state the law of conservation of momentum prove it by using Newton's third law of motion
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Law of conservation of momentum states that. For two or more bodies in an isolated system acting upon each other, their total momentum remains constant unless an external force is applied. Therefore, momentum can neither be created nor destroyed.
Newton’s third law states that for a force applied by an object A on object B, object B exerts back an equal force in magnitude, but opposite in direction.
Consider two colliding particles A and B whose masses are m1 and m2 with initial and final velocities as u1 and v1 of A and u2 and v2 of B. The time of contact between two particles is given as t.
A=m1(v1−u1) (change in momentum of particle A)
B=m2(v2−u2) (change in momentum of particle B)
FBA=−FAB (from third law of motion)
FBA=m2∗a2=m2(v2−u2)t
FAB=m1∗a1=m1(v1−u1)t
m2(v2−u2)t=−m1(v1−u1)t
m1u1+m2u2=m1v1+m2v2
Therefore, above is the equation of law of conservation of momentum where m1u1+m2u2 is the representation of total momentum of particles A and B before the collision and m1v1+m2v2 is the representation of total momentum of particles A and B after the collision.
The law of conservation of momentum states that the initial and final momentum of a system is equal if no external force is being applied to the body.
- It is a major law of physics, and it follows Newton's law of inertia.
- Newton's third law of motion states that to every action there is an equal and opposite reaction.
→ Newton’s third law states that for a force applied by an object A on object B, object B exerts back an equal force in magnitude, but opposite in direction.
→ This idea was used by Newton to derive the law of conservation of momentum.
Consider two colliding particles A and B whose masses are m₁ and m₂ with initial and final velocities as u₁ and v₁ of A and u₂ and v₂ of B. The time of contact between two particles is given as t.
A = m₁ (v₁ - u₁). It is the change in momentum of particle A
B = m₂ (v₂ - u₂). it is the change in momentum of particle B
According to Newton's third law, Fba = -Fab
Fba = m₂a₂ = m₂( v₂ - u₂ )/t
Fab = m₁a₁ = m₁ (v₁ - u₁)/t
Since two forces are equal and opposite reaction,
Therefore, m₂( v₂ - u₂ )/t = - m₁ (v₁ - u₁)/t
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Therefore, above is the equation of the law of conservation of momentum where mu + mu is the momentum of particles A and B before the collision, and mv + mv is the momentum of particles A and B after the collision.