## Mechanical Springs

Consider a helical compression spring has a free length of 200 mm and a spring constant of 40 N/mm. What force is required to compress the spring to a length of 100 mm?

Hint
The force in a spring is:
$$F_s=k\delta$$$where $$k$$ is the spring constant, and $$\delta$$ is the change in spring length from the un-deformed spring length. Hint 2 $$\delta=free\:length-compressed\:length$$$
The force in a spring is:
$$F_s=k\delta$$$where $$k$$ is the spring constant, and $$\delta$$ is the change in spring length from the un-deformed spring length. Since $$\delta=free\:length-compressed\:length=200mm-100mm=100\:mm$$ , the required force is: $$F_s=(40\frac{N}{mm})(100mm)=4,000\:N$$$
4,000 N