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## Hooke's law (my brain just reached it's elastic limit)

I was very daring and entered the intro to engineering class as my elective in my first year of highschool. It turns out that I am in over my head. I am always up for a challenge, so I am sticking with the course I am one of the 3 freshmen in the class. On the first day of class our teacher was introducing the class and brought up that we would have to use some trigonometry and other math that the freshmen have no learned yet but he is willing to help us out with that... Anyhow today at the end of class we were given a hand out about "hooke's law" because we had just done a lab where we attached weights to a spring. The paper is pretty straight forward about hooke's theory and the formula F= K (delta)L (Force = K times the change in length) it defines k as the "proportionality constant" which I do not understand. What is a proportionality constant? wikipedia says its a force or spring constant which I still do not understand. Wiki also gives the formula F= -K x (with arrows over the k and x). help please!

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Kiteman10 years ago
It is the measure of how easy it is to deform the material.

The large k is, the more force it takes to extend a material by a given amount.

It only holds for the first part of the graph you produced, when the line was straight. It is the gradient of the straight line.

(Sometimes the k is a lambda)
astrozombies138 (author)  Kiteman10 years ago
erm, so in the equation how would k come into play?
10 years ago
If K is low, then K is not a very strong (spring, in this case). If that's what you meant....
astrozombies138 (author)  Bran10 years ago
well somewhat, but in the equation Force = K times the change in length so K must be a number, how do I get that number
10 years ago
. That number will either be a given (eg, you know the specs of the spring and want to compute how far it will stretch under a given load) or to be solved for (eg, you know the mass and amount of stretch).
10 years ago
Oh. That's a good question, I'll get back to you on that (should be a few minutes, if I can figure it out.)
10 years ago
From what I've found, the "number" for K is N/m, or Newtons/meter.

Does that help?
astrozombies138 (author)  Bran10 years ago
it does, so basically I need would need to find out how many newtons it takes to pull down the spring say 1 centimeter. And I can get my newtons using mass in kg x 9.8 because 1kg = 9.8 newtons
10 years ago
From what I know, yup. Hope all works out for ya.
westfw10 years ago
If Y is proportional to X, that means that you can make a nice equation for the value of Y that involves X multiplied by some constant number (without more complicated factors like powers, logarithms, etc.) The "proportionality constant" is just a fancy name for that constant. So in your classic algebraic equation for a line
• Y = m X + b
you could call m the "proportionality constant" instead of the slope.

Relating such constants to intuitive real-world characteristics can be challenging. As Kiteman says, for Hooke's law it's related to the stiffness or strength of the spring...
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