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Inelastic Collision Calculator

This calculator determines the final velocity and kinetic energy lost during a perfectly inelastic collision in one dimension, where two objects collide and stick together. Enter the masses and initial velocities of both objects to find the combined velocity after impact and the amount of kinetic energy dissipated.

Inelastic Collision Calculator

Input Fields
If enabled, the result will update automatically when you change any value.

Inelastic Collision Formulas

Formula
$$v = \frac{m_1 u_1 + m_2 u_2}{m_1 + m_2}$$ $$KE_{lost} = KE_{before} – KE_{after} = \frac{1}{2}m_1 u_1^2 + \frac{1}{2}m_2 u_2^2 – \frac{1}{2}(m_1 + m_2)v^2$$

Where:

  • $$v$$ = final velocity of the combined mass (m/s)
  • $$m_1$$, $$m_2$$ = masses of the two objects (kg)
  • $$u_1$$, $$u_2$$ = initial velocities of the two objects (m/s)
  • $$KE_{lost}$$ = kinetic energy lost during the collision (J)

In a perfectly inelastic collision, momentum is conserved but kinetic energy is not. The two objects stick together and move with a common final velocity.

Inelastic Collision – Worked Example

Example: A 2 kg object moving at 5 m/s collides with a 1 kg object at rest. They stick together.

  • $$m_1$$ = 2 kg
  • $$u_1$$ = 5 m/s
  • $$m_2$$ = 1 kg
  • $$u_2$$ = 0 m/s
  1. $$v = \frac{2 \times 5 + 1 \times 0}{2 + 1} = \frac{10}{3} \approx 3.33\ \text{m/s}$$
  2. $$KE_{before} = \frac{1}{2} \times 2 \times 5^2 + \frac{1}{2} \times 1 \times 0^2 = 25\ \text{J}$$
  3. $$KE_{after} = \frac{1}{2} \times 3 \times (3.33)^2 \approx 16.67\ \text{J}$$
  4. $$KE_{lost} = 25 – 16.67 \approx 8.33\ \text{J}$$

The combined mass moves at 3.33 m/s and 8.33 J of kinetic energy is lost.

Perfectly inelastic collisions are a fundamental concept in physics and mechanics. This calculator is useful for students, engineers, and anyone studying momentum conservation and energy dissipation in collisions where objects stick together after impact.

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