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Basic concept of Momentum
It determins the quantity of motion in a body.
It is defined as the “mass of the body multiplied by its velocity”.
It is measured in kilogram metre per second (kgm/s) or newton second (Ns).
Momentum = mass X velocity
P = m v
As velocity is a vector quantity, so momentum is a vector quantity too. We must give a direction when we talk about momentum.
Momentum is very useful when we meet problems involving collisions or explosions. There is always as much momentum after a collision as there is before it (Principle of conservation of momentum).
Note:
It is clear from the formula that momentum of the body is zero if it is at rest.
Basic Concept of Impulse
If a steady force F acting on a body of mass m increases its velocity from u to v in time t, the acceleration a is given by,
a = (v-u) / t
We have force, F = ma
Substituting for a in above equation gives,
F / m = (v-u) / t
F=m (v-u) / t
Force = change of momentum / time
Ft =m (v-u)
Here Ft is called the impulse, mu is the initial momentum and mv is the final momentum.
Momentum Equation, P = mv
As we know that
Momentum = (mass) X (Velocity)
P = mv
Solved Example
Question:
What is the momentum of a runner of mass 70kg running at 10 m/s.
Solution:
As
P = mv
p = (70) X (10)
p = 700 kg m / s
Equation For Impulse, Ft = mv – mu
As Ft is called impulse and has unit of Newton seconds.
In words the equation can be expressed as:
impulse = change of momentum
So to cause a change of momentum of 100 kg m/s, for example, we must apply an impulse of 100Ns. We could apply a force of 100N for 1s, or 1N for 100s. Each causes the same change of momentum.
Law of Conservation of Momentum
When two or more bodies interact (collide) with each other, the total momentum of the bodies remain constant before and after interaction (collision), provided no external forces (e.g.: friction) is involved. This statement is called principle of conservation of momentum.
Total momentum before collision = Total momentum after collision