The Law of Conservation of Momentum
This fundamental law states that the total momentum of a closed system (one where no external forces act) remains constant. In other words, momentum is neither lost nor gained in a collision.
Momentum
Momentum is a measure of an object's mass in motion. It's calculated as:
* Momentum (p) = mass (m) x velocity (v)
Collisions and Conservation
Let's consider a simple collision between two objects, A and B:
1. Before the Collision:
* Each object has its own momentum:
* p(A) = m(A) * v(A)
* p(B) = m(B) * v(B)
* The total momentum of the system is the sum of their individual momenta:
* p(total) = p(A) + p(B)
2. During the Collision:
* The objects interact, exerting forces on each other. These forces are equal and opposite (Newton's Third Law).
* Crucially, no external forces are acting on the system.
3. After the Collision:
* The objects have new velocities, let's call them v'(A) and v'(B).
* The total momentum of the system is still:
* p'(total) = p'(A) + p'(B)
The Key Point
The law of conservation of momentum dictates that the total momentum *before* the collision must equal the total momentum *after* the collision:
* p(total) = p'(total)
Examples
* Billiard Balls: When two billiard balls collide, the total momentum of the system (both balls) is conserved. Some momentum is transferred from one ball to the other, but the total momentum remains the same.
* Car Crash: In a car crash, the total momentum of the vehicles involved is conserved. This is why airbags help to reduce injuries by increasing the time over which the momentum change occurs.
Types of Collisions
There are different types of collisions, but the law of conservation of momentum applies to all of them:
* Elastic collisions: Kinetic energy is conserved (no heat or sound is generated).
* Inelastic collisions: Some kinetic energy is lost, typically as heat or sound.
Conclusion
Collisions are excellent illustrations of the law of conservation of momentum. No matter the type of collision, the total momentum of a closed system remains constant, even though the individual momenta of the colliding objects may change.
