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°)
$\Sigma F$	0	0

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

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