|
|
Momentum
|
|||
| Physical quantity that describes the quantity of motion in a body is called momentum. | |||
| The momentum of a moving body is defined as | |||
|
"the
product of mass and velocity of a moving body is called linear momentum"
|
|||
| Mathematically, | |||
 |
|||
| Momentum is a vector quantity and its direction is the same as that of velocity. | |||
|
Explanation
|
|||
| Momentum is that property of a moving body which determines how much effort is required to accelerate or stop a body.. Hence it may also be termed as quantity of motion of a body. From various observations it is concluded that greater effort is required to stop a body if it possess either greater mass or greater velocity or both. | |||
|
Units
Of Momentum
|
|||
| In
S.I. system : NS [1 NS = 1 kg m/s] In C.G.S. system : Dyne.S In F.P.S. system : Lb.S |
|||
|
Dimensions
Of Momentum
|
|||
| The dimension of momentum is [MLT-1] | |||
|
Law
Of Conservation Of Momentum
|
|||
| The law of conservation of momentum states that: | |||
|
"When
some bodies constituting an isolated system act upon
one another, the total momentum of the system remains constant." |
|||
| In other words | |||
|
"Total
momentum of an isolated system before and after collision is constant."
|
|||
|
Proof
|
|||
| Consider an isolated system of two bodies "A" & "B" having masses m1 & m2 moving initially with velocities u1 & u2 respectively. They collide with each other and after the impact their velocities become v1 & v2. | |||
   |
|||
|
Total
momentum of system before collision = m1u1 + m2u2
|
|||
|
Total
momentum of system after collision = m1v1 + m2v2
|
|||
| When the two bodies collide with each other, they come in contact for a short time "t". During this interval, let the average force exerted one of the bodies is F. | |||
| We know that the rate of change of linear momentum is equal to applied force, therefore | |||
|
FA
= ( m1v1- m1u1)/t -------------(1)
|
|||
|
FB
= ( m2v2- m2u2 )/t--------------(2)
|
|||
| According to the third law of motion : | |||
|
FA
= -FB
|
|||
| Putting the values of FA and FB | |||
|
(
m1v1- m1u1)/t = - (
m2v2- m2u2 )/t
|
|||
|
m1v1
- m1u1 = - ( m2v2-
m2u2 )
|
|||
|
m1v1
- m1u1 = - m2v2 + m2u2
|
|||
 |
|||
| This is known as the Law of conservation of momentum. This expression shows that the total momentum of an isolated system before and after collision remains constant i.e. the total momentum of the system is conserved. | |||
|
Isolated System |
|||
| An
isolated system is one in which constituents of the system interact with
one another and no external force is applied on any of them. Actually a
perfect isolated system is not possible in the physical world, but a group of objects whose mutual interaction with other objects can frequently be treated as if they are isolated. For example molecules of gas enclosed in a vessel at constant temperature. |
|||