Question

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What is the purpose of Conservation of linear momentum experiment?

And what is the theory of Conservation of linear momentum experiment? Write a paragraph on elastic and inelastic collision. Include related equations as well

Answer 1

The law of conservation of energy and linear momentum is useful when dealing with collisions. Therefore we make use of this law of conservation to analyze collisions. Indeed, the law of conservation of momentum is particularly useful when dealing with a system of two or more objectsthat interact with each other, such as in collision of ordinary objects. The behaviour of any moving object can be completely described by its momentum and kinetic energy. Thus linear momentum is a conserved quantity hence allowing for prediction of motions of objects after events like collisions, where energy and momentum are transferred.

Collisions are classified as

elastic (kinetic energy is conserved)

Inelastic(kinetic energy is lost) or completely inelastic whereby objects stick together after collision.

The magnitude of an object’s linear momentum (P) depends on the object’s mass (m) and velocity (v).

P = mv................(1)

As long as there are no external forces acting on a system, the total momentum is conserved, which means, it will not change with time. The object’s kinetic energy (KE) also depends on its mass (m) and speed (v).

KE = ½mv²................. (2)

Since the total momentum of two objects of mass (m1) and (m2) is always conserved, their initial (i) and final (f) momentum should be equal.

m1 v1 i + m2 v2 i = m1 v1 f + m2 v2 f................ (3)

The kinetic energy will be also conserved, but only for elastic collisions.

For inelastic collision, after the collision the total mass will be (m1 + m2) moving at a new speed (Vf).

m1 v1 i + m2 v2 i = (m1 + m2) vf ......................(4)

In conclusion the initial and the final Kinetic energy will be calculated as;

KEi = ½m1 vi2 .............(5)

KEf = ½(m1 + m2) vf2 .............(6)