# Stretching a rubber band increase its mass but how?

• I
• Patrick Pihl
In summary: And if anyone is curious about how faster than light implies time travel... Google for "tachyonic anti-telephone" and (more seriously) for "closed time-like curve".Time travel might be possible, but that's not what this discussion is about. This discussion is about the mass of an object when energy is transferred to it to increase its mass. Mass is related to the energy content of an object, so when energy is transferred to the object, its mass increases.
Patrick Pihl
Stretching a rubber band increase its mass due to e=mcc, but how?

Patrick Pihl said:
Stretching a rubber band increase its mass due to e=mcc, but how?
What do you think is the definition of the mass of an object?

Patrick Pihl
PeroK said:
What do you think is the definition of the mass of an object?

Number and kind of particles in the object?

Patrick Pihl said:
Number and kind of particles in the object?
A better example than the rubber band is the hydrogen atom: one proton and one electron. The mass of the atom, however, is less than the mass of the proton plus the mass of the electron. The difference is the binding energy released when the atom is formed. The same energy is required to ionise the atom by separating the two particles.

From this, you can see that the mass of a collection of particles is not simply the sum of the masses of each individual particle.

Patrick Pihl, Battlemage!, stoomart and 1 other person
Patrick Pihl said:
Number and kind of particles in the object?
This is not correct. The classical definition of the (inertial) mass is related to an objects resistance to acceleration. In relativity, it is related to the energy content of an object in its rest frame. It then turns out that this also is the inertia of the object, which is one of the great insights from special relativity!

Patrick Pihl and stoomart
Patrick Pihl said:
Stretching a rubber band increase its mass due to e=mcc, but how?

When you transfer energy to the rubber band to stretch it, you increase its energy. If the energy increases by ##E## the mass increases by ##E/c^2##. You correcty noticed that stating this doesn't explain how it happens.

To understand how it happens you need to understand what mass is. It's not a measure of the quantity of matter, it's a measure of the rest energy. Stretching the rubber band increases the rest energy. It turns out that in this case ##E/c^2##, the amount it increases by, is very very small compared to the rubber band's mass. So small in fact that the most precise measuring devices cannot detect it. Ignoring it is therefore justified when measuring the mass, so that is the approximation people use.

But just because the approximation is valid doesn't mean it constitutes a valid way of defining mass. There are plenty of other examples where the opposite is true. That is, the contribution to the mass is very very large compared to the mass of the object. Perhaps the most famous example is the atomic nucleus.

Patrick Pihl
Thank you all! That gives me a slightly better understanding :)
I should have thought about that myself when knowing that mass also increase with speed.

Patrick Pihl said:
when knowing that mass also increase with speed.
It does not. What is called "relativistic mass" is an antiquated concept. See my PF Insight on relativisic mass (link in my signature). When we talk about mass today we talk about the invariant mass of a system.

stoomart and Patrick Pihl
Orodruin said:
When we talk about mass today we talk about the invariant mass of a system.
It's not just a matter of "today." Even forty years ago when I was a grad student in experimental elementary particle physics, everyone that I worked with used "mass" to mean "invariant mass" a.k.a. "rest mass."

Patrick Pihl said:
I should have thought about that myself when knowing that mass also increase with speed.

That's an increase in relativistic mass. We're talking instead about an increase in mass.

You can't increase the mass just by increasing the speed. This confusion is best remedied by never introducing relativistic mass.

Mister T said:
This confusion is best remedied by never introducing relativistic mass.

Too late - unless you have a time machine.

DrStupid said:
Too late - unless you have a time machine.
I do. It turns out relativistic mass is imaginary.
For anyone not getting the joke: it turns out that traveling faster than light allows time travel (unless you restrict the allowable velocities somewhat). But anything with a real rest mass traveling at v>c would have an imaginary relativistic mass.

Ibix said:
For anyone not getting the joke: it turns out that traveling faster than light allows time travel (unless you restrict the allowable velocities somewhat). But anything with a real rest mass traveling at v>c would have an imaginary relativistic mass.
And if anyone is curious about how faster than light implies time travel... Google for "tachyonic anti-telephone" and (more seriously) for "closed time-like curve".

Of course, and kidding aside, the correct conclusions are not that time travel might be possible or that objects might have imaginary masses, but rather that equations derived under assumptions that are equivalent to "no FTL travel" cannot be used to predict what would happen if FTL were possible.

## 1. How does stretching a rubber band increase its mass?

Stretching a rubber band increases its mass because as it is stretched, the polymer chains within the rubber band are pulled apart, allowing more space for air to enter and increase the overall volume of the band. This increase in volume results in an increase in mass.

## 2. Why does the mass of a rubber band change when stretched?

The mass of a rubber band changes when stretched because the stretching process causes an increase in volume, which in turn increases the amount of air trapped within the band. This increase in air volume leads to an increase in mass.

## 3. Does stretching a rubber band change its density?

Yes, stretching a rubber band changes its density. As the rubber band is stretched, the volume increases but the mass remains the same. This means that the density decreases, as density is equal to mass divided by volume.

## 4. How does stretching a rubber band affect its properties?

Stretching a rubber band affects its properties in several ways. Besides increasing its mass and changing its density, stretching also changes the band's length and elasticity. The more a rubber band is stretched, the longer it becomes and the more elastic it becomes. This is because stretching aligns the polymer chains and allows them to stretch further, giving the band more elasticity.

## 5. Is there a limit to how much a rubber band can be stretched?

Yes, there is a limit to how much a rubber band can be stretched. The limit is determined by the strength of the polymer chains within the rubber band. If the band is stretched beyond this point, the chains will break and the band will snap. Additionally, the more a rubber band is stretched, the less force it can withstand before breaking.

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