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In this article it says "It is commonly known that, if you accelerate an object, its mass will increase; however, to understand why this phenomenon occurs, we mustn’t think of the object’s mass increasing. Instead, we should think of its energy... when we speak of an objects mass increasing due to acceleration, we are really talking about its inertial mass increasing."

I understand that. But let's say I'm pushing a rock East at 100kph. I understand that if I suddenly wanted to push it West, I would be pushing the weight plus the momentum of the rock (the total of these would be the inertial mass). But if I only want to accelerate the object in the East direction, Does it take more energy for me to accelerate it from 1000kph to 1001kph than it took for me to accelerate it from 100kph to 101kph?

I have looked at all the links from questions like this, but I can't find that particular answer.

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    $\begingroup$ Futurism.com is a bad place to learn physics. $\endgroup$ – G. Smith Nov 8 at 17:35
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    $\begingroup$ Does it take more energy for me to accelerate it from 1000kph to 1001kph than it took for me to accelerate it from 100kph to 101kph? Yes, even in non-relativistic mechanics. Try calculating the kinetic energy $\frac{1}{2}mv^2$ at each of those four speeds. Relativistically, the energy increases even faster. $\endgroup$ – G. Smith Nov 8 at 17:38
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    $\begingroup$ Mass doesn't get bigger, 4-velocity's time and space comments get bigger: $p_{\mu} = mu_{\mu}$, after all. $\endgroup$ – JEB Nov 8 at 17:39
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    $\begingroup$ In any case, none of this has anything to do with relativity. $\endgroup$ – G. Smith Nov 8 at 17:55
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    $\begingroup$ This question and uncertainty is a prime example of why the concept of relativistic mass should be abandoned. Relativistic mass is different for forces applied in different directions. BTW, I read the article you linked. I agree with the first comment. I wouldn't read anything from that website from now on. $\endgroup$ – garyp Nov 8 at 18:05
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The relativistic increase in mass is calculated from the instantaneous speed of the object. Different observers, who may be travelling at different speeds themselves, will see different relativistic masses for your object. The relativistic change in mass is not a property of the object, it belongs to the individual observer and depends on the object's velocity as seen by that observer.

But the question you ask can be answered without any consideration of relativity. It takes in rough terms 10 times more energy to increase an object's speed from 1000 kph to 1001kph as it does to increase its speed from 100 to 101kph irrespective of relativistic effects.

That is because kinetic energy is proportional to the speed squared, nothing to do with Einstein's theory of Special Relativity.

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  • $\begingroup$ "Different observers, who may be traveling at different speeds themselves, will see different relativistic masses for your object." If I'm on a train traveling at 1000kph and I accelerate the rock from 0-1kph it only increases energy by 0.5 from my position. But to an outside observer, it increases energy by 1000.5 from his position. Seems like it has lots to do with relativity. I think I just asked my original question incorrectly. Thanks. $\endgroup$ – foolishmuse Nov 8 at 23:00
  • $\begingroup$ You're right of course. Relativity doesn't have to mean Einstein's Special Relativity. $\endgroup$ – DrC Nov 9 at 17:36

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