Why does the rest mass of an object increase when it's in motion?

[Freeze3018]

If mass of a moving object is as below:

What is the value of Mo(Rest Mass) Since in relativity everything is relative and no object is actually at rest. Is the term 'Rest Mass' just theoretical assumption?
Please make me clear i am new to Relativity.

 

[Hootenanny]

If mass of a moving object is as below:

What is the value of Mo(Rest Mass) Since in relativity everything is relative and no object is actually at rest. Is the term 'Rest Mass' just theoretical assumption?
Please make me clear i am new to Relativity.

The rest mass by its definition is measured in the rest frame of the object. In other words, you measure the rest mass when you are not moving relative to the object.

 

[Freeze3018]

The rest mass by its definition is measured in the rest frame of the object. In other words, you measure the rest mass when you are not moving relative to the object.

So let's assume that I am in rocket B and a pen is in Rocket A. When there is no relative velocity if i measure the pen's mass i get Rest mass and when there is relative velocity betn Rocket A and B if i measure the pen's mass again i find it increased?

 

[Hootenanny]

So let's assume that I am in rocket B and a pen is in Rocket A. When there is no relative velocity if i measure the pen's mass i get Rest mass and when there is relative velocity betn Rocket A and B if i measure the pen's mass again i find it increased?

Before moving into relativity, let's address a more fundamental question. If you and pen are separated by some finite distance, how do you propose to measure his mass?

As an aside, you will not usually hear a serious physicist talking about "relativistic mass" or "an object's mass increasing", in non-popular literature. When a physicist says "mass" he universally means "rest mass". One can work in relativity without ever having to consider "relativistic mass" and dealing exclusively with rest mass. In general, I find that for introductory courses, the concept of "relativistic mass" seems to obfuscate matters. Think of it this way: Einstein's famous equation would be better written as $E = \gamma m_0 c^2$, with the product $\gamma m_0$ being what some people call "relativistic mass".

 

[Freeze3018]

you measure the rest mass when you are not moving relative to the object.

You yourself said to measure the mass when not moving relative to the object. I, personally, don't think we can measure mass at a distance without going into general relativity first or by using special relativity!

 

[Hootenanny]

You yourself said to measure the mass when not moving relative to the object. I, personally, don't think we can measure mass at a distance without going into general relativity first or by using special relativity!

That it my point, you don't directly measure on object's mass - even in classical physics, you measure how it interacts with something. Now, when you do this in relativity you will find that the object's energy is greater if you are moving relative to it. You don't measure its mass.

 

[Freeze3018]

But again how can we find its associated-energy increased at a distance? can we measure energy at a distance?
help me pls

 

[tom.stoer]

The rest mass has the interesting property that it is an invariant, i.e. it has the same value in all reference frames!

You can measure energy E and momentum p of a moving object in an arbitary reference frame and calculate the invariant rest mass using the formula (mc²)² = E² - c²p²

 

[harrylin]

So let's assume that I am in rocket B and a pen is in Rocket A. When there is no relative velocity if i measure the pen's mass i get Rest mass and when there is relative velocity betn Rocket A and B if i measure the pen's mass again i find it increased?

We cannot measure that pen's mass on a balance, nor on a scale; it would be necessary to use indirect means. Note that already a scale is an indirect measurement, based on theory.

One indirect way to determine the increase of m_r is by measuring kinetic energies. Bertozzi gave a very neat demonstration with an experiment in which he measured both the speed and the kinetic energy of accelerated electrons by determining the heat of impact. At high speeds, a triple field strength only resulted in a small speed increase; however it still resulted in a tripling of kinetic energy.
- http://spiff.rit.edu/classes/phys314/lectures/relmom/bertozzi.html