Principles of Conservation

The law of conservation of energy is the name given to this rule.A system’s entire linear momentum is conserved if no external force acts on it.Although linear momentum is affected by the frame of reference, the law of conservation of linear momentum is not.Only in an inertial frame of reference are Newton’s equations of motion valid.The law of conservation of energy states that energy cannot be created or destroyed. It can, however, be transformed into a different shape. When all forms of energy are examined, the overall energy of an isolated system remains constant.

Momentum Analysis: The mass of an object multiplied by its velocity is its momentum. p = mv is the formula for expressing this. It is a vector quantity since it has both direction and magnitude.

The Logic Behind Momentum Conservation:

Consider the following scenario: two objects, object 1 and object 2, collide. The forces acting on the two objects in such a collision are equal in magnitude and opposing in direction (Newton’s third law). The following equation can be used to express this assertion.

F1=-F2

The force are equal in magnitude and opposite in direction 

For a set amount of time, the forces act between the two objects. In some circumstances, the period is extensive, while in others, it is brief. It can be claimed that the time the force acts on item 1 is equal to the time the force acts on object 2 regardless of how lengthy the time is. This is only common sense. Interactions (or contact) between two objects produce forces.If object 1 makes contact with object 2 for 0.050 seconds, object 2 must be making contact with object 1 for the same length of time (0.050 seconds). The equation represents:

t1=t2

The impulses experienced by the two objects are equal in magnitude and opposite in direction because the forces between the two items are equal in magnitude and opposite in direction, and the times during which these forces act are equal in magnitude. The equation represents:

F1t1=-F2t2

The impulses are equal in magnitude and opposite in direction 

However, an object’s impulse is equal to the change in momentum of that object (the impulse-momentum change theorem). As a result, because each object feels equal and opposing impulses, they must likewise suffer equal and opposite momentum changes. This can 

be expressed as an equation:

m1 Δv1= -m2 Δv2

The momentum changes are equal in magnitude and opposite in direction.

Principle of conservation with example :

A common physics experiment includes:

The fallen brick is at rest and has no momentum to begin with. The laden cart (one that has a brick on it) is moving with a lot of force. The velocity (typically estimated by a ticker tape analysis) and mass of the loaded cart can be used to calculate its actual momentum. The entire quantity of momentum is equal to the sum of the momentum of the dropped brick (0 units) and the momentum of the loaded cart.The momenta of the two independent items (dropping brick and laden cart) may be computed after the impact based on their measured mass and velocity (often found from a ticker tape analysis). If momentum is preserved during the collision, the total of the momentum of the dropped bricks and the loaded cart after the impact should be the same as before. The momentum obtained by the dropped brick should be equivalent (or nearly equal) to the momentum lost by the laden wagon.

The laden wagon lost 14 units of momentum, but the dropped brick gained 14 units. It’s also worth noting that before and after the collision, the system’s total momentum (45 units) was the same.

Rocket as an example of Conservation of momentum:

The fuel in a rocket burns and creates gas at a high temperature. These gases are blasted from the rocket through a nozzle on the rocket’s back side. The rocket accelerates due to the forward force exerted by the ejecting gas. Due to their high velocity of escape, the mass of gases departing per second is relatively little, but their momentum is very large. The rocket receives an equal and opposing momentum, allowing it to achieve a high velocity despite its great mass.

Conclusion:

The conservation of momentum, like the conservation of energy and mass, is a fundamental concept in physics. The definition of momentum is the mass of an object multiplied by its velocity. The conservation of momentum states that the amount of momentum inside a problem domain remains constant; momentum is never generated or destroyed, but only changed by the action of forces described by Newton’s equations of motion. Momentum is more difficult to deal with than mass or energy since it is a vector quantity with both a magnitude and a direction.