State the law of conservation of momentum derived from third newton law of motion
Answers
when two objects collide the total Momentum before collision is equal to the total Momentum after collision
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
=
m
1
(
v
1
−
u
1
)
(change in momentum of particle A)
B
=
m
2
(
v
2
−
u
2
)
(change in momentum of particle B)
F
B
A
=
−
F
A
B
(from third law of motion)
F
B
A
=
m
2
∗
a
2
=
m
2
(
v
2
−
u
2
)
t
F
A
B
=
m
1
∗
a
1
=
m
1
(
v
1
−
u
1
)
t
m
2
(
v
2
−
u
2
)
t
=
−
m
1
(
v
1
−
u
1
)
t
m
1
u
1
+
m
2
u
2
=
m
1
v
1
+
m
2
v
2
Therefore, above is the equation of law of conservation of momentum where
m
1
u
1
+
m
2
u
2
is the representation of total momentum of particles A and B before the collision and
m
1
v
1
+
m
2
v
2
is the representation of total momentum of particles A and B after the collision.