Conservation of Momentum Calculator

Conservation of Momentum

In an isolated system with no net external force, total linear momentum is conserved. For a one-dimensional collision between two objects, the sum of momenta before equals the sum after the collision.

Momentum Conservation Equation

$$m_1 u_1 + m_2 u_2 = m_1 v_1' + m_2 v_2'$$

For a perfectly elastic collision in one dimension, kinetic energy is also conserved. The final velocities are:

$$v_1' = \frac{(m_1 - m_2)u_1 + 2m_2 u_2}{m_1 + m_2}$$ $$v_2' = \frac{2m_1 u_1 + (m_2 - m_1)u_2}{m_1 + m_2}$$

Example: an 8 kg object at 10 m/s hits a 4 kg stationary object elastically. Object 1 slows to about 3.33 m/s and object 2 moves at about 13.33 m/s, while total momentum stays 80 kg·m/s.

Frequently Asked Questions

When is momentum conserved?

Momentum is conserved when the net external force on the system is zero. Internal forces between colliding objects cancel out.

What is an elastic collision?

In a perfectly elastic collision, both momentum and kinetic energy are conserved. Objects bounce apart without permanent deformation or heat loss.

What happens in an inelastic collision?

Momentum is still conserved, but kinetic energy is not. Objects may stick together or lose energy to deformation and heat.

Can one object stop after a collision?

Yes. When a lighter object hits a much heavier stationary one elastically, the light object can bounce back while the heavy object barely moves.

What is an example of momentum conservation?

Recoil when firing a gun: the bullet moves forward and the gun kicks backward so total momentum remains zero if both started at rest.

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Conservation of Momentum Calculator