Question

The law of conservation of momentum states that the total momentum of interacting objects does not change . This means the total momentum a collision or explosion is equal to the total momentum a collision or explosion.what is momentum

Answer 1

The momentum of an object is equal to the product of its mass and its velocity.

Step-by-step explanation:

Consider an object of mass
`m` travelling at a velocity
`\vec{v}`. The momentum
`\vec{p}` of this object would be:

`\vec{p} = m \cdot \vec{v}`.

For the law of conservation of momentum, consider two objects: object
`\rm a` and object
`\rm b`. Assume that these two objects collided with each other.

• Let
  `m_(\rm a)` and
  `m_(\rm b)` denote the mass of the two objects.
• Let
  `\vec{v}_(\rm a)(\text{initial})` and
  `\vec{v}_(\rm b)(\text{initial})` denote the velocity of the two object right before the interaction.
• Let
  `\vec{v}_(\rm a)(\text{final})` and
  `\vec{v}_(\rm b)(\text{final})` denote the velocity of the two objects right after the interaction.

• The momentum of the two objects right before the collision would be
  `m_(\rm a)\cdot \vec{v}_(\rm a)(\text{initial})` and
  `m_(\rm b)\cdot \vec{v}_(\rm b)(\text{initial})`, respectively.
• The momentum of the two objects right after the collision would be
  `m_(\rm a)\cdot \vec{v}_(\rm a)(\text{final})` and
  `m_(\rm b)\cdot \vec{v}_(\rm b)(\text{final})`, respectively.

The sum of the momentum of the two objects would be:

• 
  `m_(\rm a)\cdot \vec{v}_(\rm a)(\text{initial}) + m_(\rm b)\cdot \vec{v}_(\rm b)(\text{initial})` right before the collision, and
• 
  `m_(\rm a)\cdot \vec{v}_(\rm a)(\text{final}) + m_(\rm b)\cdot \vec{v}_(\rm b)(\text{final})` right after the collision.

Assume that the system of these two objects is isolated. By the law of conservation of momentum, the sum of the momentum of these two objects should be the same before and after the collision. That is:

`m_(\rm a)\cdot \vec{v}_(\rm a)(\text{initial}) + m_(\rm b)\cdot \vec{v}_(\rm b)(\text{initial}) = m_(\rm a)\cdot \vec{v}_(\rm a)(\text{final}) + m_(\rm b)\cdot \vec{v}_(\rm b)(\text{final})`.