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1. Dynamics
so i learnt that mass doesnt change a few years ago.Then my lecturer tells me mass varies in some cases..?in what cases?why?

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2. Re: Dynamics
I was taught that as things approach the speed of light there's a relativistic mass increase.
I could be completely wrong in saying this (and I don't even know what it really means, maybe related to E=mc^2??) but its just one of them things I picked up from A-Level
3. Wow thx ~ 0.o i still dont get it though :P

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4. Re: Dynamics
Well E = mc^2 gives a rule for converting mass to energy (and vice versa) - in nuclear fusion, say, the product element weighs slightly less than the reactants. This small loss of mass is converted into energy, governed by the equation above (note c^2 is around 9 x 10^16, so a large amount of energy results from a small amount of mass).
5. Re: Dynamics
Even in non-relativistic mechanics you sometimes need to deal with varying mass, eg a rocket losing mass as it burns fuel, or raindrops getting heavier as they fall through clouds
6. Hmm...very insightful.But in short,mass increases as velocity increases? Assuming the object doesnt lose any mass due to loss of fuel etc

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Last edited by Vadevalor; 24-07-2012 at 15:34.
7. Re: Dynamics
Hmm...very insightful.But in short,mass increases as velocity increases? Assuming the object doesnt lose any mass due to loss of fuel etc

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No

momentum increases as the velocity of a mass increases.

the mass does not change.

I think give the title dynamics, the mass change is due to loss of fuel or the gain of more mass in a collision.
8. Re: Dynamics
(Original post by kingkongjaffa)
No

momentum increases as the velocity of a mass increases.

the mass does not change.

I think give the title dynamics, the mass change is due to loss of fuel or the gain of more mass in a collision.
In a Newtonian limit that is correct but in Einsteinian physics it is very, very wrong.

In relativity, a massive object travelling very close to the speed of light will be measured to be much heavier than one which is stationary. It comes from the proof of time dilation coupled with the conservation of momentum.
9. Re: Dynamics
(Original post by 3nTr0pY)
In a Newtonian limit that is correct but in Einsteinian physics it is very, very wrong.

In relativity, a massive object travelling very close to the speed of light will be measured to be much heavier than one which is stationary. It comes from the proof of time dilation coupled with the conservation of momentum.
He's actually right, and relativistic mass is a misleading, wrong, concept. The better, more advanced formulations of special relativity by such physicists as John Wheeler have scrapped the idea entirely. The gamma in the expression for momentum should be tied to the velocity, and not the mass; the mass does not increase, the velocity transforms due to the existence of an upper limit (note that if c = infinity (and hence we'd live in a Galilean universe), then gamma becomes 1, and Einstein's relativity obsolete).
Last edited by FireGarden; 26-07-2012 at 00:11.
10. Re: Dynamics
(Original post by FireGarden)
He's actually right, and relativistic mass is a misleading, wrong, concept. The better, more advanced formulations of special relativity by such physicists as John Wheeler have scrapped the idea entirely. The gamma in the expression for momentum should be tied to the velocity, and not the mass; the mass does not increase, the velocity transforms due to the existence of an upper limit (note that if c = infinity (and hence we'd live in a Galilean universe), then gamma becomes 1, and Einstein's relativity obsolete).
Hmmm, that's interesting, I've never heard that before. Do you have a source?

From a purely experimental point of view, I suppose all we can really be sure of is that the lorentz transform acting on the product on m and v...and so there is potentially a debate about which term it is associated with. And yes, I am familiar with the Newtownian limit being c----> infinity.

It's a bit late now but this will get me thinking.
11. Re: Dynamics
(Original post by FireGarden)
He's actually right, and relativistic mass is a misleading, wrong, concept. The better, more advanced formulations of special relativity by such physicists as John Wheeler have scrapped the idea entirely. The gamma in the expression for momentum should be tied to the velocity, and not the mass; the mass does not increase, the velocity transforms due to the existence of an upper limit (note that if c = infinity (and hence we'd live in a Galilean universe), then gamma becomes 1, and Einstein's relativity obsolete).
How can we put c as infinity?
12. Re: Dynamics
(Original post by TheGrinningSkull)
How can we put c as infinity?
Newton assumed that the gravitational force between the earth and the sun was communicated instantaneously. The term c, known as the speed of light, is the maximum speed at which two objects can communicate with each other. Thus in the Newtonian formalism, time taken to communicate = 0 and so c = distance/time = distance/0 ---> infinity.

In the framework of Einstein's relativity, the speed of light is finite and defined to be constant in all frames of reference.
13. Re: Dynamics
(Original post by 3nTr0pY)
Hmmm, that's interesting, I've never heard that before. Do you have a source?

From a purely experimental point of view, I suppose all we can really be sure of is that the lorentz transform acting on the product on m and v...and so there is potentially a debate about which term it is associated with. And yes, I am familiar with the Newtownian limit being c----> infinity.

It's a bit late now but this will get me thinking.
Taylor and Wheeler both rejected the concept of relativistic mass and I think Einstein did as well later. The concept of relativistic mass is equivalent to that of energy as can easily be seen when working in natural units. Mass is the the length of a four vector and so is an invariant. The energy-momentum four-vector is what undergoes the Lorentz transforms.
14. Re: Dynamics
(Original post by suneilr)
Taylor and Wheeler both rejected the concept of relativistic mass and I think Einstein did as well later. The concept of relativistic mass is equivalent to that of energy as can easily be seen when working in natural units. Mass is the the length of a four vector and so is an invariant. The energy-momentum four-vector is what undergoes the Lorentz transforms.
Aha, I am familiar with this:

m^2 = E^2 - p^2, setting c=1 for convenience.

I now see what you and FireGarden are alluding to. That does make sense. (Although from an experimental/practical point of view I suppose it could still be argued that mass does increase at relativistic speeds)

When I was first taught SR, relativistic mass was taught as being correct, to my memory. When I later learnt the above equation I never really considered how it conflicted with my previous understanding of the subject. Thanks.
Last edited by 3nTr0pY; 26-07-2012 at 01:09.
15. Re: Dynamics
(Original post by 3nTr0pY)
Although from an experimental/practical point of view I suppose it could still be argued that mass does increase at relativistic speeds
I think the prevalent view now is that mass is relativistically invariant. Mass is generally considered to be an inherent property of matter much like charge and for that to change depending on your reference frame is a slightly strange notion. Energy on the other hand is velocity and therefore frame dependent.

The physics is still the same, it's really just the name that's been changed.
16. Re: Dynamics
(Original post by 3nTr0pY)
Newton assumed that the gravitational force between the earth and the sun was communicated instantaneously. The term c, known as the speed of light, is the maximum speed at which two objects can communicate with each other. Thus in the Newtonian formalism, time taken to communicate = 0 and so c = distance/time = distance/0 ---> infinity.

In the framework of Einstein's relativity, the speed of light is finite and defined to be constant in all frames of reference.
How have we arrived at the time to be 0 though?

In your first sentence, speed is not a force, so where did we arrive at the conclusion that speed communication is instantaneous from a force being instantaneous?
17. Re: Dynamics
(Original post by suneilr)
I think the prevalent view now is that mass is relativistically invariant. Mass is generally considered to be an inherent property of matter much like charge and for that to change depending on your reference frame is a slightly strange notion. Energy on the other hand is velocity and therefore frame dependent.

The physics is still the same, it's really just the name that's been changed.
Bloody hell, it just clicked - up until today, I've never thought that mass was anything other than an invariant. So I have no idea why I made my first comment saying that it varies. Perhaps it was some pop sci crap kicking around in the back of my mind.

I blame a lack of sleep.