Momentum and Conservation of Momentum

Introduction

In daily life, we see that a fast-moving or heavy object is harder to stop than a light or slow-moving object. This is because moving bodies possess momentum. Momentum helps us understand motion during collisions and interactions between bodies.

Momentum

Momentum is the quantity of motion possessed by a moving body.

It is equal to the product of mass and velocity of the body.

Momentum = mass × velocity

p = m × v

Here, p is momentum, m is mass, and v is velocity.

Momentum is a vector quantity because it has both magnitude and direction. Its direction is the same as the direction of velocity.

Explanation

If the mass of a body is large, its momentum will be large. If the velocity of a body is large, its momentum will also be large. Therefore, momentum depends on both mass and velocity.

  • A heavy truck moving slowly may have large momentum.
  • A light ball moving very fast may also have momentum.
  • A body at rest has zero momentum because its velocity is zero.

Conservation of Momentum

The law of conservation of momentum states that if no external force acts on a system, then the total momentum of the system remains constant.

This means total momentum before interaction is equal to total momentum after interaction.

Total momentum before = Total momentum after

Explanation of Conservation of Momentum

Suppose two bodies collide. During collision, they apply equal and opposite forces on each other. These internal forces do not change the total momentum of the system. So, one body may lose momentum and the other may gain momentum, but the total momentum remains the same.

For two bodies, it can be written as:

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Here, u₁ and u₂ are initial velocities, and v₁ and v₂ are final velocities.

Examples from Daily Life

  • When a gun is fired, the bullet moves forward and the gun recoils backward.
  • A rocket moves upward by throwing gases downward.
  • When two balls collide, momentum is transferred from one ball to another.
  • A moving trolley can set another trolley in motion after collision.

Illustration

Before Collision A u₁ B u₂ = 0 After Collision A v₁ B v₂ Total momentum before = Total momentum after

In the figure, body A moves towards body B and collides with it. After collision, the momentum is shared between the two bodies, but the total momentum of the system remains the same.

Important Points

  • Momentum is equal to mass multiplied by velocity.
  • Momentum is a vector quantity.
  • A body at rest has zero momentum.
  • Total momentum remains constant if no external force acts on the system.
  • The law of conservation of momentum is very useful in studying collisions, recoil, and rocket motion.

Conclusion

Momentum tells us how much motion a body has. The law of conservation of momentum states that the total momentum of an isolated system always remains constant. This law helps us understand many motions and collisions in daily life.

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