Academic Success

Should I Use Energy or Momentum Conservation in Collision Problems?

Momentum is conserved in all collisions, while kinetic energy is conserved only in elastic ones. Here is a checklist for solving mixed physics problems.

By Fermi Editorial

26 Oct 2026, 8:07 PM IST4 min read

Bar charts showing momentum and kinetic energy before and after elastic and inelastic collisions — In a perfectly elastic collision, both total momentum and kinetic energy are conserved. In a perfectly inelastic collision where two equal masses stick together, the final velocity halves, so exactly half of the initial kinetic energy is lost, while momentum remains conserved. Fermi

On this page

One of the most common hurdles in physics is deciding whether a problem calls for conservation of momentum or conservation of energy. A 2003 study in the American Journal of Physics found that most students have difficulty interpreting basic principles of energy and momentum and applying them in physical situations (10.1119/1.1571832).

If you find yourself stuck on a mixed problem, the key is knowing what happens during the exact moment of impact.

Why is momentum conserved in every collision?

Whenever two objects collide, the force the first exerts on the second is equal and opposite to the force it receives back. Because these internal forces cancel each other out over the exact same time interval, the total momentum of the system cannot change.

This means you can always rely on conservation of momentum for the brief moment of a collision. It holds true as long as there are no massive external forces (like a wall or friction) interfering during that split second. It does not matter whether the objects bounce off cleanly, stick together, or explode into pieces.

When is kinetic energy conserved in collisions?

Unlike momentum, which is a vector that points in a specific direction, kinetic energy is a scalar quantity of motion. During a collision, objects compress and deform.

In a perfectly elastic collision (like idealized billiard balls or gas molecules), the objects spring back to their original shapes perfectly. This returns all the stored energy back into kinetic energy, meaning the total kinetic energy is conserved.

In an inelastic collision (like a car crash or two lumps of clay sticking together), the objects are permanently deformed and generate heat or sound. That energy has to come from the initial motion, so the total kinetic energy of the system drops.

How do you solve a ballistic pendulum problem?

A classic example of needing both conservation laws is the ballistic pendulum. In this setup, a fast-moving bullet embeds itself into a heavy wooden block hanging from a string, and the block swings upward.

The problem must be split into two distinct stages. In the first stage, the bullet hits the block. This is a perfectly inelastic collision. Because it happens so quickly, the string has no time to swing, so gravity and tension do not interfere. You must use conservation of momentum to find the speed of the block and bullet just after they stick together. The kinetic energy is not conserved here; a significant fraction is lost to heat and deforming the wood.

In the second stage, the combined block and bullet swing upward to a maximum height. There is no longer any collision happening, but gravity is now doing work. Since the tension in the string is always perpendicular to the motion, it does no work. Here, you use conservation of mechanical energy. The kinetic energy the block had just after the collision converts entirely into gravitational potential energy at the peak of the swing.

Attempting to apply energy conservation across the entire event from the initial bullet to the peak swing will give the wrong answer, because it ignores the energy lost during the impact itself.