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Elastic collision against a wall

by davidbenari
Tags: collision, elastic, wall
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davidbenari
#1
Aug1-14, 11:49 AM
P: 78
In an elastic collision against a wall, where the angle of incidence is equal to the angle of deflection, why is it assumed that friction effected no impulse, and only the normal force did? I can understand if this was stated in the problem by saying "frictionless surface, or whatever" but this seems to be the case if a shoot a tennis ball against the floor or a wall too. Why is it that friction is almost negligible here? Is this a property of very-quick collisions, like in Kinetic Theory?

Thanks.
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olivermsun
#2
Aug1-14, 12:17 PM
P: 862
Well, you did specify an elastic collision, which means perfect conservation of kinetic energy. If friction did anything at all, then there would be dissipation and no longer conservation of energy.

If you shoot a tennis ball against a floor at an angle, the interaction is vastly different from an elastic collision: friction plays a big role, as do deformation, angular momentum, etc. It's a very complicated interaction that makes for a pretty poor intro physics textbook problem.
Nugatory
#3
Aug1-14, 12:22 PM
Mentor
P: 3,954
Quote Quote by davidbenari View Post
In an elastic collision against a wall, where the angle of incidence is equal to the angle of deflection, why is it assumed that friction effected no impulse, and only the normal force did? I can understand if this was stated in the problem by saying "frictionless surface, or whatever" but this seems to be the case if a shoot a tennis ball against the floor or a wall too. Why is it that friction is almost negligible here? Is this a property of very-quick collisions, like in Kinetic Theory?
The frictional force acts parallel to the direction of the wall. Does the momentum of the ball in that direction change? If not, there was no impulse from that force - and that's the case for the idealized elastic collision that you're describing.

It pretty much has to be that way because you've specified that the collision is elastic so kinetic energy is conserved and the speed of the ball on the way out is the same as the speed in, and that the angle of incidence is equal to the angle of deflection.

davidbenari
#4
Aug1-14, 12:35 PM
P: 78
Elastic collision against a wall

Oliver, Nugatory: Suppose you've never seen a tennis ball collide with a wall when thrown at an angle. What would make you predict that the outcome of this collision would be the way it's normally seen? Namely, angle of incidence = angle of deflection, collision is almost elastic.

Also, in the case of Kinetic Theory, is friction negligible when particles collide against the container? If this is the case, then why don't they slide along the container during the collision? Is this because the collision is almost instantaneous ?

Thanks.
olivermsun
#5
Aug1-14, 01:14 PM
P: 862
Quote Quote by davidbenari View Post
Oliver, Nugatory: Suppose you've never seen a tennis ball collide with a wall when thrown at an angle. What would make you predict that the outcome of this collision would be the way it's normally seen? Namely, angle of incidence = angle of deflection, collision is almost elastic.
I don't think I'd make a good prediction based on the theory of elastic collisions, because the physics of tennis ball bounces isn't much like an elastic collision (except superficially!).

That's what makes the physics of sports such an interesting topic. We have some idea from experience how certain kinds of balls, bats, etc. behave. What we observe usually doesn't fit very well with very simple (ideal physics) type models, and so we get to figure out why.

Also, in the case of Kinetic Theory, is friction negligible when particles collide against the container? If this is the case, then why don't they slide along the container during the collision? Is this because the collision is almost instantaneous ?
Well, I think in kinetic theory the point is all the molecules basically undergo elastic collision, and some molecules are more free to move than others. There is this notion, however, of a "no-slip boundary," which means the molecules don't just slip past the walls of the container uninhibited.
Nugatory
#6
Aug1-14, 05:13 PM
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Quote Quote by davidbenari View Post
Oliver, Nugatory: Suppose you've never seen a tennis ball collide with a wall when thrown at an angle. What would make you predict that the outcome of this collision would be the way it's normally seen? Namely, angle of incidence = angle of deflection, collision is almost elastic.
I wouldn't make such a prediction until I had seen it - and in fact a tennis ball/wall collision isn't an especially good example of an elastic collision. A steel ball bearing bouncing off a polished steel plate might be easier to predict, as the modulus of elasticity of steel is so very high that we could safely ignore all the second-order effects that come from the deformation of the ball on impact.

But do remember that physics starts with observations, and the mathematical models follow from what has been observed and must be explained. We study the idealized perfectly elastic collision because it's a useful and computationally tractable model of the collisions that we've observed; when we see a collision in which the kinetic energy loss is insignificant and the incident and deflection angles are near as no never mind the same we use this model. Asking why the collision obeys the rules of the model is getting things backwards - we chose the model because it matched the observation.


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