# Why we take $k=1$ in $F=ma$? [duplicate]

I know that $$F$$ is directly proportional to mass and acceleration but why in formula we take $$k=1$$ not other constant?

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May 27 at 12:40
• Why the close vote? This is a perfectly good conceptual question. Sure, if you've done this stuff for years, you've internalized the concept and can perhaps no longer perceive it... May 27 at 12:57
• Possible duplicates: physics.stackexchange.com/q/104101/2451 and links therein. May 27 at 13:13

This depends on your system of units. For SI units $$\Sigma \vec F = m \vec a$$ but for US customary units $$\Sigma \vec F = k \ m \vec a$$ where $$k=\frac{1}{32.2}\mathrm{\ \frac{lb_f \ s^2}{lb_m \ ft}}$$
This is not limited to Newtons laws. Any time that you see a dimensionful universal constant in a law of physics, that constant can be removed by choosing appropriate units. For example, Gauss’ law has $$\epsilon_0$$ in SI units, but it goes away in Heaviside Lorentz units. Similarly Coulomb’s law has $$k_e$$ in SI units, but it goes away in Gaussian units.
The force was found to be proportional to the acceleration, not $$ma$$. This means that $$F=ma$$ with $$m$$ the constant of proportionality.