Mass is a quantity which is a little elusive, the more we think we know what mass is, the less we really do! No physicist in the world really understands it but we do have a fairly good idea of what it does.
 

• It creates and reacts to gravity.

• It combines with velocity to make an important set of concepts.

• It is related to energy.

In 2012, the operators of the accelerator on the Swiss-French border at CERN announced that they had probably discovered a sub-atomic particle or field called a Higg's Boson that produces some of the properties of mass for atoms.

The effect of mass on motion is important. Imagine two objects moving towards you, a tennis ball at 2 ms^-1 and a car at the same speed. Your impression of danger is implicitly linked to your estimation of both speed AND mass. The ball is clearly less dangerous.

The person who saw this and incorporated mass into his dynamics for the first time ever was Isaac Newton.

We shall start by looking at mass and velocity combined.

Imagine the process of catching a ball thrown at you by your "best" friend. The ball hurtles into your hand and your hand moves back as a result. Your hand acquires some of the motion of the ball. The effect is changed by both the velocity of the ball and the mass of the ball.

We can think of plenty of cases where motion is transferred and even cases where motion disappears! The head on collision of two netball or football players are cases in point . There are, of course, situations where motion appears from no motion - an exploding handgrenade or when two people push away from each other !
 
 

We make a new quantity to describe the combined velocity - mass effect.

MOMENTUM ( p ) - is the product of the mass and the velocity of a body.

The crucial thing about momentum is that it obeys a "conservation" rule !
 

Conservation rules are extremely important because they say something about the nature of our Universe. ( What, we are not entirely certain about. )

A Conservation rule allow us to calculate a quantity which does not alter thereafter and enables us to predict outcomes as a result.
 
 

THE PRINCIPLE OF CONSERVATION OF MOMENTUM

" In a closed system the total momentum remains at all times constant."

A closed system is one in which we can account for everything.
 
 
 
 

Eg;

The boxes above represent a "closed system". There are only two bodies in it and we can account for their individual momentum exactly.

Something happens in the system, the two objects combine for some reason ( which we are not particularly interested in at the moment ).

In the example above; Let the direction of p₁ be positive, then p₂ is negative.

Total momentum p = + p₁ + ( - p₂ )

= momentum of combined masses by Conservation of Momentum.

Suppose now the balls separate, they have bounced apart;

each has a new momentum, p₃ and p₄.

Then; Total momentum p = ( - p₃ ) + p₄ = + p₁ + ( - p₂ )

by Conservation of Momentum.

"p" is fixed throughout all possible interactions in the box !

( Note; Some teachers use arrows in brackets behind the value of the momentum instead of, or as well as, +,- . Fine ! This reinforces a sense of direction which is useful at a more advanced level. )

Notice the use of "BEFORE" and "AFTER"  continuously in solving these situations - BEFORE the explosion ( or whatever ) and AFTER the explosion
 
 

 Numerical examples of Conservation of Momentum in use.

Eg 1; A girl is to fire a shotgun mounted on a trolley to measure the speed of the shot. The gun and trolley has a mass of 5 kg while the bird shot has a combined mass of 100 gram ( = 0.1 kg ).

After firing, the gun and trolley recoils at 8 ms^-1. What is the speed of the bird shot on leaving the barrel ?
 

Soln;
Before the explosion

the total momentum of the gun and shot = 0 ( not moving )
 

After the explosion

the total momentum of the gun and shot = m_gun.v_gun (left ) + m_shot.v_shot ( right)

= 5( - 8 ) + 0.1 . v_shot

By Cons. of Mom. , Initial momentum = Final Momentum

thus 0 = -40 + 0.1 .v_shot

so v_shot = +400 ms^-1

Eg 2; Ted, 45kg, running to the right at 8 ms^-1, in a friendly SRC game of touch football, collides front on with Alice, 65 kg, running to the left at 9 ms^-1. During the collision, Alice gives Ted a little shove so Ted finds himself moving to the left at 5 ms^-1 immediately after. At what velocity does Alice find herself moving after this minor fracas?

Soln;

Before collision

= 45 .( +8) + 65 . ( -9 ) kgms^-1

= 360 - 585 kgms^-1

= -225 kgms^-1

The total momentum is to the left , and has size 225 kgms^-1

After the collision

= 45. ( - 5 ) + 65 v_A

= - 225 + 65 v_A

But , Initial Mom. = Final Mom. ( Cons. of Mom. )

Thus -225 = - 225 + 65 v_A

So 0 = 65 v_A , thus v_A = 0

Alice is stopped by the collision.
 
 
 

The rule of Momentum Conservation works in all dimensions and under every circumstance where we can account for every item.

It is used to deduce the masses of subatomic particles like Z^o particles in supercolliders, and is used in Astronomy. It tells us nothing about collisions or explosions as such, but a great deal about the rules of the Universe.

Link to Forces             Two Dimensional Momentum Conservation

Link to Vectors Tutorial

Return to Year 11 Phys tutes list

PROBLEMS

1. Your "new" car, a Datsun 180B, has a mass of 900kg including you and your friends. What momentum has it when travelling at 60km/h due North? ( 1.5 x 10⁴ kg ms^-1 N )

2. Taking your car as above, and another car coming South, find the total momentum if the other car is a Commodore of mass 1300kg travelling at 70km/h.

You then have a head-on collision ( not pleasant ) - what is the total momentum immediately after the collision? ( 1.03 x 10⁴ kg ms^-1S )

When the wreckage has stopped moving, where has this momentum gone?

3. You are standing on a skateboard and attempt to step off forwards. Explain the skateboard shooting off backwards in terms of momentum conservation.

4. In a game of squash, Jim and Alice collide, Jim is moving at 2ms^-1 to his left with a mass of 55kg, Alice to her right at 1.5ms^-1with a mass of 60kg. The two entangle. What is the total momentum of the pair? With what velocity sideways does the two entangled people fall to the ground? (20 kgms^-1 left, 0.17ms^-1 left )
 

5. In question 3, your mass is 40kg while the skateboard has a mass of 1kg. If you manage to get a velocity of 0.05ms^-1, what velocity is given to the skateboard? ( 2ms^-1)

6. A trolley ( 10kg ) is rolling along at 5ms^-1and has a 5kg mass dumped straight down on it. The trolley promptly slows. What to? ( 3.3 ms^-1)

7. A cricket ball, mass 0.14kg is hurtling down towards you at 30ms^-1 . Your bat, mass 1.2kg, accidentally stops the ball. Ignoring your arms and hands, how quickly will the bat move backwards? (3.5ms^-1 backwards )

8. In the same match as the above, you have now gained confidence and the bat is now moving forwards at 5ms^-1 to strike the same speed ball. The ball is sent off past the bowler at 20ms^-1. What is the bat's new speed immediately after contact?  ( 3.9ms^-1 forwards )

9. Due to inattention whilst driving, you bump into the back of the car in front. Your car has a mass of 1 tonne and hits the car in front at a speed of 3ms^-1. Your car locks its bumper bar into the wreck of the boot in front. The car in front has a mass of 1.5 tonnes. What is the speed of the mess immediately after impact before you belatedly hit the brakes? ( 1.2 ms^-1 forwards )

10. Tom ( 30kg, a skinny young man ) and Raewyn ( 70kg ) are desperately in love but only get an opportunity to meet once a week in the middle of York Park when they rush from either end into each others arms. On impact Tom was moving at 5ms^-1while Raewyn at 8ms^-1. Comment on the subsequent collision!

( Raewyn is overpowering, the entangled mess moves in the direction of Raewyn at a speed of 4.1ms^-1)