In Newton's 2nd Law, does $m$ stand for rest mass? - Physics Stack Exchange most recent 30 from physics.stackexchange.com 2019-07-20T06:03:13Z https://physics.stackexchange.com/feeds/question/360877 http://www.creativecommons.org/licenses/by-sa/3.0/rdf https://physics.stackexchange.com/q/360877 0 In Newton's 2nd Law, does $m$ stand for rest mass? Tuna https://physics.stackexchange.com/users/167499 2017-10-04T01:27:00Z 2017-10-04T06:48:00Z <p>I just learned that almost %99 percent of an atom's mass comes from Strong Force Field Energy. But this energy is counted as my rest mass nevertheless. So in $F=m.a$, should i take $m$ as rest mass (as standard description)? Or should i take $m$ as total energy that an object has? To make it more clear; if an object's kinetic energy increases, would it be harder to accelerate? </p> https://physics.stackexchange.com/questions/360877/in-newtons-2nd-law-does-m-stand-for-rest-mass/360879#360879 2 Answer by Señor O for In Newton's 2nd Law, does $m$ stand for rest mass? Señor O https://physics.stackexchange.com/users/43294 2017-10-04T01:42:18Z 2017-10-04T01:42:18Z <p>$F = ma$ is the approximation for when an object's rest mass is much greater than it's kinetic energy. This approximation is good for anything traveling less than 50 million mph. </p> <p>For objects moving 10% of the speed of light or more, you have to worry a little more about the 'total energy' of the particle. Then it's better to use the definition of force:</p> <p>$F = \frac{\partial}{\partial t} p$ Where $p$ is the momentum; $p = \gamma mv$.</p> <p>$m$ is the rest mass of the particle, so it has no time dependence. Note that $\gamma$ and $v$ both have time dependence, so you have to use the product rule.</p> <p>For slower objects (relative to the speed of light), $\gamma \approx 1$ and this reduces to $F = m\frac{\partial}{\partial t}v = ma$, the familiar result.</p> https://physics.stackexchange.com/questions/360877/in-newtons-2nd-law-does-m-stand-for-rest-mass/360919#360919 0 Answer by DanielC for In Newton's 2nd Law, does $m$ stand for rest mass? DanielC https://physics.stackexchange.com/users/40726 2017-10-04T06:48:00Z 2017-10-04T06:48:00Z <p>In Newton's 2nd law, written in terms of force, mass and acceleration, <em>m</em> stands for the mass in the original Newton's work, i.e. the quantity of the substance which makes up a material body. This quantity is absolute, i.e. will not change if a body is at rest or moves (which is fine, because a body could be at rest in some Galilean inertial frame while moving with constant velocity in another). </p> <p>In the theory of special relativity, $\vec{F} = m\vec{a}$ is derived as the low-velocity approximation of $f^{a} = m \dot{u}^{a}$, where "a" is a generic index (in the sense of Wald's book), f is the 4-force, u is the 4-velocity, the dot stands for the derivative with respect to proper time, and m is the invariant mass (or simply mass). </p>