# Acceleration and mass

1. Nov 26, 2015

### Andrew Lokkebo

I'm not educated in physics but I'm trying to learn some things. As I understand it light speed is the speed limit of the universe because objects gain mass as they accelerate and it takes more and more energy to continue accelerating, as the object approaches light speed it's mass begins to reach infinity and its impossible to have enough energy to go faster. Ok so if I accelerate an object and the mass increases where is this mass coming from? Just guessing I would think it has to come from the kinetic energy. If not where else? If that guess is right then it is correct that adding energy to an object increases it's mass? Or am I getting it totally wrong. But if I'm right and kinetic energy increases mass, then wouldn't thermal energy do that too? And would that increase the gravitational force of the object? If mass does increase it has to right? That would explain why time is effected by speed, because gravity gets stronger the faster you go. But I'm probably just an idiot.

2. Nov 26, 2015

### andrewkirk

The way to understand the idea that 'mass increases with speed' is not that somehow more mass is gained when an object is accelerated, but rather that the measurement of mass depends on the frame of reference.

If an inertial observer O watches an object B of mass 10,000 kg that is initially stationary next to her, as it is accelerated to a speed of c/2, the observer will measure the object's mass after the acceleration as 11,547 kg. But a person travelling in or alongside B will measure its mass as still 10,000 kg.

Conversely, an observer travelling in or alongside B will observe the mass of observer O to have increased by 15.47%, even though O has not been accelerated.

3. Nov 26, 2015

### Staff: Mentor

Take a look at this FAQ entry: https://www.physicsforums.com/insights/what-is-relativistic-mass-and-why-it-is-not-used-much/

The idea that mass increases with velocity is not exactly wrong (and andrewkirk's explanation of how to properly understand this effect is correct), but it in the century since Einstein first proposed it it has become increasingly clear that it's not the most effective way of thinking about kinetic energy.

But with that said:
1) You are right that if you do want to think in terms of mass increasing with speed, the increased mass does come from the kinetic energy. That's how Einstein originally described it. However, we've since discovered that you are better off (simpler math, easier to build on, fewer funny special cases, no messing with the obscure notions of "longitudinal" and "transverse" mass) thinking in terms of the total energy of an object given by the equation $E^2=(m_0c^2)^2+(pc)^2$ where $m_0$ is the mass of the system as measured by an observer who is at rest relative to it, $p$ is the momentum, and the kinetic energy is all in the $pc^2$ term. Note that when $p=0$ (the system is not moving) this equation reduces to the famous $E=mc^2$.
2) You are also right that thermal energy increases the mass. So do other forms of internal energy: the mass of a spring is very slightly greater when it is stretched because of the potential energy in the spring; a charged lead-acid automobile battery has a very slightly greater mass because of the chemical energy it contains. (It is a good exercise to use $E=mc^2$ to calculate how much more mass we're talking about). All of these forms of internal energy count towards the rest mass $m_0$ because they are present even when the system is not moving so the kinetic energy is zero.