3

Yes, your calculations look correct. The energy lost in an inelastic collision are often turned into sound, light, or heat energy. As the clay hits the door, one or both of the objects deform, and it's the original object's kinetic energy that goes into rearranging the molecules. You may notice that an object usually heats up when it is deformed, this a ...


3

The thing that went wrong in your approach is that the total linear momentum is not conserved, because there is an external force on the door: namely, the constraint force of the door's hinge, that fixes one part of the door to the wall. When analyzing the problem using angular momentum, we cleverly choose the coordinate system so that the origin is located ...


3

Your question contains a contradiction. You imagine a world without any forms of non-mechanical energy- in such a world, inelastic collisions could not exist. The whole point of inelastic collisions is that mechanical KE is lost to non-mechanical forms of energy.


2

Even in a vacuum, the inelastic deformation would result in an increase in the temperatures of the blocks. An increase in temperature means there is an increase in the kinetic energies (KE) of the atoms and molecules of the blocks, i.e., an increase in KE at the microscopic level. In effect, the macroscopic KE of the blocks associated with their overall ...


2

So, looks like 90% of initial energy is lost in the process of clay ball sticking to the door! Is my calculation correct? What is the intuitive explanation for this loss of energy? Permanent deformation of the ball. This requires work, Sound is a minor contribution: such collisions usually generate a 'thudding' noise, Viscous deformation of the ball ...


1

The general (vector) formula you are looking for can be simply derived from the condition of elastic collision against a (locally) flat wall characterized by a normal unit vector ${\bf \hat n}$: $$ \begin{align} {\bf v'}_{\parallel}&={\bf v}_{\parallel}\\ {\bf v'}_{\perp}&=-{\bf v}_{\perp}, \end{align} $$ where the subscript $_{\parallel}$ indicates ...


1

Interesting question. The cross product does generalize to higher dimensions. Especially, for 1+3d spacetime, i.e., Minkowski, we can either consider $(A^\mu,B^\nu)\mapsto u^\mu\varepsilon_{\mu\nu\rho\sigma}A^\rho B^\sigma$ with $u^\mu$ a timelike unit vector (e.g., the observer’s 4-velocity) or $(F^{\mu\nu},G^{\mu\nu})\mapsto\Delta^{\kappa\lambda}{}_{\mu\nu\...


1

If you have a perfectly inelastic collision, you either are working in a system which does not have conservation of energy, or you have another way of tracking the energy which is "lost" in the collision. If you have neither, then you do indeed have a contradiction. We have a similar problem in electronics. You can develop idealized circuits ...


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