 m $\cdot$ 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, $\frac{1}{2} (m_{1} v_{i 1}^{2} + m_{2} v_{i 2}^{2}) = \frac{1}{2} (m_{1} v_{f 1}^{2} + m_{2} v_{f 2}^{2})$
Choose a frame of reference
Choose to the right as positive.
Draw a rough sketch of the situation
Solve the problem
Momentum is conserved. Therefore:

$\begin{matrix} p_{i} & = & p_{f} \\ m_{1} v_{i 1} + m_{2} v_{i 2} & = & m_{1} v_{f 1} + m_{2} v_{f 2} \\ (0, 3) (0) + (0, 3) (2) & = & (0, 3) v_{f 1} + 0 \\ v_{f 1} & = & 2 m \cdot s^{- 1} \end{matrix}$
Write down the final answer
The final velocity of ball 1 is 2 m $\cdot$ s $^{- 1}$ to the right.

Got questions? Get instant answers now!

Questions & Answers

First aid and basic life support with answer like rarely, always,never

Eddie Reply

can you please help me with organic reactions

Bohlale Reply

if someone can please do a lil summary of organic reactions

Alicia

I olso need help

Noko

hi I need help

Zamokwakhe

In organic chemistry we have prefixes used to indicate the number of carbon atoms in a organic compound Which are: 1~Meth 2~Eth 3~Prop 4~But 5~Pent 6~Hex 7~Hept 8~Oct

Ofentse

meaning of homologous series and functional series and hydrocarbon

Lusanda Reply

who can explain mechanics parts for me

Sifiso Reply

difference between a and g

Tshwaranang Reply

when dealing with vertical projectile motion you can threat it as if it is the same thing

Akhona

a is the acceleration and therefore when dealing with your calculations you always have to change the sign conversion if it, it will depend on which direction you're taking as positive and g is the gravitational force and remember that it always acts downwards.

Thato

functional chain of Alcohol

Naledi Reply

Hi Guys

Sinetemba

Magdeline

hey

Tlhonolofatso

hello guys

Mukona

Akhona

hey

Boitumelo

Kwonda

Mabatho

Fortunate

Johnson

Desiree

Yoanda

Celvin

I'm fine and you

Ntuthuko

eyy

Noko

Kagiso

what is the definition of work

Berdes Reply

Sifiso

so peoples what is meant when objects are directly or inversely proportional to each other?

Asanda Reply

when they're directly proportional they both decrease or increase at the same time....but when they're inversely proportional the other one increases while the other one decreases

Tiisetso

how do we draw a velocity vs time graph for bouncing ball

Jojo Reply

what is an atom

Jimmy Reply

an atom is an small particle of matter

Asanda

I don't understand the part about the objects sharing the same time when falling and reaching the initial and maximum height. Could you explain it?

Liyakha Reply

same here I don't understand

Lusanda

wat formula do you use for that

Lithemba

what is phosphorus?

Rasool Reply

what is isomers

Iphithule Reply

what are isomers

Iphithule

are compound that have the same molecular formula but different structural formulae

Lizzbeth

types of isomers?

Khensani

Chain isomer functional group isomer positional isomer

Lizzbeth

a learner is standing on a stationary 2,3kg skateboard. if the learner jump at a velocity of 0.37m.s forward.,the skateboard velocity become 8,9m.s backwards. calculate the mass of the learner

Sbongakonke Reply

initial velocity before the explosion

Tiisetso Reply

<< Chapter < Page Page > Chapter >>

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

100% Free Mobile Applications
Receive real-time job alerts and never miss the right job again

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

	24 AP Key Terms 24 Metabolism Nutrition By OpenStax Start Key Terms
	Anatomy & Physiology By OpenStax Read Online Course
	Music 113 By Eric Crawford Start Quiz
©flickr: Gareth	Professional Etiquette MCQ By Abby Sharp Start Quiz
	3 Biology 03 Biological Macromolecules MCQ By OpenStax Start Quiz
©flickr: Donnie	How well do you know Beanie Boos? By Angela Eckman Start Quiz
	2 Timeshare 2 By Jams Kalo Start Quiz
	17 Sociology 17 Government and Politics MCQ By OpenStax Start Quiz
	Anthropology Politics Culture By Richley Crapo Start Assignment
©flickr:	Word Roots and Prefixes By Ellie Banfield Start Quiz