Exploring the Curious Case of Non-Conserved Momentum: A Scientific Perspective

[adjacent]

I remember throwing clay balls at walls in my childhood and observing them stick to the wall. In a more scientific perspective, considering the ball and wall as a system, I can say that the total momentum before collision is greater than 0. But then, after the collision, the kinetic energy of the ball got converted to thermal energy and work was done to deform the ball, resulting in 0 velocity which implies 0 momentum.

I know that momentum is always conserved and kinetic energy need not be, but what isn't it the case here?

 

[Dale]

considering the ball and wall as a system,

Is the ball and wall system an isolated system or does it have external forces acting on it? Is momentum conserved in such systems?

 

[adjacent]

Is the ball and wall system an isolated system or does it have external forces acting on it? Is momentum conserved in such systems?

It has no external forces acting. It's just a wall, ball and air surrounding them.

I never learned about momentum conservation is different kinds of systems. All I was taught us that momentum is always conserved

 

[phinds]

It has no external forces acting. It's just a wall, ball and air surrounding them.

So the wall is free-floating with nothing supporting it anywhere.

 

[PeroK]

It has no external forces acting. It's just a wall, ball and air surrounding them.

I never learned about momentum conservation is different kinds of systems. All I was taught us that momentum is always conserved

Suppose it was a fence on shaky foundations. Would the clay knock the fence back in that case?

 

[adjacent]

So the wall is free-floating with nothing supporting it anywhere.

Suppose it was a fence on shaky foundations. Would the clay knock the fence back in that case?

Yes. But this wall is rigid and standing firmly on the ground on Earth which revolves around the sun and so on, I left the details because it might get too complicated.

 

[phinds]

Yes. But this wall is rigid and standing firmly on the ground on Earth which revolves around the sun and so on, I left the details because it might get too complicated.

So the wall is attached to the ground and yet you are contending that it is free-floating and supported by nothing.

 

[Ibix]

What would happen if the wall were floating in free space? What if it were glued to a pebble? What about a small rock? A large rock? A boulder? An asteroid? A planet?

 

[Dale]

It has no external forces acting. It's just a wall, ball and air surrounding them.

So the wall is floating in the air? Your childhood must have been very interesting.

But this wall is rigid and standing firmly on the ground

Do you think that the description "firmly on the ground" may be indicative of an external force from the ground which is acting on the wall?

 

[PeroK]

Yes. But this wall is rigid and standing firmly on the ground on Earth which revolves around the sun and so on, I left the details because it might get too complicated.

And the Earth has momentum?

 

[adjacent]

Hmm, so the ball kicks the wall which kicks the Earth and Earth gains momentum but it's almost negligible?
But what if all of the Ball's kinetic energy gets converted to heat at the collision giving the wall no kinetic energy at all?

 

[PeroK]

Hmm, so the ball kicks the wall which kicks the Earth and Earth gains momentum but it's almost negligible?
But what if all of the Ball's kinetic energy gets converted to heat at the collision giving the wall no kinetic energy at all?

The change in the Earth's momentum and Kinetic Energy are not just negligible: children are playing with clay all round the globe, so it's impossible to isolate your experiment from everything else that is going on. Also, where did your clay ball get its momentum from in the first place?

 

[jbriggs444]

Hmm, so the ball kicks the wall which kicks the Earth and Earth gains momentum but it's almost negligible?
But what if all of the Ball's kinetic energy gets converted to heat at the collision giving the wall no kinetic energy at all?

Why not do some calculations? How much mass does the blob of clay have? How much mass does the wall have? How much velocity does the wall gain as a result of the collision? How much energy does that mean that the wall gains?

For extra credit, repeat the same computations using a frame of reference in which the wall is not initially stationary.

 

[phinds]

Hmm, so the ball kicks the wall which kicks the Earth and Earth gains momentum ...

... where did your clay ball get its momentum from in the first place?

Pay attention to this.

You have said that you left out details to avoid complication. Simplification can be good but massive oversimplification, such as in this case, leads to the kind of misunderstandings that you are experiencing.

 

[Dale]

But what if all of the Ball's kinetic energy gets converted to heat at the collision giving the wall no kinetic energy at all?

There is a maximum fraction of the KE which can get converted to heat in a perfectly plastic collision. That maximum is determined by the conservation of momentum.

 

[CWatters]

Hmm, so the ball kicks the wall which kicks the Earth and Earth gains momentum but it's almost negligible?

No, the change in the Earth's angular velocity is very small but the Earth has a huge mass so the change in the Earths momentum (the product of the two) cannot be neglected.

But what if all of the Ball's kinetic energy gets converted to heat at the collision giving the wall no kinetic energy at all?

What Dale said. It is possible for some of the balls KE to be converted to heat but momentum is always conserved. That means it's not possible for all of the balls KE to be converted to heat.

Do think about what Perok asked you...

where did your clay ball get its momentum from in the first place?

 

[adjacent]

Thanks everyone, after thinking about it for a bit, I can now understand.

 

[mridul]

Momentum is conserved only in elastic collision. So your observation is true .

 

[jbriggs444]

Momentum is conserved only in elastic collision. So your observation is true .

Momentum is always conserved. Presumably you had meant to say that "[kinetic] energy is conserved only in an elastic collision". That is true, by definition.

 

[mridul]

Nope see coefficient of restitution

 

[mridul]

Sorry

 

[jbriggs444]

Nope see coefficient of restitution

The coefficient of restitution is a measure of how much relative velocity is lost in a collision between two objects.

If one considers the total momentum of the system, momentum is strictly conserved. It is not lost. The relative velocity of both objects is reduced, but regardless of what frame of reference one chooses, the changes in momentum of the two objects are equal and opposite. That's Newton's third law.

If one considers the total kinetic energy of the two bodies according to $E=\frac{1}{2}mv^2$ then total kinetic energy [as judged in the center-of-momentum frame] will have been reduced by the square of the coefficient of restitution.

 

[hackhard]

I know that momentum is always conserved

and yes it is, say on hitting wall Earth gains speed of 10^-15 m/s multiply it with mass of Earth , so momentum gets conserved