What happens when two objects have equal and opposite momentum?

When two objects have equal and opposite momentum, they will collide and come to a stop, assuming an elastic collision.

In physics, momentum is a vector quantity, meaning it has both magnitude and direction. When two objects have equal and opposite momentum, their magnitudes are the same, but their directions are opposite. This is often the case in a head-on collision, where two objects are moving towards each other with the same speed but in opposite directions.

According to the law of conservation of momentum, the total momentum of a closed system is constant unless acted upon by an external force. In the case of two objects with equal and opposite momentum, the total momentum before the collision is zero. Therefore, the total momentum after the collision must also be zero. This can only happen if the two objects come to a stop after the collision.

However, this is assuming an elastic collision, where kinetic energy is also conserved. In an elastic collision, the two objects will bounce off each other and come to a stop. If the collision is inelastic, where kinetic energy is not conserved, the two objects may stick together and continue moving in the direction of the object with greater mass. The concept of impulse also plays a significant role in the outcome of collisions, affecting the change in momentum and, consequently, the final velocities of the objects involved.

It's also important to note that this scenario assumes that there are no external forces acting on the system. If there are external forces, such as gravity or friction, they could affect the outcome of the collision. The effects of acceleration on objects, as detailed in the notes on acceleration, must be considered when analysing real-world collisions.

IB Physics Tutor Summary: When two objects have equal and opposite momentum and collide, they typically stop if the collision is elastic, as momentum and kinetic energy are conserved. If it's inelastic, they may stick together and move as one. External forces like gravity or friction could alter these outcomes. This scenario assumes no external forces are acting.