state law of conversation of momentum and write expressian
Answers
Explanation:
The law of momentum conservation can be stated as follows. For a collision occurring between object 1 and object 2 in an isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision.
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The law of conservation of momentum is one of the most prominent laws in physics. The principle of conservation of momentum law tells us that the total momentum of a system is always conserved. Let us learn more about the conservation of momentum along with derivation and solved problems.
Momentum Conservation Principle
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.
The principle of conservation of momentum is a direct consequence of Newton’s third law of motion.
Derivation of Conservation of Momentum
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.