# 1N Force and going near the speed of light?

ZapperZ
Staff Emeritus
My understanding is this has all been verified in particle accelerators up to 0.9999999c and beyond ?

I'm an accelerator physicist, just so you know.

Secondly, we don't measure "mass". We only obtain mass based on the measurement of something else. If I send a stream of particles into a dipole magnetic field and measure the "bending" amount, what I get DIRECTLY is the MOMENTUM. It is only after applying some physics will I be able to extract the "mass" of the object.

You are exhibiting a bit of stubbornness here in the sense that you haven't shown any indication that you've read the sources you've been given. The fact that there were at least 2 different links given to you that CLEARLY indicated why the concept of "relativistic mass" can be problematic somehow appeared to have been ignored.

If you ever get into trouble later on due to your insistence of using this concept, please note THIS DAY where you have been warned.

Zz.

• PeroK
PeroK
Homework Helper
Gold Member
2020 Award
Lets suppose we are in a space and theres no external force that affects our system,which our system is simply one object which we can think it is a box and it has 1 kg mass and there is us.

The object ,lets call it A,Its initally rest relative to us so it can be our inertial referance frame So We pushed the A and we applied a force to the A ( Lets call it 1N).It started to accelerate.(I am not sure at this point A will be still our inertial referance frame or not).

In this case we are observer and we will think we are stationary so the A will start to accelerate with constant acceleration ## \vec F=m \vec a## (The motion is only in one direction like +x) so, ##F=1N## and ##m=1kg## so ##a=1\frac m s^2##

We know that theres no external force affecting our system.So after some time the objects speed will increase.And after a period we will use relativity theories to calculate A 's speed.The thing is I just wanted know In this circumtances , With ##1N## force object can reach ##0.9999999....c## if its given enough time ?

If you also give an answer to the question that I wrote in bold I'll happy,

Thank you

Leaving aside all the nonsense in your post and simpifying your question to:

A ##1kg## object is constantly accelerated by a ##1N## force. How long will it take to reach a speed ##v##, which is close to the speed of light?

There is a very nice formula for this. If we let ##\gamma = \frac{1}{\sqrt{1-v^2/c^2}}##, then

##t = \gamma \frac{mv}{F}##

This differs from the classical case, ##t_c##, where ##v## is much less than the speed of light, only in the ##\gamma## factor:

##t_c = \frac{mv}{F}##

The classical time to get to a speed close to ##c## is about ##10## years (very approximately) with ##m = 1kg## and ##F = 1N##

In the relativistic case, with ##v= 0.99c## we have ##\gamma = 7##, hence ##70## years to get to 99% of the speed of light (as measured in the original rest frame of the particle being accelerated).

And, with ##v = 0.999c## you get ##\gamma = 22##, hence ##220## years. Etc.

Gold Member
A 1kg1kg1kg object is constantly accelerated by a 1N1N1N force. How long will it take to reach a speed vvv, which is close to the speed of light?

You dont need to say it nonsense and you dont need to insult that someone who doesnt know and trying to leanr..Real nonsene is I didnt ask such question.Where that came from ?

Can someone close this thread pls.It going out of topic

PeroK
Homework Helper
Gold Member
2020 Award
You dont need to say it nonsense and you dont need to insult that someone who doesnt know and trying to leanr..

That's fair enough and I apologise. What I should have said is that most of your post is so muddled that it is difficult to answer, but it does contain an interesting question.

It is 1 kg. Because "mass" means "invariant mass"="rest mass".
You can use the concept of a relativistic (velocity-dependent) mass, but no one does that any more.

Your factor of 1000 is wrong.

$$\gamma_{99.99\%c} = \frac 1 {\sqrt {1-0.9999^2} }= 70.71$$

##E=\gamma_{99.99\%c} 1kg~c^2 = 6.36 \cdot 10^{18} J##

Can we come back to the original topic?

My apologies mfb ...your figure is correct ...

But I still don't get this mass thing ..... we seem agreed that at 0.9999c the 1kg mass now has a mass of 70kg .... I only know of one kind of mass... it pulls on other mass (gravitation) ...and resists acceleration , that's all mass does isn't it? I didn't know there were different kinds of mass and subdivisions in the term.

mfb
Mentor
we seem agreed that at 0.9999c the 1kg mass now has a mass of 70kg
No it has a mass of 1kg, as stated multiple times already.
Please open a separate thread if you want to discuss this further.
Can someone close this thread pls.It going out of topic
Okay.