## Spring Compression

Consider a helical compression spring with a free length of 190 mm and a spring constant of 40 N/mm. If a 2,500 N force is applied, what new length will the spring compress to in 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. Solving for the change in spring length: $$\delta=\frac{F_s}{k}=\frac{2,500N}{40N/mm}=62.5\:mm$$$
Since $$\delta=free\:length-compressed\:length$$ , the new compressed length is:
$$190mm-62.5mm=127.5\:mm$$\$
127.5 mm