# Massless body

1. Jun 26, 2008

### atavistic

What happens when the NET force on a massless body is 0. I mean what will be the acceleration , if any?

Also if we pull a massless spring, from one side with a force F1 and from the other side a force F2, what will be the spring force?

2. Jun 26, 2008

### pzlded

I suppose some neutrinos are supposed to be massless and acceleration could occur if the neutrino interacted with an atom (converting neutrino energy to kinetic energy).
If F1 and F2 are constant, but unequal, the massless spring would likely instantly reach the speed of light.

3. Jun 26, 2008

### Redbelly98

Staff Emeritus
Like anything else, it will obey Newton's 2nd Law:

F = m a
or
0 = 0 x a

So, the acceleration can really be anything.

The net force must be zero for a massless object:

F = m a = 0 x a = 0

Therefore, F1 and F2 are equal in magnitude and act in opposite directions. Use either F1 or F2 in the spring formula,
F = k x

4. Jun 26, 2008

### pzlded

Hi Redbelly,

In practice, acceleration is limited by the speed of light. For example: the speed of light limits quantized acceleration of a neutrino.

The original problem did not specify that F1 and F2 are equal or that the force is gravitational. Magnetism, the electrostatic field of a point charge and many other forces do not require interaction with mass. In other words, net F does not necessarily equal zero.

5. Jun 26, 2008

### Redbelly98

Staff Emeritus
The original problem specified a massless spring. Therefore net force is zero, and F1 and F2 are equal in magnitude.

I don't see why you're bringing up gravity, magnetism, etc. These are beginning "Physics 101" concepts at play here.

Regards,

Mark

6. Jun 26, 2008

### pzlded

Hi Mark,

The forces pulling on the spring could have been the result of a mass suspended by the spring. Perhaps I should have mentioned that if F1 equals –F2, the weight of the mass equals the pull on that end of the spring, equals the pull on the supporting bracket.

When F1 does not equal -F2, the spring could result in accelerate to light speed. However, this requires that the assembly of forces and a spring are massless and isolated.

Best Wishes

7. Jun 26, 2008

### atavistic

redbelly, I am talking about the case when a spring is kept on a horizontal surface, and if a pull of magnitude F1 and F2 (not equal) respectively are given to the ends. Then how will F1 = -F2. For e.g. I give a force of 10 N and 20N , then for the spring

10 - 20 = m *a
=> 10 =0 !!!?

pzlded: Is there any proof for your claim?

8. Jun 26, 2008

### Xezlec

This is exactly why, in classical physics, there's no such thing as zero mass (I once asked a similar question about zero resistance in an introductory EE class... the answer is about the same).

The answer is, you "can't" apply a net force to a zero mass. It's just against the rules. If you do, you have a paradox, which just means that your description of reality was wrong... and it was! There are no classical massless objects, which is the only reason all values of force applied on any object are OK.

So the answer is throw away that "zero mass"; it's nonsense for precisely the reason you show. In relativity, however, zero mass is just fine, and it can experience forces, but that's only because the laws of physics get changed around so F doesn't equal m a anymore.

9. Jun 26, 2008

### Xezlec

If there is zero force on a zero mass, then RedBelly is correct: the acceleration can be whatever you like. It is "unconstrained" as a technical person would say. Of course this is kind of silly, but that's only because zero mass is silly to begin with.

10. Jun 27, 2008

### pmb_phy

When you use the term "mass" do you mean rest mass or inertial mass? If you mean inertial mass then the acceleration can be anything you'd like. If the mass is zero then that means that the momentum is zero regarless of the velocity. Since force is the time rate of change of momentum it follows that the force is zero so this is consitent with the condition of zero force you are imposing.
What is this spring force that you speak of?

Pete

11. Jun 27, 2008

### pmb_phy

What's so silly about zero mass?

It theoretically possible within the theory of relativity, although perhaps not in practice. Even negative values of mass have been discussed in the physics literature. Stress contributes to the inertial mass of a body while tension subtracts from it. I.e. there could be enough tension in a body to reduce its inertial mass to zero.

