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Calcimator

Elastic Collision Calculator

Final velocities and energy transfer in 1D elastic collisions.

Inputs

Results

Velocity 1 Final (m/s)

-3.4

Velocity 2 Final (m/s)

3.6

Total KE Before (J)31
Total KE After (J)31
Momentum Before (kg·m/s)4
Momentum After (kg·m/s)4
KE Transferred (J)13.44
How to Use This Calculator
  1. Enter mass 1 (kg) and mass 2 (kg) for the two colliding objects.
  2. Enter initial velocity of object 1 (m/s) and initial velocity of object 2 (m/s) — use negative for leftward.
  3. Read final velocities of both objects after the elastic collision.
  4. Verify conservation: total kinetic energy before should equal total kinetic energy after (J).
  5. Review kinetic energy transferred (J) and momentum before and after to confirm conservation laws.

What each input means

Mass 1 (kg)
Mass of object 1.
Mass 2 (kg)
Mass of object 2.
Velocity 1 Initial (m/s)
Initial velocity of object 1 (positive = right).
Velocity 2 Initial (m/s)
Initial velocity of object 2 (negative = left).

What each result means

Velocity 1 Final (m/s)
Final velocity of object 1 after collision.
Velocity 2 Final (m/s)
Final velocity of object 2 after collision.
Total KE Before (J)
Total kinetic energy before collision.
Total KE After (J)
Total kinetic energy after (should equal before).
Momentum Before (kg·m/s)
Total momentum before collision.
Momentum After (kg·m/s)
Total momentum after (should equal before).
KE Transferred (J)
Kinetic energy transferred between objects.

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Mass 1 (kg) = 2, Mass 2 (kg) = 3, Velocity 1 Initial (m/s) = 5, Velocity 2 Initial (m/s) = -2 = 4 input(s) provided
  2. Calculate Velocity 1 Final
    Velocity 1 Final = ((m1 - m2) * v1i + 2 * m2 * v2i) / totalMass
    -3.4 = -3.4
  3. Calculate Velocity 2 Final
    Velocity 2 Final = ((m2 - m1) * v2i + 2 * m1 * v1i) / totalMass
    3.6 = 3.6
  4. Calculate Total KE Before
    Total KE Before = ke1i + ke2i
    31 = 31
  5. Calculate Total KE After
    Total KE After = ke1f + ke2f
    31 = 31

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