# Increase of mass and legth contracts with speed?

1. Jan 15, 2008

### Masest

OK, i have a final coming up, and i need a little help.... i need to know how and why an object moving faster acquires more mass..... it doesn't make sense.... mass is how much matter somethign has as far as i know, but when you speed up, you acquire more mass? this goes hand in hand with the length contraction i think... the faster you go, the shorter in length you seem, and if that is true, then your mass is going to be the same, and your density will increase...... for the mass part, i have a handout that says this "The faster a particle is pushed, the more its mass increases, there by resulting in less and less response to the accelerating force" i don't get this

2. Jan 15, 2008

### Staff: Mentor

As an object moves faster it acquires more kinetic energy. By the famous e=mc^2 mass-energy equivalence you can also say that it has more mass. However, that use of the word mass (a.k.a. relativistic mass) fell out of favor with physicists decades ago. Now, when scientists use the word mass they refer to the invariant mass (a.k.a. rest mass).

3. Jan 16, 2008

### Masest

So what you are saying is that Mass ir the rest mass? then what is the mass called when something is moving? i don't quite understand what you are trying to say

4. Jan 16, 2008

### Staff: Mentor

That is correct, in modern physics circles the word "mass" refers to the mass when the object is at rest. The word that people use to describe the "mass" that increases when something is moving is called "relativistic mass", but physicists don't like or use that term very much. The reason "relativistic mass" is not considered very useful is that it does not add any information beyond the KE.

Mrelativistic = Mrest + KE/c^2
or equivalently by e = m c^2
Etotal = Mrest c^2 + KE

5. Jan 16, 2008

### Staff: Mentor

In relativity, there is no single quantity that can be used for all the things that the classical mass is used for: as an intrinsic defining property of an object (the "quantity of matter" in Newton's words); as a measure of the effect of force on it (F = ma or F = dp/dt); and as a measure of the gravity it produces or the effect gravity has on it.

Different people focus on different things and therefore tend to use different kinds of "mass" in relativity. Most physicists (at least particle and nuclear physicists) focus on mass as an intrinsic property of an object, and use the invariant mass which is often called the rest mass $m_0$. Some people focus on the fact that moving objects in relativity have more momentum than in classical physics, and use the so-called relativistic mass $m_{rel}$ such that

$$\vec p = m_{rel} \vec v = \frac{m_0 \vec v}{\sqrt{1 - v^2/c^2}}$$

Finally, when you talk about gravity in relativity, you really have to use general relativity. A pure GR analysis of gravity doesn't use the concept of mass at all, but deals instead with the stress-energy tensor which combines energy and momentum. (At least that's the way I understand it; I'm not an expert on GR myself)

6. Jan 16, 2008

### Masest

well, i got what dale was saying, but which mass is it that would be increasing? the relativistic mass or the invarient mass? i finally got the concept that there are two masses, but does it increase becuase the acceleration will stay the same, but it is going to take more force to push it closer to the speed of light? if so, then acceleration will stay the same, but the force will increase, hence the mass will have to increase?

7. Jan 16, 2008

### Masest

or am i completely off with the F=MA formula?

8. Jan 16, 2008

### rbj

the more fundamental formula (which is used with this concept of relativistic mass) is

$$F = \frac{dp}{dt} = \frac{d(mv)}{dt} = m\frac{dv}{dt} + v\frac{dm}{dt}$$

in Newtonian mechanics, we normally think that the mass is not changing so the second term on the right goes to zero.

9. Jan 16, 2008

### Masest

what is the dp and dt?

10. Jan 16, 2008

### rbj

sorry, i didn't realize that you weren't post calculus. mathematics is the language of physics and, although we can simply tell you what dp and dt (infinitely small changes in momentum and time, they're common symbols in calculus and fundamental physics) are, if you don't have the needed mathematical background, i dunno how to explain any of this.

11. Jan 16, 2008

### rbj

that's a pretty sweeping statement.

not all scientists.

Last edited: Jan 16, 2008
12. Jan 16, 2008

### arbol

In order to understand relativity of lengths and times, one must understand what it means to say that c is constant.

if v = 29,800m/s, then if t = 2s, x is 59,600m, by using the velocity as a conversion factor.

for example, if t = 2s, then

x = 2s*(29,800m/s).

