# How we know which mass would be heavier.

1. Nov 16, 2013

### Twich

The theory describes that the faster the mass travels , the heavier it is. But since everythig is relatively measure its velocity. Then How we know which mass would be heavier ???

2. Nov 16, 2013

### Staff: Mentor

The theory of relativity does not say that the faster a mass travels, the heavier it is.

It says (or used to say - see below) that an observer will measure the mass of an object moving relative to him to be greater than the mass of the same object at rest relative to him. If you have two objects that would have the same mass if measured while at rest, and they're moving relative to one other... An observer moving along with (at rest relative to) the first object would say that the second object has increased its mass because of its relative velocity, and an observer moving along with (at rest relative to) the second object would say the same thing about the first object.

So you are right - we can't say which object is "really" heavier because it all depends on your point of view.

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Be aware, however, that the idea of relativistic mass increase fell out of favor some decades ago. It's a valid way of thinking about relativity, but a mathematically cleaner and more powerful approach is to focus on the energy of the moving object instead, using the equation $E^2=(pc)^2+(m_0c^2)^2$ where $p$ is the momentum and $m_0$ is the mass of the object as measured by an observer who is at rest relative to that object.

Last edited: Nov 16, 2013
3. Nov 16, 2013

### Twich

About mass, because relativistic mass is concerned as enerygy or momentum, how to calculate the accerelation of the mass when force F on it. Only m0 is considered as its inertia, isn't it?

and another question?
A rocket speed v relative to the earth.
1. how much relativistic mass (energy) of the rocket?
2. how much relativistic mass (energy) of the earth?
3. are both relativistic mass equal ? why?

4. Nov 17, 2013

### jartsa

Easy cases:

Steering an object by a transverse force: a= F/(m0*gamma)

Changing the speed of an object slightly by a longitudinal force: a= F/(m0*gamma³)

A difficult case:

Changing the speed of an object a lot: the relativistic mass changes

Some definitions:

gamma is the lorentz factor, which is very close to one at normal speeds, and becomes larger than one at relativistic speeds.
gamma= 1 / sqrt(1-(v²/c²))

relativistic mass = m0 * gamma
transverse mass = same as relativistic mass
longitudinal mass = m0*gamma³

Last edited: Nov 17, 2013
5. Nov 17, 2013

### Twich

Still have three question left!

6. Nov 17, 2013

### Staff: Mentor

The total energy of the Earth, as viewed from the frame of the rocket, is FAR greater than that of the rocket when viewed from the frame of the Earth.

To figure out the total energy of each, plug their mass and momentum into the equation linked in post 2.
Also, have a look at the Relativistic Momentum section of the following link: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html#c3

7. Nov 19, 2013

### gabriel.dac

That's actually a good question, I'd like to read more replies