## 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**

**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**

**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