## myininaya 5 years ago Someone explain springs and work to me?

1. myininaya

How is the following set up: Find the work required to compress a spring from its natural length of 1 ft to a length of .75ft if the force constant is k=16lb/ft

2. myininaya

I know how to do the integration

3. myininaya

Just the setup is my problem

4. anonymous

Hooke's law says that the force exerted by a spring of force constant k is $F=-kx$where x is the displacement from equilibrium. The work is defined as$W=\int\limits_{x_i}^{x_f}F.dx={-k}\int\limits_{x_i}^{x_f}x.dx=-k \left[ \frac{x^2_f}{2}-\frac{x^2_i}{2} \right]$Now, x_i=0 (there's no initial displacement from equilibrium) and x_f is 0.25 (you've displaced it from 1ft to 0.75ft). Your force constant should be negative too.

5. myininaya

So are you an engineer?

6. myininaya

If you are, maybe you can give me a rough explanation of what a spring being compressed is -kx and not kx? So I know work is force times distance. Does k or x have anything to do with the force or the distance?

7. myininaya

oh wait

8. myininaya

the force is k

9. myininaya

so x is the distance over the interval xi to xf

10. anonymous

x is the distance you displace the spring FROM its equilibrium position. k is a 'fudge' constant that's used...if you take a spring and compress over several distances, and plot against force used, you'll get (roughly) a straight line. So the force is approximately linear in displacement.

11. anonymous

x_i = 0 because it's not initially displaced from equilibrium. Some questions start with the spring already displaced and ask you to calculate the work done when you INCREASE displacement, say...in that case, x_i won't be 0.

12. anonymous

Whether k is positive or negative depends on whether you're measuring the force as the force exerted by the spring when it's displaced, or the force *you* exert on the spring when it is displaced. If it's displaced and not moving anywhere, the forces are balanced, and since the magnitude of the force is kx, if the force exerted by you is F(you)=kx, the force exerted by the spring must be F(spring)=-kx so that net force is F(you)+F(spring) = 0.

13. myininaya

14. anonymous

No probs.

15. anonymous

K is the spring constant, which is relative to each spring. In real life, that constant would be affected by things such as how thick the spring is and what the spring is made out of.