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The Principle of Conservation of Momentum

09 Aug

Principle of Conservation of Momentum:

The principle of conservation of momentum states that in a system make out of objects that react (collide or explode), the total momentum is constant if no external force is acted upon the system.

Sum of Momentum Before Reaction = Sum of Momentum After Reaction

FORMULA:

m1u1 + m2u2 = m1v1 + m2v2

m1 = mass of the 1st object
m2 = mass of the 2nd object
u1 = initial velocity of the 1st object
u2 = initial velocity of the 2nd object
v1 = final velocity of the 1st object
v2 = final velocity of the 2nd object

Example:

A Car A of mass 600 kg moving at 40 ms-1 collides with a car B of mass 800 kg moving at 20 ms-1 in the same direction. If car B moves forwards at 30 ms-1 by the impact, what is the velocity, v, of the car A immediately after the crash?
Answer:

m1 = 600kg
m2 = 800kg
u1 = 40 ms-1
u2 = 20 ms-1
v1 = ?
v2 = 30 ms-1

According to the principle of conservation of momentum,

m1u1 + m2u2 = m1v1 + m2v2
(600)(40) + (800)(20) = (600)v1 + (800)(30)
40000 = 600v1 + 24000
600v1 = 16000
v1 = 26.67 ms-1

 

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