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In a collision between two objects or in an explosion, the total momentum of the objects in the system remains unchanged. The Principle of Conservation of Momentum states that in a collision, the total momentum in the system is conserved provided no external forces are acting.

          Total momentum before a collision =

            Total momentum after a collision

When snooker ball A strikes snooker ball B, the momentum is transferred from snooker ball A to ball B. The momentum of snooker ball A decreases as its velocity slows down. Thus, the momentum of snooker ball B increases as it gains velocity. The total momentum of the snooker balls do not change but is conserved.

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In an explosion such as firing a shotgun, the total momentum of the shotgun and bullet before the explosion is zero since is no motion. After the shotgun is fired, the bullet moves forward with high velocity whereas the shotgun will recoil with a much lower velocity. The total momentum of the bullet and the shotgun is zero since they move in opposite directions. The forward momentum of the bullet is positive whereas the backward momentum of the gun is negative.

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There are two types of collision: a) An elastic collision b) An inelastic collision. Photograph below shows a Newton’s cradle. It consists of four or five identical steel balls hung just touching one another.

 

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Steel ball A is displaced and then released. When ball A hits ball B, all its momentum is quickly transferred to ball B. Ball A stops while ball B moves with the velocity of ball A. Similarly, when ball B hits ball C, ball B stops while ball C moves with the velocity of ball B. Ball C will transfer all its momentum to ball D when it hits it.

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Since the mass of all the steel balls are equal, ball D moves with a velocity equal to the velocity of ball A just before it hits ball B. The process will repeat when ball D hits ball C, ball C hits ball B will transfer all its momentum to ball A. As a result, ball A moves with a velocity equal to that of ball D just before it hits ball C.

Application of Momentum in Every day Life

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The Principle of Conservation of Momentum is used in the motion of rockets, air-crafts and ships. In rockets engine, the combustion of fuel in the combustion chamber produces a blast of hot gases. The hot gases are expelled from the rear of the engine with a very high velocity.

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In a jet engine, the combustion of kerosene and air produces a blast of hot gases. The hot gases are ejected with a very high velocity through an exhaust nozzle at the rear of the aircraft.

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According to the Principle of Conservation of Momentum, the expulsion of hot gases through the rear of rockets or air crafts will produce a large momentum in the opposite direction. The forward thrust of a jet engine enables the aircraft to move forward while the upthrust of a rocket engine enables the rocket to propel upwards.

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In a shipping vessel or boat, the rotation of propellers pushes the water backwards at a high velocity. This backward momentum of water produces a forward thrust which enables the vessel or boat to sail forward.

Safety Features Used in Vehicles that are related to Change of Momentum

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Force is required to change the velocity of an object. On the other hand, when there is a change of velocity, there is a change of momentum. An impulsive force is produced when there is a change of momentum in a short time interval.

Impulse force = Rate of change of momentum

                       = Change of momentum

                                    Time Taken

The longer the time taken to change the momentum, the smaller is the impulsive force. In a collision, vehicles are brought to a complete stop. The sudden change of momentum will produce a large impulsive force. Modern vehicles are incorporated with safety features that help reduce the magnitude of the force produced in a collision. This is done by prolonging the period of collision.

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The following safety features are incorporated when designing vehicles: a) Collapsible steering column. The collapse of a steering column will swing it away from the driver’s chest during a collision. It also prolongs the impact of the passenger against the steering wheel and reduces the magnitude of the force that acts against the driver b) easily dented front and rear bumpers to decrease the rate of change of momentum during a collision.

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c) Rigid compartments with an easily smashed front and rear body. Easily smashed front and rear bodies of a vehicle are designed to absorb impact in the event of a collision. The smashing of the front body of the vehicle will prolong the time taken to bring the vehicle to rest. Hence the forces that acts against the passenger are reduced d) the windscreen of the vehicles are made from a substance that will crack but will not shatter into many small pieces in the event of a collision.

e) the seats of most vehicles are made from soft materials that is able to absorb a large force f) steel bars are used as reinforcements in the doors and side bodies of vehicles to withstand a large crashing force.

Pile Driver

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A pile driver is a heavy concrete weight that is used to drive in pile or timber into the ground when the foundations for bridges or high rise buildings are being constructed. The pile driver is first raised high above the pile with an engine. When the pile driver falls, the heavy weight and high velocity of the pile driver produces a high momentum just before crashing into the pile. When it crashes into the pile, the high momentum of the pile driver is transferred to the pile. A large impulsive force is produced, driving the pile into the ground.

Speed and Weight Limits for Heavy Vehicles

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The speed limit imposed on large vehicles is necessary to reduce the impact in a collision. The higher the speed of the vehicle, the higher is its momentum. Therefore, the impulse force will be higher when the vehicle is brought to rest during an accident. Similarly, overloading heavy vehicles with goods and passengers is against the law. The weight limit imposed on heavy vehicles is necessary to reduce fatal accidents. Overloaded heavy vehicles will not only be difficult to stop but the higher momentum of the vehicle will produce a much greater impact on vehicles during an accident.