Will a Rigid Ball Bounce off a Wall?

[Kaneki123]

Okay...If we consider two bodies which are perfectly rigid (meaning they can't deform under any conditions), let's say a ball and a wall...If we throw the ball at the wall, will the ball bounce back?Any answer in terms of action/reaction pair will be appreciated...

 

[hilbert2]

The kinetic energy of the ball can't just disappear when it collides with the wall, so some of it has to turn into heat (heating of the objects at point of collision due to inelasticity) and some into kinetic energy of motion to the opposite direction (bouncing back). The relative amounts of these depend on the material properties.

 

[Khashishi]

Perfect rigidity isn't possible. Either the ball will shatter, or something will bend.

 

[Zach S]

The ball will always have to some what bounce back unless the ball went through the wall.

 

[Kaneki123]

The ball will always have to some what bounce back unless the ball went through the wall.

Let me state it in terms of forces...The ball striking the wall will apply some force on the wall, the wall will apply some reaction force back on the ball...As a result of this reaction force, there will be a deceleration in the ball...At some point, its velocity will become zero...NOW at this point the ball will not be striking the wall (applying some force) as both the bodies are perfectly rigid...Normally in case of a normal ball, this is the point when the ball is deformed and it starts reforming (which allows it to bounce back)...But in the case of rigid bodies, no deformation occurs, so there should be no bouncing back?

 

[jbriggs444]

.But in the case of rigid bodies,

See #3. There is no such thing as a perfectly rigid body.

 

[Nidum]

For simple geometries the two objects colliding can each be modeled as spring/mass/damper systems .

The stronger the springs the less effect the dampers have on the response motions and the less energy that is lost in the dampers as heat .

 

[Zach S]

Let me state it in terms of forces...The ball striking the wall will apply some force on the wall, the wall will apply some reaction force back on the ball...As a result of this reaction force, there will be a deceleration in the ball...At some point, its velocity will become zero...NOW at this point the ball will not be striking the wall (applying some force) as both the bodies are perfectly rigid...Normally in case of a normal ball, this is the point when the ball is deformed and it starts reforming (which allows it to bounce back)...But in the case of rigid bodies, no deformation occurs, so there should be no bouncing back?

well for the wall to sustain the force exerted from the ball without breaking it has to exert some force back into the ball making it go into the other direction

 

[Kaneki123]

See #3. There is no such thing as a perfectly rigid body.

Thats why I said the word ''If"'...Like if we have two perfectly rigid bodies, would this be possible?

 

[Kaneki123]

well for the wall to sustain the force exerted from the ball without breaking it has to exert some force back into the ball making it go into the other direction

The wall will only exert the force on the ball as long the ball is striking against it...When the velocity of the ball reaches 0 (not negative velocity), the ball will not be continuosly striking now...So the wall will not be exerting a force on the ball now...So there is no force on the ball, no acceleration and hence no change in speed from 0 to negative.?

 

[jbriggs444]

Thats why I said the word ''If"'...Like if we have two perfectly rigid bodies, would this be possible?

What happens when an irresistable force meets an immovable object? Our laws of physics do not say.

In their general form, our laws of motion take the form of differential equations. We have various rules for how much force there is as a function of position or velocity or temperature or whatever. And we have Newton's second law for how velocity changes over time based on the imparted force:

$$F = \frac{dp}{dt}$$

As long as the forces stay finite, this equation is predictive (*). We can run a simulation forward in time and see how a given system will evolve. But now invoke a situation where there will hypothetically be infinite forces applied over zero duration and zero displacement. The above differential equation ceases to be usable. It can make no prediction. It is an indeterminate case.

Edit to add:

As a practical matter, we can do as @Nidum hints. Take the limit as we adjust some parameters to make a realistic system more and more rigid and see if it converges on some limiting behavior. Since there are known theoretical limits that prevent a real system from being perfectly rigid, this method gives us as good an answer as we are likely to get.

(*) The differential equations of motion are not always predictive. There is a very nice series of insights articles that touches on some of the problems. Here is one part of that...

https://www.physicsforums.com/insights/struggles-continuum-conclusion/

 

[jbriggs444]

The wall will only exert the force on the ball as long the ball is striking against it.

That interval of zero duration both starts and ends at the instant of impact and involves more than any finite force.