Spring Force

What force is required to compress a 200 mm free length spring to 110 mm if the 45 mm diameter helical compression spring has a 2.5 mm wire diameter and 10 coils? Assume the shear modulus of elasticity is 400 N/mm^2.

Hint
The spring force:
$$$F=kx$$$
where $$k$$ is the spring constant, and $$x$$ is the spring’s displacement.
Hint 2
$$$k=\frac{d^4G}{8D^3N}$$$
where $$G$$ is the shear modulus of elasticity, $$d$$ is the wire diameter, $$D$$ is the mean spring diameter, and $$N$$ is the number of active coils.
A spring’s deflection and force are related by $$F=kx$$ where the spring rate (spring constant) $$k$$ is given by:
$$$k=\frac{d^4G}{8D^3N}$$$
where $$G$$ is the shear modulus of elasticity, $$d$$ is the wire diameter, $$D$$ is the mean spring diameter, and $$N$$ is the number of active coils.
$$$k=\frac{(2.5mm)^4(400N/mm^2)}{8(45mm)^3(10)}=\frac{15,625N\cdot mm^4}{7,290,000mm^5}=0.00214\:\frac{N}{mm}$$$
Finally, to find the force required to compress the spring:
$$$F=0.00214\frac{N}{mm}\times (200-110)mm=0.19\:N$$$
0.19 N