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Old Mar 14th 2011, 12:09 AM   #1
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Mass dilation question

Hey guys, i was just wondering what would happen if a person was on a spacecraft traveling at 0.9c was standing on a set of scales that measured his mass, went past a stationary observer.

Would the stationary observer see the reading on the scales increase due to mass dilation?

I asked a few people in our physics class, they kinda said that since the total mass of the spacecraft increases in the reference frame of the stationary observer, for example the springs and stuff in the scales would have more mass and and be harder to push down therefore the reading will not increase?

will there be a contradiction?

could you hopefully explain this in high-school level terms, all we've learnt are the mass dilation equations lol

thanks
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Old Mar 14th 2011, 09:52 AM   #2
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Originally Posted by aonin View Post
Hey guys, i was just wondering what would happen if a person was on a spacecraft traveling at 0.9c was standing on a set of scales that measured his mass, went past a stationary observer.

Would the stationary observer see the reading on the scales increase due to mass dilation?

I asked a few people in our physics class, they kinda said that since the total mass of the spacecraft increases in the reference frame of the stationary observer, for example the springs and stuff in the scales would have more mass and and be harder to push down therefore the reading will not increase?

will there be a contradiction?

could you hopefully explain this in high-school level terms, all we've learnt are the mass dilation equations lol

thanks
I'm a bit surprised in hearing that schools are still teaching relative mass increases. Most people that study SR anymore use the concept that mass stays constant and it is the momentum that experiences relativistic changes.

Anyway, I'm going to support what your Physics class told you. Scales do not actually measure mass, they measure weight. Since w = mg we can simply change the scale of the numbers by a factor of g and use it to represent the mass. Scales are made with counterweights or springs. For the case of the counterbalances, your classmates are correct: they will change in mass just as you do, so there will be no change in your weight measurement. I really don't know about the case of springs. Here we are dealing with the size of the spring constant, k, and it makes sense to me that the spring constant would increase with a relativistic mass increase, but I can give you no proof that that happens. All I can say is that the two kinds of scales should give you the same weight so to avoid a paradox.

Interesting question!

-Dan
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Old Mar 27th 2011, 08:50 AM   #3
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I presume that the scale is moving with the person! And that answers your question. If the scale showed the "mass increase" due to motion, the person standing on the scale could read it and calculate his speed contradicting the fact that motion is purely relative.
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Old Apr 1st 2011, 02:53 PM   #4
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[quote=aonin;16663]Hey guys, i was just wondering what would happen if a person was on a spacecraft traveling at 0.9c was standing on a set of scales that measured his mass, went past a stationary observer.

Would the stationary observer see the reading on the scales increase due to mass dilation?
[/quote
The scale would be measuring the inertial force which is being applied to the pan of the scale. The inertial force is related to the inertial mass by F = dP/dt where P = mv. This F and thus the m would be different for each observer. You can't really use a "scale reading" since the scale is calibrated to be read from the rest frame of the scale.

topsquark - see [0709.0687] On the concept of relativistic mass and the reference material which relates the relative percentages of what is being printed in newer relativity texts.

re - "Scales do not actually measure mass, they measure weight. "

That is incorrect. If a scale is being accelerated then it's measuring inertial force, not weight. Weight requires a gravitational field since it is related to passive gravitational mass. These quantities, passive gravitational mass and inertial mass, are defined differently but are postulated to have the same value. See article I wrote which is linked to above.
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