Momentum and impulse

Defining Momentum and Impulse

  • Momentum is the product of an object’s mass and its velocity. This is a vector quantity.

  • Momentum can be calculated using the formula: momentum (p) = mass (m) x velocity (v)

  • The impulse of a force is the force applied multiplied by the time it is applied over. It is also a vector quantity.

  • Impulse can be calculated using the formula: impulse (J) = force (F) x time (t)

Conservation of Momentum

  • In a closed system, the total momentum before a collision or explosion is equal to the total momentum after. This is called the principle of conservation of momentum.

  • A closed system is one where no external forces act. In reality, there’s usually some external force, like friction, but we often ignore this for simplicity.

Impulse and Change in Momentum

  • Impulse is equal to the change in momentum of an object.

  • When a force is applied to an object for a period of time, it changes the object’s velocity and therefore its momentum. This change of momentum is what we call impulse.

  • This relationship can be represented by the formula: impulse (J) = change in momentum (Δp), where Δp = mv - mu (final momentum - initial momentum).

Car Safety and Impulse

  • Cars are designed to increase the time over which a collision occurs, thereby reducing the force felt by the passengers. This is due to the relationship F = Δp / t, i.e., the force experienced is inversely proportional to the time the force is applied.

  • Safety features like seat belts and airbags work on this principle, and are examples of how understanding momentum and impulse can be applied in real-life situations.

Solving Momentum and Impulse Problems

  • When solving problems involving momentum and impulse, it’s often useful to create a momentum table. This is a table that lists the momentum of each object before and after an event (like a collision or explosion), which can help to clearly see how momentum is conserved.

  • To calculate an unknown in a problem, you need to use a combination of the formulae given above and the principle of conservation of momentum.