Question

state and prove the principal of conservation of linear movementem

Answer 1

Formula used: p = mv, FAB=−FBA and F=dpdt. Complete answer: Law of conservation of momentum states that unless an external force is applied, the two or more objects acting upon each other in an isolated system, the total momentum of the system remains constant.

According to the law of conservation of linear momentum, for an object or system of objects, the total momentum of the system is always conserved if no external force acts on them

The unit of kg.m.s-1 and the dimensional formula is MLT-1. The mathematical representation of the law of conservation of linear momentum is given as:

m1u1 + m2u2 = m1v1 + m2v2

Proof:

Consider collision between two balls. The momentum of these two balls before collision is given as:

P1i = m1u1

P2i = m2u2

The total momentum of the balls before the collision is given as:

Pi = P1i + P2i

Pi = m1u1 + m2u2

F12 is the force exerted by the m1 during the collision on m2.

F21 is the force exerted by the m2 during the collision on m1.

Therefore, F12 = F21

There is a change in the velocity of these balls after the collision which is given as:

P1f = m1v1

P2f = m2v2

The total momentum of the balls after the collision is given as:

Pf= P1f + P2f

Pf= m1v1 + m2v2

From Newton’s second law:

Force = Change in momentum / time interval

F12 = m2v2 – m2u2 / t

F21 = m1v1 – m1u1 / t

From Newton’s third law:

F12 = F21

Therefore, we get:

m1u1 + m2u2 = m1v1 + m2v2

Answer 2

Answer:

We'll start with a statement of the law of conservation of momentum. Then, using Newton's second and third laws, we will consider the example of two bodies colliding in an elastic manner.

The following formulas were used: p = mv, FAB=FBA, and F=dpdt.

Explanation:

• The law of conservation of momentum asserts that unless an external force is introduced, the total momentum of two or more objects operating on each other in an isolated system remains constant. This also implies that the total momentum of an isolated system prior to isolation is equal to the total momentum of the isolated system after isolation.
• Consider two particles, A and B, of mass m 1 and m 2, colliding, and the forces acting on these particles are solely those exerted by these particles on one other. There is no outside force at work.
• Let u 1 and v 1 be the initial and final velocities of particle A, and u2 and v 2 be the initial and final velocities of particle B, respectively. Allow the two particles to come into contact for t seconds.
• So, A=m 1 momentum change (v 1 u 1). eq. 1: Change in momentum of B=m 2 (v 2 u 2) 2 eq.
• Allow A to exert an average force equal to F BA on B during the collision, and allow B to exert an average force equal to F AB on A. We know from the third law of motion that F BA