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When a spaceship moving in a space at a high speed its mass will be increase due to it's high velocity. If there's an astronaut inside this ship does his mass also increase or the spaceship protect the astronaut from this increase in mass.

Nemo
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محمود
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  • This so called relativistic mass is equal to the rest mass in the spaceship's frame of reference. – Nemo Jan 16 '18 at 08:34
  • Dear sir ,I am sorry for not understand what you mean' do you mean that the mass of astronaut will not change and still it's rest mass without any change when the spaceship moving and the change in mass be only on the spaceship? – محمود Jan 16 '18 at 08:40
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    It seems to me another instance of taking relativistic mass as an increased rest mass. Once again showing the confusion created by the very concept of relativistic mass if not carefully introduced. Can someone points OP to old related Qs? guess there's plenty of them – Alchimista Jan 16 '18 at 13:31
  • Der sir according to calculate the wavelength of electron move at high speed we don't use the relativistic mass on this calculation does it mean this increase of mass not real and don't affect on the size of electron and depends on the sights person. – محمود Jan 18 '18 at 09:18
  • @محمود, The length contraction is real, but it is frame dependent. – Nemo Jan 18 '18 at 12:34
  • @محمود, Please read this – Nemo Jan 18 '18 at 12:38
  • Possibly useful reading as well: https://physics.stackexchange.com/q/3436/25301 – Kyle Kanos Jan 21 '18 at 12:20

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The relativistic mass has the following expression: $$m=m_{0}\gamma=\frac{m_{0}}{\sqrt{1-\frac{v^2}{c^2}}}$$ If an object is moving with velocity $v$ relative to a reference frame $S$, its relativistic mass as seen from this reference frame is greater than its rest mass - as you can see from the formula above. But in your own frame of reference, your relativistic mass is equal to the rest mass because you're not moving with respect to yourself.

In the scenario that you have described, the relativistic mass of the spaceship and the relativistic mass of the astronaut increase with the same amount, but only relative to other frames of reference (that are not moving along with the spaceship). But he will not feel heavier. He will not experience any increase in mass because he's not moving relative to himself, so there is no relativistic mass in his frame of reference.

Working physicists do not use the concept of relativistic mass anymore. It is better to think in terms of energy-momentum. The total energy of a free particle is:

$$E^2=p^2c^2+m^2c^4$$

here $m$ is just mass. It is redundant to say rest mass. Also in high energy physics natural units are often used. In natural units the energy-momentum equation is:

$$E^2=p^2+m^2$$

so the mass of a particle is just the difference between its total energy and its momentum:

$$m^2=E^2-p^2$$

$m$ is a Lorentz invariant quantity meaning that is has the same value in every inertial reference frame. The energy and momentum in a particular reference frame may differ from the energy and momentum as seen from another reference frame, but their difference will always give the same quantity (the mass).

E.g. A photon is massless, so its energy is equal to its momentum (in every inertial reference frame).

Nemo
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  • Der sir according to you have illustrated,if we imagine there is a spaceship made frome particles and elements which have the ability to overcome the increase of its mass due to move at a high speed and it's mass doesn't change at any speed ,does the mass of astronaut in this case will be increase or be similar with the spceship's mass and don't increase. – محمود Jan 16 '18 at 13:17
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    I've downvoted this because the notion of relativistic mass is outdated (borderline wrong) and confuses too many people, hence it bring dropped from lexicon for the last few decades. – Kyle Kanos Jan 16 '18 at 14:29
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    @KyleKanos, It's ok. I also think that this is an outdated concept, as I stated in my other comments on PSE. But we have to face it, this concept is still very much used in high school and even at the undergraduate level. Considering OP's level, just saying that the notion of relativistic mass is outdated is not going to be very helpful. Let's not be pendantic. – Nemo Jan 17 '18 at 12:40