# Math Help - Spring Problem

1. ## Spring Problem

A spring of natural length 10 in. stretches 1.5 in. under a weight of 8 lb. Find the force function F(x).

A spring of natural length 10 in. stretches 1.5 in. under a weight of 8 lb. Set up an integral to find
the work done in stretching the spring from its natural length to a length of 14 in.

A spring of natural length 10 in. stretches 1.5 in. under a weight of 8 lb. Find the work done in
stretching the spring from its natural length to a length of 14 in.
Help is always appreciated

2. F(x) = $\frac{8lb}{15}$ = 5.3x

$\int{5.3x * dx}$ from 10 to 14 = 256 inch-pounds

3. Originally Posted by Selim
A spring of natural length 10 in. stretches 1.5 in. under a weight of 8 lb. Find the force function F(x).
F(x)=kx

Use 1.5 for x and 8 for F(x) to find k.

You probably want to use the exact value k=16/3

Originally Posted by Selim
A spring of natural length 10 in. stretches 1.5 in. under a weight of 8 lb. Set up an integral to find
the work done in stretching the spring from its natural length to a length of 14 in.
x is the amount the spring stretches.
When the spring is at its natural lenth of 10 in., x=0
When the spring is at a length of 14 in., x=4
Use those values of x as your limits of integration.

4. Thank you very much. I was wondering why that number was so odd. So I shall begin the integration from 0 until the distance stretched and it comes out to 128/3.

5. Originally Posted by Selim
Thank you very much. I was wondering why that number was so odd. So I shall begin the integration from 0 until the distance stretched and it comes out to 128/3.
Good job, Selim