How can momentum be conserved in collisions?

Momentum is conserved in collisions if the total momentum before the collision equals the total momentum after the collision.

In more detail, the principle of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it. This principle is applicable to all types of collisions, whether they are elastic, inelastic, or perfectly inelastic.

Let's consider an example of two objects colliding. Before the collision, each object has its own momentum, which is the product of its mass and velocity. The total momentum of the system is the sum of the momenta of these two objects. When they collide, their velocities change, and hence their individual momenta change. However, the total momentum of the system remains the same. This is because the momentum lost by one object is gained by the other.

In an elastic collision, both momentum and kinetic energy are conserved. This means that the total momentum and total kinetic energy before the collision are equal to the total momentum and total kinetic energy after the collision.

In an inelastic collision, only momentum is conserved. The kinetic energy is not conserved because some of it is transformed into other forms of energy, such as heat or sound.

In a perfectly inelastic collision, the objects stick together and move as one after the collision. Even in this case, the total momentum before the collision is equal to the total momentum after the collision.

In all these cases, the key point to remember is that the total momentum remains constant if no external forces are acting on the system. This is the essence of the principle of conservation of momentum.