Why Does Mass Increase with Speed?

[Mr. Tambourine Man]

OK, I'll admit...I am only a beginner, if even. I understand why time and length are effected by speed. But I've never understood why mass increases. Would someone kindly show me how and why mass increases the faster an object goes (using mathematical language understandable by someone who has not gone further than calculus)? Thank you.

 

[pmb_phy]

OK, I'll admit...I am only a beginner, if even. I understand why time and length are effected by speed. But I've never understood why mass increases. Would someone kindly show me how and why mass increases the faster an object goes (using mathematical language understandable by someone who has not gone further than calculus)? Thank you.

If you understand algebra then that's all you'll need. I placed the definitions and derivations on a web page. See - http://www.geocities.com/physics_world/sr/inertial_mass.htm

Pete

 

[bernhard.rothenstein]

have a look please at
http://arxiv.org/abs/physics/0306059

 

[pervect]

OK, I'll admit...I am only a beginner, if even. I understand why time and length are effected by speed. But I've never understood why mass increases. Would someone kindly show me how and why mass increases the faster an object goes (using mathematical language understandable by someone who has not gone further than calculus)? Thank you.

I think the single most important thing to learn about "mass" is that the same name has spawned several different concepts.

In SR, for instance, we have "invariant mass", which does not change with velocity, and "relativistic mass", which does. There are many people such as myself who rarely use the "relativistic mass" concept, including myself.

See for instance the sci.physics.faq http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html"

Things continue on in this fashion in GR, where one may eventually learn (with enough study) about Komar mass, ADM mass, and Bondi mass.

These ideas are all closely related, but not necessarily the same.

To sum it up, when talking about mass, the best reaction is to think "what sort of mass?".

 

[Garth]

Whenever we talk about a quantifiable concept such as "rest mass" the question must be asked: "How do we measure it?"

The only way to measure rest mass is in a frame of reference in which the mass is at rest, i.e. one co-moving with it.

In this frame the mass of a fundamental particle is constant, at least by definition. (As the only way of measuring any such variation is to compare it with a similarly co-moving standard mass they both could vary, but you would be unable to detect it unless you had another non-varying alternative to make the comparison.)

The inertial mass of a object moving relative to an observer does increase with velocity as SR predicts and that has been confirmed in particle accelerators: "The faster it goes the harder it is to 'push'"

Whether you want to call such "relativistic mass" or not is a matter of convention, the standard convention is to leave the term 'mass' for only the rest mass of an object.

Garth

 

[pmb_phy]

Whether you want to call such "relativistic mass" or not is a matter of convention, the standard convention is to leave the term 'mass' for only the rest mass of an object.
Garth

That is the more popular convention. It is not exclusively true in all cases. Texts such as that by Rindler, Mould, d'Inverno, Misner, Thorne and Wheeler, and Peacock use mass in most places to mean "relativistic mass."

Pete

 

[pervect]

That is the more popular convention. It is not exclusively true in all cases. Texts such as that by Rindler, Mould, d'Inverno, Misner, Thorne and Wheeler, and Peacock use mass in most places to mean "relativistic mass."
Pete

I'll have to disagree with this characterization of MTW, while agreeing with the general principle that there is the possibility for a significant amount of confusion between the usage of "mass" to mean "relativistic mass" or "invariant mass".

 

[bernhard.rothenstein]

I think the important problem is how we derive the formula that relates mass to rest mass. It can be done using energy (mass) and momentum conservation but even not using them. During tghe derivation we can give up the concept of mass using instead the concept of energy.

 

[daniel_i_l]

It is possible to measure inertial mass with a clock and ruler, if they give different measurements then the mass will be measured differently to.

 

[bernhard.rothenstein]

It is possible to measure inertial mass with a clock and ruler, if they give different measurements then the mass will be measured differently to.

how? should our message contain? at its end?

 

[daniel_i_l]

how?

You mean how can you measure mass with a ruler and clock?
Well, atleast in Newtonian physics, F=ma. So m = F/a.
a = m/s/s - all of those units can be measured with a clock and ruler. So move an object with a known amount of force, measure its acceleration, and the you can find its intristic mass.

 

[pmb_phy]

It is possible to measure inertial mass with a clock and ruler, if they give different measurements then the mass will be measured differently to.

It depends on what the object is whose mass you wish to measure. E.g. if its charged particle of charge q then we can launch it into a uniform magnetic field, of strenght B, in a direction which is perpendicular to the field lines. The charged particle will move in a cirlce of radiius r. As shown here

http://www.geocities.com/physics_world/sr/cyclotron.htm

that the following relationship holds true.

p = qBr = mv

or

m = qBr/v

Therefore one can use a ruler and clock to determine the speed of the particle and then plug it into m = qBr/v to obtain the mass.

Pete