# Motion caused by Internal force

I would like to clarify whether an internal force in a system can cause it a motion externally? My Physics teacher and also other tuitions in my area tell that only external forces can cause motion of a system.

Last day I conducted an experiment (if you can call it one):

I filled a bucket half full of water then gave it a hard push (don't ask me the magnitude of force) on a smooth tiled floor. The observation was that after the bucket (didn't topple nor did the water spill out, it just reached the brim) skidded about a meter and a half, then it recoils about a foot (backwards). What I infer from this is that the inertia of the water (internal force) in the bucket (system) caused the water to exert adequate internal force on the (opposite) wall of the bucket which produced an external (recoil) motion for the system as a whole. I conclude that internal force can indeed cause external motion of the system (at times).

Now anyone who reads me, tell me if:

• I went wrong anywhere.
• my conclusion was wrong.
• my reasoning was incorrect.

Please be open and preferably detailed. I don't mind criticism, because I'm a learner. I'm humbly requesting your answers and opinions!

• Please format your question properly. Its difficult to read and understand. – SchrodingersCat Oct 23 '15 at 17:36
• You can't have a frictionless surface in your bathroom, no matter how smooth and tiled the floor is....so then you forgot one vital force : friction which is an external force in this case – Shubham Oct 24 '15 at 7:46
• But you see, frictional force cannot produce recoil motion...whatever magnitude of force may it produce its maximum is the value of limiting friction which has only the equivalent force to stop the motion. – Chrisle J.Charls Oct 26 '15 at 8:06

It depends what you mean by external motion.

If you had a box in space and you were sitting on one end with some baseballs and you threw a baseball at the opposite side then the whole box would move in the opposite direction as you threw the baseball, during the time the baseball was in flight.

Someone on the outside that can't see what you did would see the box move while the ball was in flight. If you had multiple balls you could move multiple times. But the momentum of the whole system of you, box, and baseballs isn't changing. And neither is the center of mass. The outside parts move because the internal parts are moving the opposite way.

• I like your answer (coz it's the same thought i had) but can you conclude that external motions can be triggered by internal forces? [isn't it a perfectly elastic collision?] – Chrisle J.Charls Oct 26 '15 at 8:23
• @ChrisleJ.Charls You keep asking the same question when my response is that it depends strongly on your definitions. The example I gave might look like external motion to someone on the outside that doesn't see the back end getting heavier as the front end gets lighter. I'd they just see the front end go forward they might mistake it for external motion even though the center of mass didn't move. – Timaeus Oct 26 '15 at 14:24

Without seeing it, it's difficult to know exactly what happened. But there are two main areas that I would expect to find some resolutions.

• You can see the pail easily, but you cannot see the center of mass easily.

When it says can't move the system as a whole, that doesn't mean you can't move parts of it. As the water sloshes, it can be deceptive to know if the system is moving or not.

• Your system (bucket and water within) is not isolated

I think this is the bigger one from your description. The bucket has some interactions with the floor and friction. It's very possible to get the water sloshing in a way that pushes back on the floor for a second to get the system moving back to you, and then slides a way with less friction.

Redoing your experiment on a "frictionless" table to remove that external force would see the pail not return. It might oscillate as it went, but the whole thing would not stop and come back.

• That's something close because the recoil was somewhat a half oscillation backwards...so my question is that if i can conclude 'external motions of the system can be triggered by internal forces of the system'...? – Chrisle J.Charls Oct 26 '15 at 8:11
• No. The bucket is not "the system". Internal forces can move the outer shell, but not the center of mass. – BowlOfRed Oct 26 '15 at 8:14

Other answers discuss external and internal motion rather than forces, as the question states. Is this what you are asking?

Coming from the engineering world, Internal forces refer to stresses ($\sigma = F/A$)- they are reaction forces within a material to external forces applied at the material boundaries. It is impossible to apply a force inside a material without redefining the external boundary (magnetized materials might be an exception?). It is worth mentioning for clarity that internal stresses and forces are synonymous because at infinitely small scales (used to derive equilibrium equations), the area term disappears.

Since liquids have little resistance to shear stress (measured by viscosity)- they readily deform/flow. Ultimately, the bucket recoils because the water deforms, shifting its center of mass when accelerated:

You are correct in your analysis of inertia, except that all forces between bodies are external, as they act on boundaries.

Regardless of friction between the bucket and floor, the water will have a damped oscillation, where its center of mass shifts back and forth until it is level and centered. Each oscillation applies external loads to the bucket, causing the bucket to recoil.
If friction is present, the bucket will stop but will recoil in alternate directions from each external oscillation force until they are less than the frictional force. At this point the bucket no longer moves but the water continues to oscillate until it is level and centered.

The following stress plot shows how the external force is transmitted through the solid bucket via stress. Note that internal forces are limited by the material strength.

You would be well served to consider the context of the lesson that your instructor is giving you. For less experienced physics students, the physics lesson involves either point objects or rigid bodies, not buckets full of water. For those cases, internal forces do not cause objects to move.

If you take a given physics class with "hidden" assumptions about how the real world works, and you diligently attempt to find "exceptions to the rule" of what your instructor is teaching you, you will very likely never let go of those hidden assumptions, which will often cost you dearly on test day. Learn to accept what is taught, and quit attempting to find exceptions to every rule or concept.

• I'm sorry for the delayed reply...but i would like you to consider the question on my exam paper: A sailboat has a electric fan mounted on it facing the sail. Will the boat move if the fan is turned on? – Chrisle J.Charls Dec 22 '16 at 17:12
• No. Newton's 3rd law guarantees that there is an equal and opposite force on the fan. That force will offset the force on the sails, and the boat will not move. – David White Dec 22 '16 at 19:43

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