Conservation Of Momentum

Momentum

According to this principle In the absence of an external force, the total momentum of a system remains constant or conserved and does not change with time.

F (external) = 0

In an isolated system mutual forces between pairs of particles in the system causes Momentum change in individual particles. But as the mutual forces for each pair are equal and opposite, the linear momentum of the individual particle cancel in pairs and the total Momentum remains unchanged. This fact is known as the law of conservation of momentum.

Equilibrium Of a Particle

Forces which are acting at the same point or on a particle are called concurrent forces. These forces are said to be in equilibrium when their resultant is zero.

Equilibrium Of a Particle
Equilibrium Of a Particle

1. If two forces F₁ and F₂ act on a particle, then they will be in equilibrium if F₁ = -F₂ i.e two forces on the particle must be equal and opposite.

2. If three concurrent forces F₁, F₂ and F₃ acting at the same point O of a body.

Equilibrium Of a Particle
Equilibrium Of a Particle

By parallelogram law, the resultant of F₁ and F₂ will be (F₁ + F₂).

If a third force F₃ acts on the body such that

F₃ = – (F₁ + F₂), then the body will be in equilibrium

So, F₁ + F₂ + F₃ = 0

Thus, three force in equilibrium can be represented by the sides of a triangle taken in the same order.

Then, the condition for the equilibrium of a number of forces acting at the same point is that the vector sum of all these forces is equal to zero.

F₁ + F₂ + F₃ + F₄ +———- + Fₙ = 0

In general, The principle is in equilibrium under the action of n forces can be represented by the sides of closed n-sides polygon taken in the same order.

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