# Thread: Force to hold a spring

1. ## Force to hold a spring

A force of 4 pounds is required to hold a spring stretched 0.3 feet beyond its natural length. How much work (in foot-pounds) is done in stretching the spring from its natural length to 0.9 feet beyond its natural length?

2. Originally Posted by derekjonathon
A force of 4 pounds is required to hold a spring stretched 0.3 feet beyond its natural length. How much work (in foot-pounds) is done in stretching the spring from its natural length to 0.9 feet beyond its natural length?
$\displaystyle F = kx$

use the 4 lb force and 0.3 ft to determine the spring constant k in lbs/ft.

then integrate the variable force over the interval of the spring's displacement to find the work

$\displaystyle W = \int_{x_0}^{x_1} kx \, dx$

3. Originally Posted by derekjonathon
A force of 4 pounds is required to hold a spring stretched 0.3 feet beyond its natural length. How much work (in foot-pounds) is done in stretching the spring from its natural length to 0.9 feet beyond its natural length?
First you must find the spring constant, $\displaystyle k$, using $\displaystyle F=-kx$.
You are given $\displaystyle x_1=0.3$ feet, and $\displaystyle F= 4$ lbs.

$\displaystyle k=\frac{-F}{x_1}$.
You are also give $\displaystyle x_2=0.9$ feet, which is how much the spring is stretched beyond its natural length.
Work = $\displaystyle \int dW=\int_{0}^{x_2} F dx =-\int_{0}^{x_2} kx dx$