One-Dimensional Elastic Collision Calculator
Finds the first object's final velocity in a one-dimensional elastic collision. On this One-Dimensional Elastic Collision page, changing an entry updates the result and visible checking path.
Describe the system state
First final velocity
Read the conservation model first
Finds the first object's final velocity in a one-dimensional elastic collision. In laboratory collision data, this relationship is meaningful only when the reference frame, direction convention, and units remain consistent.
The named fields are first mass, first initial velocity, second mass, second initial velocity. Each belongs in a defined position within v₁f = ((m₁-m₂)u₁+2m₂u₂)/(m₁+m₂); writing values beside the symbols helps catch a transposition.
On this One-Dimensional Elastic Collision page, the sign of first final velocity follows the stated axis, work, or rotation convention. Keep that convention unchanged from the inputs through the reported answer.
Ways to catch a conservation-model error
Start the dimensional check with v₁f = ((m₁-m₂)u₁+2m₂u₂)/(m₁+m₂). After cancellation, the surviving dimension should align with m/s; a mismatch means the setup needs correction.
Then change one input by a controlled amount and predict how first final velocity ought to respond before recalculating. Direction and sensitivity provide separate checks on the arithmetic.
Following v₁f = ((m₁-m₂)u₁+2m₂u₂)/(m₁+m₂)
The worked case uses First mass = 2 kg, First initial velocity = 5 m/s, Second mass = 3 kg, Second initial velocity = 0 m/s. These values provide a reproducible example, and no unannounced unit conversion is applied to them.
Arrange v₁f = ((m₁-m₂)u₁+2m₂u₂)/(m₁+m₂) symbolically before substitution. That order makes an inverted ratio, omitted exponent, or misplaced number easier to identify.
Reading first final velocity in context
The calculator reports first final velocity in m/s. If that number enters a later formula, retain guard digits until the final operation.
Compare first final velocity with the scale of the one-dimensional elastic collision scenario. A metric-prefix mistake or inconsistent time unit can produce tidy arithmetic that is physically implausible.
For reproducibility, record first mass, first initial velocity, second mass, second initial velocity, their units, the reference direction, and v₁f = ((m₁-m₂)u₁+2m₂u₂)/(m₁+m₂) rather than recording only the final numeral.
A sensible next calculation
Useful follow-up calculations include perfectly inelastic collision calculator and coefficient of restitution calculator.
Continue with the page that matches the next system state, not merely one that repeats an input. Here, that choice follows from the one-dimensional elastic collision result.
Assumptions behind the number
The One-Dimensional Elastic Collision model uses the stated one-dimensional quantities. Conservation requires negligible external impulse during the event, while rotation, deformation, sound, heat, or off-axis motion can change first final velocity.
The precision of first final velocity is limited by the least reliable measurement. Extra displayed digits enable verification, but safety-critical work needs validated data and a suitable engineering procedure.
Common questions about the calculation
What does the first final velocity represent?
It is first final velocity under v₁f = ((m₁-m₂)u₁+2m₂u₂)/(m₁+m₂) and the field definitions printed on this page.
How can the One-Dimensional Elastic Collision result be checked?
Rearrange v₁f = ((m₁-m₂)u₁+2m₂u₂)/(m₁+m₂) to recover one entered quantity, then confirm that the remaining unit is m/s.
Do these inputs need consistent units?
Yes. Match every value to the unit beside its field before using v₁f = ((m₁-m₂)u₁+2m₂u₂)/(m₁+m₂).
Why could another first final velocity differ?
Gravity choice, rounding, sign conventions, reference frames, or different assumptions can shift the reported first final velocity.