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

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__Solution
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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 *

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

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? __
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__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?

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__Solution __

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*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.

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?

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__Solution __

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__Example 6
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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

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__Solution
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*Explosion
*

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

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?

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__Solution __

**Similarities and Differences between Inelastic Collision and Elastic Collision**

**Similarities**

Total momemtum is conserved

Total energy is conserved

Total mass is conserved

### Differences

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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 .
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__Rocket Engine __

__Jet Engine __

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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