# Mass due to velocity

1. Jun 28, 2009

### Bjarne

How much more mass would the Earth have when it was moving let’s say 1000km/s faster than now. And how can it be calculated?

2. Jun 28, 2009

### Civilized

The mass of the earth is independent of its relative speed to an observer.

3. Jun 28, 2009

### DrGreg

In relativity there is more than one definition of mass.

According to the definition that almost all physicists use nowadays, the rest mass or invariant mass of an object doesn't change due to speed.

According to an older definition that is still used in some coffee-table books and maybe even in some schools, the relativistic mass or inertial mass of an object increases as it goes faster relative to the observer. The increase is due to counting the object's kinetic energy (KE) as part of its mass, via E = mc2.

Strictly speaking, we should use the correct relativistic equation for KE, but 1000 km/s is still fairly slow, relativistically speaking, so the Newtonian formula mv2/2 isn't far wrong.

So this is what you do. Find the Earth's mass in kg and its speed in m/s. Calculate the KE by the formula above and divide by c2, where c is the speed of light in m/s. What answer do you get?

4. Jun 29, 2009

### infomax

The definition of mass in physics is
M=F/A
when the force is applied to body , a part of energy is used to increase of mass and rest contribute to increase in velocity
lets go by mathematical sense
when you apply force to body and the body seems not to accelerate as much is it has to then you feel the bodies mass has increased(because we conclude acceleration is inversely proportional to mass)
so there is no change in mass in our earth frame but it is for the rest frame that anybody is there

5. Jul 1, 2009

### Bjarne

How much velocity is converted to mass, when the Earth would move let’s say 1000km/s faster (than now)? How can it be calculated?

6. Jul 1, 2009

### DrGreg

I gave an answer in post #3. If you don't understand what I said, you will need to give me a clue: which bit did you not understand?

7. Jul 2, 2009

### Bjarne

I understand how to calculate how much mass would increase due to velocity, but not to calculate how much velocity to “pay” for that extra mass.

8. Jul 2, 2009

### Naty1

You original question uses a change in velocity of 1000 km/sec...that is used in DrGregs equation in post #3 to calculate the change in energy/mass as you requested.

If you are implying the increase in mass slows the velocity a bit, that's a separate question and a separate problem requiring different assumptions. The answer depends on your question assumptions.

9. Jul 2, 2009

### DrGreg

It's not as if you have a choice between velocity or kinetic energy (= extra relativistic mass). You can't convert velocity into energy, i.e. reduce the velocity to increase the energy. Both increases occur at the same time and are two different ways of measuring the same thing.

Your question is a bit like asking "how much velocity to pay for doppler shift", or even "how much velocity to pay for speed".

10. Jul 2, 2009

### Bjarne

But when velocity is converted to mass, - velocity is converted to energy.
Where does that energy come from?
Energy is never "free"

11. Jul 2, 2009

### Staff: Mentor

Velocity isn't "converted" to mass or energy.
The energy comes from whatever sped the object up. It requires work--energy--to accelerate an object.

12. Jul 3, 2009

### Bjarne

Sorry, this really sounds strange to me.

I mean to speed up an object can happens in many different way. The result is acceleration.
But what have acceleration and more mass with each other to do. – Do we know what really happens in this process?

So fare I understand we general don’t know how mass is created, - right?

Let say a-bomb is circling the Earth with huge velocity.
This bomb has now more mass compared to when it was on the Earth.
When it explodes and the energy (mass) is released, the force would be greater compared to when the explosion toke place on the Earth.

But where is the “connection” (cause-effect) between on the one hand: acceleration/velocity and on the other hand the result: more mass.

Maybe this sounds stupid to you, but I really want to understand what is going on here.

Last edited: Jul 3, 2009
13. Jul 3, 2009

### Staff: Mentor

First, the idea of "relativistic mass" (the kind of "mass" that increases with velocity) is deprecated by most modern physicsts. The reason is that it is just another name for total energy. So, if an object is at rest it has KE = 0, but by E=mc² it still has a lot of energy. If you do work on that object then its KE will increase. The total energy then has increased from the rest energy to the rest energy + the KE, and since "relativistic mass" is just the total energy then it also has increased. There is no big mystery here, work increases KE which increases total energy which is "relativistic mass".

14. Jul 3, 2009

### Bjarne

So we are not sure whether this is a fact or not ?

The mystery to me is:
1.) Either we have more mass (due to velocity) or we have not.
2.) If we really have more mass (due top velocity) we also should also be able to explain how is this possible, at least hypothetical..

15. Jul 3, 2009

### Staff: Mentor

It is not a question of fact, it is a question of definition. If you define "mass" to mean "relativistic mass" then mass increases with velocity. If you define "mass" to mean "invariant mass" then mass does not increase with velocity.

16. Jul 3, 2009

### DrGreg

As I explained in post #3, there is more than one definition of "mass" in relativity. According to the definition most physicists prefer, mass does not increase. According to another definition, it does. The difference is whether you decide to count kinetic energy as part of the mass or not. Either way, everyone agrees the kinetic energy increases, even in Newtonian (non-relativistic) physics.

The energy comes from the rockets that you use to accelerate the bomb. As the rockets fire, they put extra kinetic energy into the bomb, and when it explodes, that extra energy is released and makes the explosion a little greater.

17. Jul 3, 2009

### Staff: Mentor

As explained, it depends on the definition of mass that one is using. (Using the more standard definition of invariant mass, one would say there is no mass increase.) Don't confuse an increase in relativistic mass with an increase in "matter".
Again, it depends on what you mean by "explain". If you understand the definition of relativistic mass, then there is no mystery. (You must be reading more into this than there is. It's kind of like asking, how is it possible for an object to have zero speed in one frame yet have kinetic energy in another.)

A more productive question to ask is: Why does it take more and more energy to get a smaller and smaller increase in speed? (That can be viewed as a purely kinematic effect derived from the basic principles of special relativity.)

18. Jul 3, 2009

### Bjarne

Is it any resistance by travelling in space, except gravity and collision with particles (cosmic dust)?

19. Jul 3, 2009

### Alewhey

I'm not sure if you think that question is somehow related to your previous ones, but anyway: photons carry momentum and as such can also decelerate matter travelling through space. But there is no 'intrinsic' resistance to motion in free space. For such resistance to exist we would have to define some priviledged frame of reference as being 'stationary', which I believe is in violation of relativity.

20. Jul 4, 2009

### Bjarne

Yes this is the correct question.
Both:
1.) Why
2.) And how can we calculate it?
3.) For instance how much force does it take to accelerate the Earth up to + 100 km/s
4.) And how much to plus + 1000 km/s
5.) And let’s say we reach + 1000 km/s. - Does it require force to maintain that extra speed. (If we ignore gravity and collision with cosmic dust.) I guess no. (?)