Pete

12. Jun 27, 2008

### Xezlec

As has been pointed out, this is the classical physics forum and it's a classical physics question. I mentioned parenthetically in my first reply that zero mass was perfectly fine in relativity.

13. Jun 27, 2008

### D H

Staff Emeritus
It's nonsense in first question.

The second question is nonsense also, but not because the spring is massless. Massless springs are an idealization meant to get rid of complexities. An ideal spring is massless, frictionless, unbreakable, and has a force response that is a proportional to displacement (regardless of the frequency of the dispacement). A single massless spring often has one end fixed to a wall. Think of the wall as an object with infinite mass. The fixed end of the spring isn't going anywhere, so you don't even have to model the force at that fixed end. Massless springs are also modeled as having massive objects attached at each end. A bit tougher, but the ensemble is not massless.

Bottom line: A free-moving massless body makes no sense in classical physics. Don't ask questions about them because such questions are nonsense. A massless spring always has one end fixed to a massive object. The spring is not going to fly off at infinite speed. Don't ask questions about massless springs without any attached masses because such questions are nonsense.

14. Jun 27, 2008

### pzlded

Hi D.H.

I rebel at the thought that physics is cut and dry. I do not object to the idea that classical physics is an idealization of the real world; I object to the idea that the difference between classical physics, quantum physics and relativity are almost by definition ‘unexplainable’. Together, these disciplines are contemporary and relevant to today’s workplace problems.

The lack of explanation of differences between classical physics and other physics can cause arbitrary declarations. Consider atomic collision products that travel that travel at light speed. Perhaps all those products must have no mass, perhaps they have ‘inherent’ mass, or maybe they have more mass than either the original target mass or projectile mass alone.

Best wishes

15. Jun 27, 2008

### D H

Staff Emeritus
Rebel all you want. Physics is supposed to be cut and dry because it is science. If you want the answer to be whatever you want, study philosophy or shudder postmodernism. Physics needs to be cut and dry so that we can make predictions, falsify hypotheses, and develop really neat and useful things such as the science behind the computer on which I am typing this post.

Scare quotes. Please go back to your postmodernism studies. But please do bone up on physics while you go.

The difference between classical physics and quantum mechanics is anything but `unexplainable'. We know quite well what the differences are, where they lie, and how they come about. The same is true for classical physics and relativity. The same is not true for quantum mechanics and relativity. Physicists don't like that, so some are working on rectifying the situation.

Pretty please, with sugar on it?

Atomic collision products that travel at light speed have a name: photons. Photons have zero rest mass and a non-zero momentum given by $E=hf$. Pretty cut and dry if you ask me.

16. Jun 27, 2008

### Xezlec

The results of experiment disagree. If you're going to make this bizarre claim, you'd better have some really good evidence. Things that go the speed of light are massless. There's no mystery about this to people who have studied the subject via experiment.

Quantum physics is a more accurate approximation than classical physics. That's why it replaced it.

17. Jun 27, 2008

### Redbelly98

Staff Emeritus
Xezlec answered it well in post #'s 8 and 9. I'll just add:

Since zero-mass mechanical springs don't really exist, instead imagine that the spring's mass is much much less than ordinary everyday massive objects that are normally attached to that spring. For example, a spring might be 0.1 kg, and be connected to 100 kg objects. That's a factor of 1000 times less massive.

Next, take a net force that might be used to accelerate the massive 100 kg objects, and instead apply the same force to the 0.1 kg spring. The spring's acceleration will be 1000 times more than that of the massive objects, and would appear to move extremely fast.

Finally, if one stipulates that the spring does not accelerate or move very quickly, the net force on it would have to be rather small for that to be the case. To make calculations simple in high school and college freshman physics courses, we stipulate that this net force is zero. Though not rigorously true, it's a good enough approximation to:

1) calculate forces fairly accurately
and
2) learn some "building block" principles of how forces behave.

I would save concerns about relativity and quantum mechanics for more advanced physics courses. Learn these basics first.