I'm currently taking a high school physics class and we're doing friction problems now. I've been doing the ones that use MKS perfectly well, but when the problems start to use the FPS system, I'm always getting a relative error of around 12%. This mostly stems from my not knowing how to deal with FPS using the $ F = ma $ formula. I've tried converting FPS to MKS for it, but it still ends up with a large relative error.

How do I apply the FPS system to a formula like $ F = ma $ that is defined using MKS units and why? For the why, I'm just wondering if I'm to consider pounds when used in a physics problem at my level as a force unit and my mistakes are just the results of not using proper significant figures, or am I supposed to convert to MKS force units? If I'm to convert to MKS units, is using the rate of 4.44822162 (NIST) lbf to one Newton appropriate?

Thank you for reading my question, I hope I'm not skirting on the edge of the rules too much. I tried consulting Google and searching this site for related questions, but I guess the answer is obvious and I can't see it :(

Here are two problems that display my attempt to convert, then plug in the values, and my attempt to just use the values as-is then plug in.

Problem 1
"A horizontal force of 6 lbs is applied to a 10 lb block which moves along a horizontal surface. If the coefficient of kinetic friction is 0.4, determine the acceleration of the block. ($a = 6.4 ft/s^2$)"

$F_N$ = Normal Force, $F_k$ = Kinetic Friction Force, $F_h$ = Forward Force, $F_w$ = Weight Force

$F_h = 6 lb$
$F_h = 6 lb * 4.44822162$ (conversion factor to Newtons)
$F_h = 26.69 N$

$F_w = 10 lb$
$F_w = 10 lb * 4.44822162$ (conversion factor to Newtons)
$F_w = 44.48 N$

$F_w = mg$
$44.48 N = m * 9.8 m/s^2$
$m = 4.54 kg$

$μ_k = \frac{F_k}{F_N}$

$0.4 = \frac{F_k}{44.48 N}$

$F_k = 17.79N$

$-F_k + F_h = ma$
$-17.79 N + 26.69 N = 4.54 kg * a$
$a = 4.54 m/s^2$

Need to convert now...

Final: $a = 14.89 ft/s^2$

There's another problem where I just directly put in the FPS values without converting, but if this method is right, there's no point in posting it. If this method is wrong, I'll write it out here.

  • 1
    $\begingroup$ FPS = foot-pound-second system, I assume? Also, it might help to edit in a (short) example of a calculation in the FPS system that demonstrates the error you're getting. $\endgroup$ – David Z Dec 2 '11 at 4:16
  • $\begingroup$ @DavidZaslavsky I'll do that. I just didn't want to go into homework-helper territory and be ignored for taking advantage of you guys. $\endgroup$ – Trevor Dec 2 '11 at 4:36
  • $\begingroup$ And we do appreciate it, Trevor. Asking a general question the way you've done is the recommended way to go. But in this case, I think it would really help to have an example, because it's hard to know what sort of mistakes you're making based only on the description you've given. $\endgroup$ – David Z Dec 2 '11 at 4:57
  • $\begingroup$ You have the wrong solution for $a$: $4.54\ \mathrm{m/s^2}$ is not the solution to $-17.79\text{ N} + 26.69\text{ N} = 4.54\text{ kg}\ a$. You'll need to make sure all your math is correct before posting your example problems. (It's not within the scope of this site to check your math; try asking a friend and/or double-checking with a calculator) $\endgroup$ – David Z Dec 2 '11 at 6:10
  • $\begingroup$ @DavidZaslavsky Oh damn, I'm sorry :( Regardless, thanks for the help, I legitimately didn't see that. $\endgroup$ – Trevor Dec 2 '11 at 6:15

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