Quote:
Originally posted by HoChiMinh
If you can put an infinite amount of energy into accelerating an object, yet it will not increase in velocity as it approaches the speed of light. Where does the energy go?
Since it was explained that the object becomes more massive with speed. I was asking if the special relativity equation could be solved for mass. Then the energy that does not increase velocity of the object when it's velocity approaches c could be inserted into: m=E/(c^2). and that would account for the increase in mass.
It is just confusing because the energy that it would take to bring an object to the speed of light is finite if the mass does not change.
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First of all, I would hesitate casually using the term "infinite" to describe an amount of something. No matter how much energy you put into a mass, it will not travel at the speed of light. However, the
limit of a mass' speed as it's
kinetic energy approaches infinity (becomes arbitrarily high)
is the speed of light so,
in this sense, you can say that an infinite amount of energy
can accelerate an object to the speed of light.
Infinity isn't really an amount (a number) so it's use usually ends up obfuscating your point rather than clarifying it...
As stated (perhaps not so clearly) before, yes, the (stupidly) famous equation E=mc^2 can be used to show the relationship between an object's relative mass and it's kinetic energy. Not only that but, because the mass of an object changes as it's speed changes, you can no longer use the formula KE=(m/2)v^2 to calculate the kinetic energy. Instead, you must resort to something annoying like calculating it's relative mass and then finding the difference in the object's mass energy, E=mc^2.
Your last paragraph is the hardest one to address because it is the most subtle. It's not really fair to say "the energy that it would take to bring an object to the speed of light is finite if the mass does not change," because the
mass must change. Like the other results of special relativity, it is derived from first principles and they are all intricately related.
Indeed, little of the formulas of
Newtonian mechanics are unchanged at relativistic speeds. For example, if an object is moving at 0.9c and another objects zooms past at 0.95c, do you think that the first object will see the second one zoom past at 0.05c? According to special relativity, the second object will travel at (if I'm not mistaken) 0.34c, relative to the first object...