Newtons Laws EX 21

The diagram shows all the forces acting on the mass and draws its free-body diagram. The x-axis is chosen in the direction of the slope. The acceleration is zero.

Compute the components of all forces acting on the block:

Forces	x-component	y-component
$F_S$	$kx$	0
$F_N$	0	$F_N$
$F_G$	20 cos(-127°)	20 sin(-127°)
$\mathrm{\Sigma }F$	0	0

Write equations and solve: In this case we are only interested in the x-component.

$kx-20\cos (-127^{\circ })=0$
$kx=12$
$k=\frac{12}{x}$ 
$k=\frac{12N}{1.5\times 10^{-2}m}$
$k=8\times 10^{2}N/m$