myininaya
  • myininaya
Someone explain springs and work to me?
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
myininaya
  • 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
myininaya
  • myininaya
I know how to do the integration
myininaya
  • myininaya
Just the setup is my problem

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • 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.
myininaya
  • myininaya
So are you an engineer?
myininaya
  • 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?
myininaya
  • myininaya
oh wait
myininaya
  • myininaya
the force is k
myininaya
  • myininaya
so x is the distance over the interval xi to xf
anonymous
  • 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.
anonymous
  • 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.
anonymous
  • 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.
myininaya
  • myininaya
Thanks for your help
anonymous
  • anonymous
No probs.
anonymous
  • 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.

Looking for something else?

Not the answer you are looking for? Search for more explanations.