About Perfectly Inelastic Collisions

Currently listening to:

If we have 2 masses, $m_{1}$ and $m_{2}$, with velocities $\vec{\textbf{v}}_{1}$ and $\vec{\textbf{v}}_{2}$, respectively, and we assume they'll just head straight on and stick to each other, because of Newton's conservation of momentum, we find that:

$$m_{1} \vec{\textbf{v}}_{1i} + m_{2} \vec{\textbf{v}}_{2i} = (m_{1} + m_{2}) \vec{\textbf{v}}_{f}$$

Where $i$ and $f$ are initial and final, respectively. With this equation, we can then solve for the final velocity:

$$\vec{\textbf{v}}_{f} = \frac{m_{1} \vec{\textbf{v}}_{1i} + m_{2} \vec{\textbf{v}}_{2i}}{m_{1} + m_{2}}$$

I basically made this simulation because I am punishing myself for being a physics major and forgetting that the kinetic energy in a inelastic collision system is not conserved. Remember that the kinetic energy equation is:

$$K.E. = \frac{1}{2}m \vec{\textbf{v}}^{2}$$

And that the kinetic energy lost is the kinetic energy of all objects added, minus the kinetic energy after the collision. Of course, you can find the pre-collision kinetic energies by calculating the equations above for each, then the final kinetic energy from the inelastic final velocity and the combined mass.