Momentum and Impuls

10 Jan 2011



A. Momentum
In physics, momentum is related to the quantity of motion possessed by, a moving object. In this case, momentum is defined as the multiplication product of mass and velocity of the object. This, mathematically momentum can be determined as follows.
p = m.v
P = Momentum (kg.m/s)

B . The Relation between Momentum and Impulse
If a force (F) works upon an object with a mass of m at certain time interval so that the velocity of the object changes, then the momentum of the object will change.
F= m a
F= m ?v/?t
If both parts of the above equation is multiplied by ?t, then the equation becomes.
F ?t = m ?v
F ?t = m (v2 v1 )

From the above equation, F.?t is called impulse and mv2-mv1, is called change of momentum.
I = F ?t
I = Impulse (N s )
F . ?t = mv2 - mv1
I = p2 - p1
In other word, impulse is defined as the change of momentum possessed by an object

C. Momentum Conservation Law

m1.v1 + m2.v2 = m1.v1 + m2.v1

The above equation is called momentum conservation law. In this case, the momentum conservation law states that “the total momentum of object before collision is equal to the total momentum of object after collision”.

D. Kinds of Collision

The collision between two objects can be distinguished into several kinds, those are perfectly elastic collision, non-elastic collision, and partially elastic collision.
The difference of collisions can be found out from the value of coefficient of elasticity (coefficient of restitution) of two colliding objects. This coefficient of elasticity of two colliding objects is equal to the negative ratio between velocity difference after and before the collision.

1. Perfectly Elastic Collision
The collision between two objects is said to be perfectly elastic if the total mechanical energy of objects before and after collision is constant.
Ek1 + Ek2 = Ek1′ + Ek2′
m1v12 + m2(v2)2 = m1(v1)2 + 1 m2(v2)2
Besides complying with the kinetic energy conservation law, perfectly elastic collision also complies with the momentum conservation law. Therefore, the coefficient of elasticity for perfectly elastic collision is equal to one.

2. Non-Elastic Collision
Two objects colliding are said to be non-elastic if after collision both objects become one (merge) and have the same velocity.
V1′ = V2′ = V’
The total kinetic energy of objects before collision is larger than that after collision. In other words, in non-elastic collision there is a decrease of kinetic energy so that the law of kinetic energy conservation is not valid.
m1v1 + m2v2 = (m1 + m2) v’
In that case, the coefficient of elasticity for non-elastic collision is equal to zero, that is according to the following equation.

3. Partially Elastic Collision
In partially elastic collision, the kinetic energy conservation law is not valid because there is a change of kinetic energy before and after collision. Thus, partially elastic collision only complies with momentum conservation law.
Meanwhile, the coefficient of elasticity for partially elastic collision has a value between zero and one.




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