Purpose of calculation:
Analysis of inelastic collisions
Reproduction of a sample calculation from a published calculation reference.
In an inelastic collision, momentum is conserved, but kinetic energy is not conserved. Instead, some of the initial kinetic energy is converted into other forms of energy, such as heat, sound, or deformation of the colliding objects. In an inelastic collision, the objects may stick together and move as one after the collision (perfectly inelastic) or separate with some deformation and energy loss (partially inelastic).
Here is a comparison of elastic and inelastic collisions:
- Both momentum and kinetic energy are conserved.
- Objects rebound and separate after the collision without any permanent deformation or energy loss.
- The relative velocities of the objects before and after the collision are equal and opposite.
- Momentum is conserved, but kinetic energy is not conserved.
- Some initial kinetic energy is converted into other forms of energy, such as heat, sound, or deformation.
- Objects may stick together (perfectly inelastic) or separate with some deformation and energy loss (partially inelastic).
To calculate the final state of an inelastic collision, you only need to conserve momentum, as the conservation of kinetic energy does not apply. The conservation of momentum equation remains the same:
m1 * v1_initial + m2 * v2_initial = m1 * v1_final + m2 * v2_final
However, since kinetic energy is not conserved, you cannot use the conservation of kinetic energy equation to find the final velocities directly. Instead, you need additional information about the collision, such as the coefficient of restitution or the amount of energy lost.
For a perfectly inelastic collision, where the objects stick together and move as one after the collision, you can simplify the conservation of momentum equation to find the final velocity:
v_final = (m1 * v1_initial + m2 * v2_initial) / (m1 + m2)
In summary, the main difference between elastic and inelastic collisions lies in the conservation of kinetic energy. In elastic collisions, both momentum and kinetic energy are conserved, while in inelastic collisions, only momentum is conserved, and some kinetic energy is lost or converted into other forms of energy.
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