Conservation of momentum equation
Collision type
Don't know
Object no. 1
Mass (m₁)
kg
Initial velocity (u₁)
m/s
Final velocity (v₁)
m/s
If you are trying to solve a problem that only has one object, maybe our impulse and momentum calculator would be more useful.
Object no. 2
Mass (m₂)
kg
Initial velocity (u₂)
m/s
Final velocity (v₂)
m/s

Conservation of Momentum Calculator

By Bogna Haponiuk and Steven Wooding

The conservation of momentum calculator will help you in describing the motion of two colliding objects. Do you want to gain a better understanding of the law of conservation of momentum? Are you perplexed by the concepts of an elastic and inelastic collision? Or maybe you can't tell the difference between kinetic energy and momentum conservation principles? Whatever the reason, this article is here to help you.

Law of conservation of momentum

The principle of momentum conservation says that for an isolated system, the sum of the momentums of all objects is constant (it doesn't change). An isolated system is a system of objects (it can be, and typically is, more than one body) that doesn't interact with anything outside the system. In such a system, no momentum disappears: whatever is lost by one object is gained by the other.

Imagine two toy cars on a table. Let's assume they form an isolated system - no external force acts on them, and the table is frictionless. One of the cars moves at a constant speed of 3 km/h and hits the second toy car (that remained stationary), causing it to move. You can observe that the first car visibly slows down after the collision. This result happened because some momentum was transferred from the first car to the second car.

Elastic and inelastic collisions

We can distinguish three types of collisions:

  • Perfectly elastic: In an elastic collision, both momentum and kinetic energy of the system are conserved. Bodies bounce off each other. An excellent example of such a collision is between hard objects, such as marbles or billiard balls.
  • Partially elastic: In such a collision, momentum is conserved, and bodies move at different speeds, but kinetic energy is not conserved. It does not mean that it disappears, though; some of the energy is utilized to perform work (such as creating heat or deformation). A car crash is an example of a partially elastic collision - metal gets deformed, and some kinetic energy is lost.
  • Perfectly inelastic: After an inelastic collision, bodies stick together and move at a common speed. Momentum is conserved, but some kinetic energy is lost. For example, when a fast-traveling bullet hits a wooden target, it can get stuck inside the target and keep moving with it.

You may notice that while the law of conservation of momentum is valid in all collisions, the sum of all objects' kinetic energy changes in some cases.

How to use the conservation of momentum calculator

You can use our conservation of momentum calculator to consider all cases of collisions. To calculate the velocities of two colliding objects, simply follow these steps:

  1. Enter the masses of the two objects. Let's assume that the first object has a mass of 8 kg, while the second one weighs 4 kg.
  2. Decide how fast the objects are moving before the collision. For example, the first object may move at a speed of 10 m/s, while the second one remains stationary (speed = 0 m/s).
  3. Determine the final velocity of one of the objects. For example, we know that after the collision, the first object will slow down to 4 m/s.
  4. Calculate the momentum of the system before the collision. In this case, initial momentum is equal to 8 kg * 10 m/s + 4 kg * 0 m/s = 80 N·s.
  5. According to the law of conservation of momentum, total momentum must be conserved. The final momentum of the first object is equal to 8 kg * 4 m/s = 32 N·s. To ensure no losses, the second object must have momentum equal to 80 N·s - 32 N·s = 48 N·s, so its speed is equal to 48 Ns / 4 kg = 12 m/s.
  6. You can also open the advanced mode to see how the system's kinetic energy changed and determine whether the collision was elastic, partially elastic, or inelastic.
Bogna Haponiuk and Steven Wooding