Can a Fish Move a Ball in Water?

[.Scott]

You say the swimmer can push off. (which gives the swimmer momentum relative to the ground)

Under normal conditions, when the swimmer is pushing off, he is also pushing a quantity of water with him - although, for efficiency, as little as possible. The result is a wake that shows up at the water/air interface just as the swimmer pushes off - but it takes the right lighting to catch it. Here is a screen shot from the 2:39 mark in video Swimmer pushing off.

The wake can be seen in the areas circled - and their formation and movements can be seen in the video.

But when he is in a closed tank with no compressible fluids, he is simultaneously pushing himself forward and pushing an equal volume (and therefore mass) backwards. What exactly is happening is that he is pushing against a spreading column of water that reaches across the bowl to the opposite side. He is pushing the bowl in two opposite directions with equal force. Since we take the "water" to be incompressible and Newtonian, the speed of sound in that water would be infinite and that force would be applied simultaneous to the push-off.

 

[metastable]

What if the fish has an extremely long, extremely thin “fin” that unfolds like an arm with many elbows, and as the arm straightens out, it pushes the much more massive body of the fish all the way against the glass on the other side of the tank. When the nose of the fish reaches the other side, it’s arm can’t do any more work, and the fish’s body stops, but the water has additional energy that keeps it swirling in vortices for a time. If the main body of the fish translates across the ball, hits the other side and stops, but the water keeps moving, what momentum is equal and opposite to the continued swirling of the water after the fish stops, if translation of the entire ball doesn’t occur?

 

[jbriggs444]

but the water has additional energy that keeps it swirling in vortices for a time. If the main body of the fish translates across the ball, hits the other side and stops, but the water keeps moving, what momentum is equal and opposite to the continued swirling of the water after the fish stops, if translation of the entire ball doesn’t occur?

Repeat after me: "Energy and momentum are two different things"

It is perfectly possible to have swirling water with zero total momentum. In the case at hand, the momentum of the water after the fish stops totals zero regardless of any swirling that may continue.

 

[metastable]

Repeat after me: "Energy and momentum are two different things"

If there are 2 masses that can move independently relative to the ground, & both masses are initially at rest to the frictionless ground, I can calculate the momentum of 1 mass directly from the kinetic energy in joules the other mass acquired relative to the ground:

$m_1v_1=\sqrt{2}*\sqrt{m_2}*\sqrt{W_{kinetic_m2}}$

 

[jbriggs444]

If there are 2 masses that can move independently relative to the ground, & both masses are initially at rest to the frictionless ground, I can calculate the momentum of 1 mass directly from the kinetic energy in joules the other mass acquired relative to the ground:

$m_1v_1=\sqrt{2}*\sqrt{m2}*\sqrt{W_{kinetic_m2}}$

In this case we have many many little bits of water swirling this way and that. The fact that their aggregate energy is non-zero says nothing about their aggregate momentum.

[An astute observer could note that a known total energy together with a known total mass does place an upper bound on the magnitude of the total momentum. However, it does not impose a lower bound].

What is the total momentum of a pair of counter-rotating vortices?

 

[metastable]

Just to be clear, if the ball is floating in the space station, and the ball is filled with vacuum except for the water density fish and the fish extends its many elbowed arm to push its body from one side of the glass to the other side where its nose impacts the other side, I think we can agree an astronaut in the same compartment would observe the outside of the ball move slightly...

I think you are saying you believe if the same process occurs, but the ball is filled with water, then astronaut won't observe the outside of the ball move.

 

[A.T.]

... the ball is filled with vacuum except for the water density fish ...

Here the CoM is not fixed relative to the ball. Hamster method would work on Earth.

I think you are saying you believe if the same process occurs, but the ball is filled with water, then astronaut won't observe the outside of the ball move.

Depends on whether the CoM can move relative to the ball.

 

[jbriggs444]

I think you are saying you believe if the same process occurs, but the ball is filled with water, then astronaut won't observe the outside of the ball move.

Correct.

Assumptions: Rigid, spherically symmetric ball. Ball starts at rest, filled with incompressible fluid of uniform density. Fish is also incompressible, uniform density, same density as water. No leaks, voids or air bubbles. No external forces penetrate the ball to act directly on the fish or water.

Flashlights out the back are deemed to weak to be effective.

We are neglecting, at least for the moment, any unbalanced external forces on the ball. This includes thermal induced pressure gradients. If you wanted to turn the ball into a Crooke's radiometer then that would be an innovative solution, but let's rule it out for the moment.

