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2.4 Momentum

The definition and S.I. unit  of  momentum

 

Phenomenon

The value of momentum

A bullet  travels at very high velocity

Large

A lorry which has a large mass

Large

 

Conclusion        :  

 Momentum  of an object is defined as the  product of its  mass  and  velocity

 

or  

momentum =  mass x  velocity

                         p  = m v

 

The S.I . units of momemtum is  kgms-1 or  Ns

 

Momentum  is a vector quantity.

 

Example 1

 

A bullet of mass   0.01k g  moves with a velocity

 200 m s-1.  What is the momentum of the bullet?

 

Solution

 

 

 

Example 2

 

A trolley of mass 1.5 kg moves with a velocity 4 ms-1  hits a wall and rebounds along the initial direction with a velocity

3 ms-1  .Calculate

(i)            The initial momentum  

(ii)           The final momentum     

(iii)          The change of  momentum

Solution

 

The Principle Of Conservation Of Momentum

 

The Principle of conservation of momentum states that

“ The total momemtum of a system is always fixed if there is no external force acting on the system”

or

“ In any collision or interaction between two or more objects in an isolated system , the total momemtum of the system will remain constant ; that is the total momemtum before collision will be equal to the total momemtum after the collision”

 

Types of collision

There are two types of collision , that is

(i)            Inelastic collision

(ii)           Elastic collision

 

                Inelastic collision

 

In inelastic collision , after two objects moving with their respective velocities do collide, they stick together and move with a common velocity.

 

clip_image002

Based on The Principle Of Conservation Of Momentum,

 

    The total momemtum   =         The total momemtum

 before collision                           after collision

 

Example  3

 

A trolley of mass  1 kg  and moving with a velocity of 6 ms-1   collides with a stationary trolley with a mass 3 kg. After collision they stick together with a common velocity. What is their common velocity?

Solution

 

Example 4

 

A trolley of mass trolley M kg  and moving with a  velocity 

4 ms-1  and collides with a trolley of mass 1 kg and   moving in opposite direction  with a velocity  2 ms-1 . After collision they stick together with a common velocity 2 ms-1. What is the value of M?

 

Solution

 

 

 

Elastic collision

 

In elastic collision , after two objects moving with their respective velocities do collide, those two objects will separate and move with different velocities.


clip_image004


Based on The Principle Of Conservation Of Momentum,

 

 

The total momemtum   =         The total momemtum

 before collision                           after collision

 

 

Example 5

A trolley  of mass trolley  2 kg  and moving with a  velocity 

0.6  ms-1  and collides with a  stationary trolley with a mass 1kg . After collision  the trolley of mass 2kg  and moving with a velocity 0.2 ms-1. What is the velocity of the trolley  of mass

1 kg  after collision?

Solution

 

 

 

Example 6

clip_image006

Based on the figure above, what is the

(a)      value of  x       

(b)      direction of motion of  the ball  with a mass 2 kg after collision

 

Solution

Explosion

clip_image008

In explosion, two objects are  initially at rest and after explosion those two objects will separate and move in opposite directions.

 

clip_image008

                 Based on The Principle Of Conservation Of Momentum,

 

 

The total momemtum   =         The total momemtum

 before explosion                 after explosion

 

                                          

 

 

Example 7

 

A bullet of mass  0.05 kg is shot out from a gun of mass 1.5 kg.

If the recoil velocity of the gun is 2 ms-1,what is the velocity of the bullet ?

 

Solution

 

 

Example  8

 

A  boy of mass 60 kg and a girl of mass 40 kg stand facing each other on a skating rink. The girl pushes the boy and he moves backwards at 2 ms-1 . What is the girl’s velocity?

Solution

 

 

 

Similarities and Differences between Inelastic Collision  and Elastic Collision

Similarities

Total momemtum is conserved

Total  energy is conserved

Total mass is conserved

 

 

Differences

Inelastic collision

Elastic collision

Both objects stick together after collision and move with a common velocity

Both objects don’t stick together after collision and move with different  velocities

Total amount of kinetic energy is not conserved

Total amount of kinetic energy is conserved

 

The Applications of  the Principle of Conservation of Momentum in rockets or jet engines .

                                               

                                                                Rocket Engine

              clip_image010

                                             Jet Engine

clip_image012

A  rocket engine carries its fuel with it and can work in space as well as in atmosphere.

Two fuels, such as liquid hydrogen and liquid oxygen burn together explosively and force the gases produced out of the rocket nozzle in high speed  and hence  produces downwards  momentum.

Following the principle of Conservation of Momentum, the rocket will propel upwards with a momentum that is equal to its previous momentum because momentum is conserved.

 

A jet engine uses the same principle of momentum conservation as the rocket engine except that it takes in  air to burn the fuel.So  a jet engine will only work in the atmosphere.

In the jet engine, air is sucked into the jet engine to be compressed and is heated up in the compressor. The compressed air is then mixed with fuel which is sprayed so that it starts to burn. The exhaust chamber emits exhaust gases with a high velocity. This results in a momentum of equal magnitude but of opposite direction which moves the aeroplane forward.

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