I understand that a wall is only capable of exerting force perpendicular to it. I can't think of a reason why this is observed?
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$\begingroup$ How could the wall/floor transmit a force parallel to it, if not through friction? There's nothing to push against. $\endgroup$– Nuclear HoagieCommented Mar 16, 2018 at 13:56
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$\begingroup$ That's what I said to my instructor. He said that I need to prove that there's nothing to push against. $\endgroup$– LoneStarCommented Mar 16, 2018 at 14:11
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3 Answers
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Your instructor might be looking for a symmetry argument.
If there is no friction, then any net force would cause an acceleration. But in what direction would that force point? For a horizontal surface there's no reason to favor any particular horizontal direction. The only way to satisfy the symmetry of the situation is if the magnitude of the horizontal force is zero.
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Keep in mind that a "flat" surface is nowhere near flat at the molecular level, and usually up to some small but visible structure size. A brick wall for example, ignoring the grout joints, is still quite rough; you can see with the naked eye a rough surface. At the atomic level it is even worse.
Also keep in mind that when the two objects collide, the forces at play are not between a "ball" and a "wall" but between the atoms at the surfaces of the objects, and that the collision between the two objects is an aggregate effect of all of those atomic collisions combined. Atoms in solid objects tend to repel atoms in other solid objects - they've done all the bonding they're going to do within the molecules of the local object. That's why the ball doesn't stick to the wall.
At the atomic level, the electron clouds can be well approximated by spheres, and that's where the repulsion happens. Because the surfaces are rough at the atomic level, any given atom in the ball will meet it's match in the wall at a fairly random angle. The range of such angles is determined by the specific surface structure of the objects, but for everyday materials will still be an unbiased random distribution. Some of those angles would even continue on in almost the same direction as initial travel, if not for the overall structure of the object keeping them from wandering too far.
To summarize what I mean by an "unbiased random distribution:" individual atoms on the surface of, say, the ball will experience random deflections, but the average direction of those deflections is perpendicular to the surface of the wall, away from the wall. Since the ball as a whole is held together by its internal bonds, the average deflection is the value we're interested in for the rebound of the ball, and that's why the ball changes direction along an axis perpendicular to the wall.
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You can think of the perpendicular force acting as the force between 2 atoms. If these atoms approach each other what do you think would be the direction of the force? The direction would be towards the center of mass. But because the electron cloud exists everywhere around the atom there’s no definite center of mass. This we can average out the center of mass and say that the force would be almost perpendicular to the center of the atoms along the direction of the straight line path connecting these 2 atoms. Now consider that 1 atom is approaching 2 atoms. Since the masses are the same the average force that the atom would experience would be along a straight line path between the two atoms and joking the center of the approaching atom. If you extend this analogy to a very large number of atoms you will find that the resultant of all these forces acting will be perpendicular to this ‘plane’ of atoms.
