how do you find the magnitude of gravity if your only given the coefficients of static and kinetic friction and the weight of a box at rest?

Question

anonymous · Answer

If you mean the magnitude of the gravitational force on the box, that's just the weight.  

However, I assume you mean you want to find the magnitude of the acceleration due to gravity, g ~ 9.8 m/s^2.  Here's how you'd do it.

If you cause the box to accelerate by applying a force, then
$$F_{net} = ma $$
but you have kinetic friction acting against you, so
$$F_{net} = F_{applied} - \mu_k W = ma $$
where W is the weight of the box. 
You can measure the acceleration -- This allows you to find the mass of the box:

$$ m = \frac{F_{applied} - \mu_k W}{a} $$
Last by not least, you know that the weight W = m g -> g = W/m.  With some algebra, that means
$$ g = \frac{a\cdot W}{F_{applied} - \mu_k W} $$
or
$$ g = \frac{a}{(F_{applied}/W) - \mu_k} $$