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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2$\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$– Community BotMay 27 at 12:40
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1$\begingroup$ 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... $\endgroup$– John DotyMay 27 at 12:57
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1$\begingroup$ Possible duplicates: physics.stackexchange.com/q/104101/2451 and links therein. $\endgroup$– Qmechanic ♦May 27 at 13:13
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2 Answers
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I know that F is directly proportional to mass and acceleration but why in formula we take k=1 not other constant?
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.
Dimensionful universal constants describe your units, not nature. That is why the SI is now explicitly defined in terms of universal constants.
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The force was found to be proportional to the acceleration, not $ma$. This means that $F=ma$ with $m$ the constant of proportionality.