Not so with c.

If you say that

c = 299,792,458m/s, then

by keeping c constant in the equation

c = x/t,

if t = 2s, then

x = (299,792,458/2)m.

to say that c is constant is the same as saying that at the speed of light, the length of 299,792,458m remains constant as the duration of 1s remains constant also. In other words, the unit of lengths and times changes, but the initially length of 299,792,458m remains the same as if that length is the length of an ideal rigid rod, and the initial duration of 1s remains the same as the original length of times. It is as saying that the density of the length and the time interval changes.

Thus, speaking of mass as density p times the volume of a body,

keeping c constant changes the density p but the volume remains the same.

I hope I was able to help. Good luck.

Last edited: Jan 16, 2008
13. Jan 16, 2008

### pervect

Staff Emeritus
Pffffft. We've had this argument before. The statement you object to is right from a standard faq. There are a few rare exceptions, but they are just that - exceptions.

14. Jan 16, 2008

### Masest

um.... plz stay on topic >.< i kinda figured that the speed of light is what it is relative to what the person is experiencing.... say that they are travelling at the speed of light, then relative to them , the speed of light is the same, but to someone else who is sitting still, relative to them, the speed of light is what you are travelling.... still doesn't explain my length contraction

15. Jan 16, 2008

### Integral

Staff Emeritus
I am having trouble understanding what you write. If English is a second language could you lood\k for a different translator. If English is your primary language please learn to use complete sentences.

The speed of light is measured to be the same value, sitting still or moving, it does not matter.

It is impossible for any massive body to move at the speed of light.

Length contraction is the fact that an object moving past you, will be measured by you, to be shorter then it is measured by someone moving with the object.

16. Jan 17, 2008

### Xeinstein

Can we say the object "seems" to have more mass or it Really has more mass?
Has it been confirmed by any experiment?

17. Jan 17, 2008

### pervect

Staff Emeritus
Well, first you have to answer the question of "what is real". While this seems simple, philosophers have been arguing about it for a very long time, and there is no resolution in sight. People generally have widely divergent ideas about exactly what qualities are necessary for something to be "real".

One can more specifically ask, "Is mass independent of the observer". This is more answerable, because it avoids that annoying "REAL" word and all the philosophical baggage it carries with it.

The answer to this question is that relativistic mass, is *not* independent of the observer, as is probably obvious already. What may be less obvious is that most physicists don't actually use "relativistic mass" much (there are a few exceptions, physicists whom for whatever reason are very fond of the concept). There *is* a sort of mass that is independent of the observer (at least, as long as the observer is an isolated system). This sort of mass is known as "invariant mass".

When people say that "light has no mass", for instance, they are talking about the later sort of mass - the invariant mass - the sort that is a property of the light alone, that does not depend on the particular observer.

Last edited: Jan 17, 2008
18. May 3, 2008

### Bose

What's the reason that use of the word mass (a.k.a. relativistic mass) fell out of favor with physicists decades ago?

19. Feb 14, 2011

### schonovic

this is kind of a weird twist but in a sci-fi novel i read the crew waited until the gamma factor of the universe, in their perspective was high enough to use their hyperdrive system. i know there is no such a thing as a hyperdrive but what stops the crew of the ship from seeing things in their own perspective as if the universe is moving near the speed of light? do they see us as approaching the speed of light and our gamma factor being high as opposed to them? go ahead and tear it up but i have to know. oh i see the thread is pretty old sorry.

20. Feb 14, 2011

### Neandethal00

Is it just me or there are others who after a while get annoyed by over-use of c, speed of light in relativity. All theories, all thought experiments involve c, the light.
Light is integrated into our visual system and shape our comprehension of reality. Are this theories playing tricks on us? Mathematically they are very sound, then may be their interpretations are wrong.

Increase in mass with speed is an example. It may not be the 'mass' that increases with speed, it may be the 'inertia' which increases. Inertia is the resistance an object presents when an attempt is made to change its state of rest or motion. Inertia and mass are related. If there is an upper limit to speed, then an object must increasingly oppose it rising speed, which by defition is inertia.
Interaction between an object and its surrounding 'space' at relativistic speed may be different from the interaction at lower speed.