Caveat: While the astronaut should not see the ball move linearly, it is possible for the fish to cause a rotation. That possibility has already been explored as early as post #5 in this thread.

 

[metastable]

So what happens when I make the fish more streamlined than it was initially (lower the drag coefficient but same mass and frontal area), and using the many elbowed arm accelerate the fish to the same velocity at the same midpoint before freezing the elbows... according to $F=(1/2)*C_d*rho*A_f*V^2$ the water exerts less force on the fish with the same initial velocity in the second case, so it has more velocity relative to the space station than the less streamlined fish at every point along its journey, correct?

 

[jbriggs444]

So what happens when I make the fish more streamlined than it was initially (lower the drag coefficient but same mass and frontal area), and using the many elbowed arm accelerate the fish to the same velocity at the same midpoint before freezing the elbows... according to $F=(1/2)*C_d*rho*A_f*V^2$ the water exerts less force on the fish in the second case, so it has more velocity relative to the space station than the less streamlined fish at every point along its journey, correct?

Adding complexities to your do-nothing machine again? How tedious.

Yes, you can make the fish accelerate more strongly or make its drift last longer. But the water flowing rearward past the fish then accelerates more strongly or lasts longer. It accomplishes nothing. No matter how the fish pushes off, no matter how he coasts, no matter how hard his nose bumps the glass, no net momentum changes result due to any of it.

Internal force pairs do not affect total momentum.

 

[metastable]

no net momentum

I don't think we are trying to find the net momentum of the whole system which will of course always be 0 if the whole system starts at rest relative to the ground...

I thought we are instead looking for any net momentum of just the glass relative to the ground or walls of the space station at any point during the exercise (which would need to be offset by other momentum somewhere else to maintain net 0 momentum).

Obviously if the whole system starts at rest to the ground (such as a pair of skaters pushing off each other), one mass can acquire net momentum to the ground, while the system as a whole maintains 0 net momentum to the ground (the one skater's net momentum is offset by the other skaters net momentum in the opposite direction for a total of 0 net momentum at all times).

 

[A.T.]

I don't think we are trying to find the net momentum of the whole system which will of course always be 0 ...

If the net momentum of the whole system will always be 0, then the CoM of the whole system will always remain at rest. So whether the ball can move, boils down to whether the CoM can move relative to the ball. If it can, you can use the hamster method anyway.

 

[metastable]

whether the ball can move, boils down to whether the CoM can move relative to the ball.

Well in the skaters pushing off analogy, if they are the same weight the center of mass doesn't move at all, but both skaters do...

 

[jbriggs444]

Well in the skaters pushing off analogy, if they are the same weight the center of mass doesn't move at all, but both skaters do...

If one skater surrounds the other completely then that push-off is going to be difficult. You cannot get much relative momentum if your centers of mass are constrained to coincide.

 

[metastable]

One skater could be a ring shape around the other skater, and if they both have the same mass, and the skater on the inside pushes on the skater on the outside, they will both move in opposite directions with the same velocity for a short time...

 

[jbriggs444]

One skater could be a ring shape around the other skater, and if they both have the same mass, and the skater on the inside pushes on the skater on the outside, they will both move in opposite directions with the same velocity for a short time...

You persist in violating the assumptions of the problem.

 

[A.T.]

One skater could be a ring shape around the other skater...

You have replaced "ball" with "ring shape". The physics is still the one pointed out post #152:

Whether the ring shape can move, boils down to whether the net CoM can move relative to the ring shape.

 

[metastable]

So here we have a sealed rectangular aquarium resting on the ground, containing a floating, sealed spherical aquarium, containing a fish with an extendable arm for propulsion. The rectangular aquarium has its own fish with an extendable arm. If both fish push for the same duration with the same force, will the floating spherical aquarium move in the water?

 

[A.T.]

So here we have a sealed rectangular aquarium resting on the ground, containing a floating, sealed spherical aquarium, ...

When we answer this, will you put another aquarium in an aquarium in an aquarium... ?

Do you understand the general argument in post #152?

 

[metastable]

If the glass is initially at rest to the ground, both fish have the same mass and displace the same amount of water, both arms exert the same amount of mechanical work in joules against the glass in opposite directions at the same point, both fish require the same amount of energy to move the same distance in the same time and also move the same amount of water the same distance within their respective tanks in the same amount of time. Since fish displacement relative to ground plus internal water displacement relative to ground within both tanks is equal, there is no surplus energy or momentum to move the spherical tank sideways through the water... or am I mistaken here?

