How to calculate increase of mass in relation to increase in velocity?

In summary, the conversation discusses the relationship between energy, mass, and velocity in the context of the equation E=mc^2. It is noted that this equation is a special case and a more general equation must be used when the object is in motion. The equation for calculating the mass of an object in motion is given as m=\frac{m_0}{\sqrt{1-v^2/c^2}}, but it is also mentioned that this concept of "mass increase with velocity" is not widely used in modern physics.
  • #1
stu dent
20
0
ok, so, I know e=mc2 is a way i can find what quantity of energy a mass has.

and i know that as objects increase in speed they become more massive, which i assume is also elegantly portrayed in this equation.

but, this kind poses a problem for me, because i am wondering how much velocity increases mass.

it would seem that as you put more energy into an object to speed it up, if i am taking the meaning correctly, then it becomes more massive, and requires more energy in order to accelerate it further.

this would also mean that the more massive an object is, the more of an effect Δv will have on Δm.

I for some reason, had the impression that it was more Δv of an object that would increase its mass, rather than the quantity of energy input.

or rather, and i suppose it still may be this way, if you have 2 objects. one having mass X, and one having mass Y, if you increased their velocity N times, you'd end up with each object having bX and bY mass, by some ratio of N which may even be N=b, but i suspect not.

so, i guess what I'm wondering, is how really, i would go about calculating the increase in mass of an object in relation to a change in velocity, or an increase in velocity.
 
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  • #2
That ##E=mc^2## which is so beautiful, is really just a special case of a much more general function: ##E^2=(m_0c^2)^2+(pc)^2##. That special case only works when the particle is motionless (at least from the perspective of whoever is measuring it).

In cases where a particle (or a system of particles) is moving, you have to look at the larger equation. In the larger equation, ##P## (which stands for momentum) is dependent on velocity, so you can see how the energy would increase if the speed increased.
 
  • #3
The calculation you are looking for is [itex]m=\frac{m_0}{\sqrt{1-v^2/c^2}}[/itex].

Note the following however:
1) This is the mass of an object as observed by an observer moving relative to the object at a speed v. Because the object is at rest relative to itself, an observer moving along with the object sees nothing unusual at all, and everything out there is already moving at .99999c (or whatever speed you choose) relative to some observer somewhere.
2) As Vorde pointed out above, [itex]E^2=(m_0c^2)^2+(pc)^2[/itex] is a more powerful and general way of describing the physics, so this notion of "mass increase with velocity" is seldom used these days. It takes some care to use relativistic mass correctly, and you cn easily confuse yourself by using it incorrectly.
 

1. What is the equation for calculating increase of mass in relation to increase in velocity?

The equation for calculating increase of mass in relation to increase in velocity is m = m0/√(1-v2/c2), where m is the increase in mass, m0 is the rest mass, v is the velocity, and c is the speed of light.

2. How does an increase in velocity affect the mass of an object?

An increase in velocity causes an increase in the mass of an object according to Einstein's theory of relativity. As the velocity of an object approaches the speed of light, the mass of the object also increases.

3. Can the mass of an object increase without an increase in its velocity?

Yes, according to the equation m = m0/√(1-v2/c2), an object's mass can also increase due to an increase in its energy, even without an increase in velocity. This is known as the theory of mass-energy equivalence, famously represented by Einstein's equation E=mc2.

4. How is an object's velocity related to its mass and energy?

An object's velocity is related to its mass and energy through the equation E=mc2, where E is the energy, m is the mass, and c is the speed of light. This equation shows that energy and mass are interchangeable, and an increase in one can result in an increase in the other.

5. Does an object's mass increase continuously as its velocity increases?

No, an object's mass increases up to a certain point as its velocity increases. According to the equation m = m0/√(1-v2/c2), as the velocity approaches the speed of light, the denominator of the equation approaches 0, causing the mass to approach infinity. However, in reality, an object cannot reach the speed of light, so its mass will approach a certain maximum value and will not continue to increase indefinitely.

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