-1

Hello :) I'm a 12th grade student and I often ask myself, the speed of light is 299 792 458 m / s An object with a mass m and a constant force F has a acceleration a = F/m, for exemple, an object A with a mass m = 10kg gets a constant acceleration F = 100N, it has an acceleration a = 100/10 = 10 m/s², so why does the object A doesn't go from 0m/s to an infinite value, indeed:

299 792 458 / 10 = 299 792 45,8 s so why with more than 299 792 45,8 s the Object velocity doesn't go further? Does it mean that the formula F = ma is not true for big value ? :o

Qmechanic
  • 201,751
Antoine
  • 19
  • 2

1 Answers1

2

You're right, $F=ma$ isn't true for big velocity. When you're moving at high speed, you must use relativistic formulas, involving the gamma factor $\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$, in this case $\vec{F}=\frac{dP}{dt}$, where $P$ is the relativistic momentum, defined as $p(v)=\gamma mv$ (edited)

MatMorPau22
  • 763
  • 6
    $\vec F=\gamma m \vec a$ is not the correct relativistic correction for Newton's second law. – Chris Jan 15 '18 at 19:53
  • I would like to point to https://physics.stackexchange.com/questions/64159/mass-in-special-relativity and the @Alpha Centauri answer – Alchimista Jan 15 '18 at 21:53
  • In particular, in 1-D motion (like what OP is describing), $F=\gamma^3 ma$. – Chris Jan 16 '18 at 01:22