 

[jbriggs444]

If the glass is initially at rest to the ground, both fish have the same mass and displace the same amount of water, both arms exert the same amount of mechanical work in joules against the glass in opposite directions at the same point, both fish require the same amount of energy to move the same distance in the same time and also move the same amount of water the same distance within their respective tanks in the same amount of time. Since fish displacement relative to ground plus internal water displacement relative to ground within both tanks is equal, there is no surplus energy or momentum to move the spherical tank sideways through the water... or am I mistaken here?

Yes, you are.

 

[metastable]

If the inner tank has the same mass as the outer tank and both are initially floating at rest in a blue walled space station as shown below, and we release a spring (containers are filled with water and have water density glass of negligible mass), I don't understand why they won't simply go in opposite directions to conserve momentum, as shown below:

 

[jbriggs444]

If the inner tank has the same mass as the outer tank and both are initially floating at rest in a blue walled space station as shown below, and we release a spring (containers are filled with water and have water density glass of negligible mass), I don't understand why they won't simply go in opposite directions to conserve momentum, as shown below:

They will. The outside fish produces an external force on the inside ball, just as if the inside fish were not there. That is not your mistake.

 

[metastable]

They will.

So then the ball is observed to move (see where it crosses over the grey line).

 

[jbriggs444]

So then the ball is observed to move (see where it crosses over the grey line).

No. I do not. As I understand the drawing, the ball is pushed leftward and the surrounding water flows rightward past some imaginary line.

Edit: Sorry, I'd assumed you were sticking to the ball in an aquarium scenario. But you've changed to some kind of concentric balls in a space station scenario. In that scenario, the outer ball does not move. It obviously does not move since the only forces in play are internal and that means that the center of gravity is fixed.

 

[metastable]

you've changed to some kind of concentric balls in a space station scenario. In that scenario, the outer ball does not move.
It obviously does not move since the only forces in play are internal and that means that the center of gravity is fixed.

It isn’t necessary to change the center of gravity when forces are internal to change the external position in space. I take (2) 1kg blocks w/ a spring between them. One of the blocks is attached to the inner edge of a box of insignificant mass that encloses both blocks. the other block has a tiny weight to counterbalance the insignificant mass exterior box. when the spring between the (2) 1kg blocks is released the outer box of insignificant mass moves to one side. The position of the external enclosure shifts even though the forces are internal and the center of mass is fixed. Momentum and energy would be conserved — position isn’t necessarily.

 

[jbriggs444]

It isn’t necessary to change the center of gravity when forces are internal to change the external position in space.

Stop changing the scenario. We are talking about rigid spheres containing uniform density incompressible fluids. Do try to keep track.

 

[A.T.]

The position of the external enclosure shifts even though the forces are internal and the center of mass is fixed.

We have been through this several times already:

1) If the CoM can move relative to the ball: Translate it in front of the contact (hamster method, works continuously against resistance)

So whether the ball can move, boils down to whether the CoM can move relative to the ball. If it can, you can use the hamster method anyway.

 

[metastable]

 

[jbriggs444]

[A picture showing an un-covered containers subject to external forces]

Nothing to see here.

 

[metastable]

It would be quite interesting if someone did an experiment with a spring and covered containers...

 

[sophiecentaur]

This thread is typical of PF - but there is some excuse in this case, perhaps. Fact is that the initial assumptions were not laid down so people are bringing in more and more subtle effects. But the bottom line (i think) is that, if the fish moves through the water in one direction, water must move in the opposite direction. This will have an effect on the envelope due to friction so the envelope will move in the opposite sense to the fish. Once the fish stops swimming, fish and ball will come to a halt with the angles of the ball and fish, relative to some initial reference, different from how it started off.
If the fish can directly move the wall then it just gets more complicated and any loss of Energy will not affect the main principle because it'.
I like the wobbling ball factor! But, if the fish has the same density as water, why would the ball be displaced- unless the fish actually hits the side?

 

[jbriggs444]

But, if the fish has the same density as water, why would the ball be displaced- unless the fish actually hits the side?

You are falling into the same trap as @metastable. The ball does not move, even if the fish hits the side.

The gotcha is that if the fish comes to an abrupt stop then so does the water. Any momentum transferred from fish to wall is matched by an opposite momentum transferred from water to wall.

Subject to background assumptions of rigid wall, incompressible fluid, etc.

 

[metastable]

The gotcha is that if the fish comes to an abrupt stop then so does the water.

How can you prove when the fish hits the wall the water stops? Some glitter in the water should be able to test that proposal.

 

[jbriggs444]

How can you prove when the fish hits the wall the water stops? Some glitter in the water should be able to test that proposal.

Mathematics is your friend. The proof has been given already.