## Springs in Parallel

Consider three springs in parallel have the following spring constants (from left to right): 4 N/m, 2 N/m, & 3 N/m. What force is required to compress the springs 5 m?

##
__
__**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**

The spring constant for springs in parallel:

$$$k_{eq}=\sum_{i} k_i$$$

First, let’s determine the equivalent spring constant for several springs in parallel:

$$$k_{eq}=\sum_{i} k_i$$$

Since the problem statement has three springs in parallel:

$$$k_{eq}=k_1+k_2+k_3=4\frac{N}{m}+2\frac{N}{m}+3\frac{N}{m}=9\:N/m$$$

A spring’s deflection and force are related by:

$$$F_s=k\delta $$$

where
$$F_s$$
is the forced applied to the spring,
$$k$$
is the spring constant, and
$$\delta$$
is the change in spring length from the un-deformed spring length.

$$$F_s=9\frac{N}{m}\times 5m=45\:N$$$

45 N