Enter the masses and initial velocities of two objects to determine the common final velocity after a perfectly inelastic collision (objects move together after impact), or use the coefficient of restitution tab to find each object’s final velocity for a one-dimensional collision.
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Perfectly Inelastic Collision (Common) Final Velocity Formula
The following equation is used to calculate the common final velocity when two objects undergo a perfectly inelastic collision (they stick together and move as one) in one dimension, assuming the system is effectively closed during the impact (negligible external impulse).
V = (M1*V1 + M2*V2) / (M1+M2)
- Where V is the common final velocity of the combined objects after a perfectly inelastic collision (m/s)
- M1 and M2 are the masses of each object (kg)
- V1 and V2 are the velocities of the objects before collision along the same line (m/s)
In a closed system (with negligible external impulse during the collision), the total momentum of the objects before and after the collision is equal.
What is an Inelastic Collision Velocity?
Definition:
In this calculator, “inelastic collision velocity” refers to the common final velocity of two objects after a perfectly inelastic collision (when they stick together and share one velocity). For other collisions (with a coefficient of restitution 0 < e ≤ 1), the two objects generally have different final velocities.
How to Calculate Inelastic Collision Velocity?
Example Problem:
The following example outlines the steps and information needed to calculate the common final velocity for a perfectly inelastic collision.
First, determine the masses. In this example, the masses are found to be 10 kg and 30 kg, respectively.
Next, determine the initial velocities. For this problem, these are 40 m/s and 50 m/s, respectively.
Finally, calculate the Inelastic Collision Velocity using the formula above:
V = (M1*V1 + M2*V2) / (M1+M2)
V = (10*40 + 30*50) / (10+30)
V = 47.5 m/s
FAQ
What distinguishes an inelastic collision from an elastic collision?
In an inelastic collision, the objects involved stick together or deform, and kinetic energy is not conserved, although momentum is. In contrast, during an elastic collision, both momentum and kinetic energy are conserved, and the objects bounce off each other without any permanent deformation.
Why is momentum conserved in an inelastic collision?
Momentum is conserved in an inelastic collision due to the law of conservation of momentum, which states that the total momentum of a closed system is constant if no external forces act upon it. Even though kinetic energy may not be conserved in inelastic collisions, the momentum before and after the collision remains the same.
Can inelastic collisions occur in everyday life? Provide examples.
Yes, inelastic collisions occur frequently in everyday life. Examples include a car crash, where the vehicles may become entangled or deformed; a football player tackling another, where both players move together after the collision; and playdough being squished together, where it sticks and forms a new shape.
