What does the value for 'c' represent in Hooke's Law?

[iamBevan]

Hi guys - we did an experiment at college putting some weights on a spring for our Hooke's Law module. When I graph it I get a value for c, in the equation y=mx+c. Is this correct? Will c have a value?

Thanks.

 

[rock.freak667]

Well Hooke's law says that F is proportional to x. So if you get a value for c, then it should be small.

 

[iamBevan]

It is pretty small - I remember hearing that c would be the force required to hold the spring tight, wasn't sure if that was true or not...

 

[Mandelbroth]

When I graph it I get a value for c, in the equation y=mx+c. Is this correct? Will c have a value?

Hooke's Law states that [itex]F_{spring} = -kx[/itex], where k is the spring constant and x is the displacement vector.

Theoretically, you should get a value for c. However, this value is 0. If you are getting anything that deviates too greatly from 0, it is probably an error.

What method are you using to find the line? Are you using linear regression?

 

[iamBevan]

y2-y1/x2-x1

 

[Mandelbroth]

y2-y1/x2-x1

So...[itex]\frac{Δy}{Δx}[/itex]? How many trials did you do? I would imagine that using [itex]\frac{Δy}{Δx}[/itex] with more than 2 points would get...weird.

Try making a least-squares regression line.

The equation will follow the model of [itex]\hat{y} = a + bx[/itex], where [itex]b = r \cdot \frac{S_{y}}{S_{x}}[/itex] and [itex]a = \bar{y} - b\bar{x}[/itex].

For help...
[itex]S_{x} = \sqrt{\frac{1}{n-1}\sum{(x_{i} - \bar{x})}^{2}}[/itex], where n is the number of trials you did and x_i is the value of x for trial #i. Follow the same process for S_y, except replace the x's with y's.

[itex]r = \frac{1}{n-1}\sum{(\frac{x_{i} - \bar{x}}{S_{x}})}(\frac{y_{i} - \bar{y}}{S_{y}})[/itex].

Don't worry if this looks complicated. It really isn't. Additionally, you might get a better looking (and possibly more accurate) line.

Out of curiosity, how did you use [itex]\frac{Δy}{Δx}[/itex] to do this, if you did more than two trials?

 

[Chestermiller]

Hi guys - we did an experiment at college putting some weights on a spring for our Hooke's Law module. When I graph it I get a value for c, in the equation y=mx+c. Is this correct? Will c have a value?

Thanks.

In your experiment, what is the definition of x? Does x represent the amount that the length of the spring increases (relative to having no force on the spring), or is it the distance from some arbitrary spatial reference point to the end of the spring where the force is applied?

 

[rock.freak667]

It is pretty small - I remember hearing that c would be the force required to hold the spring tight, wasn't sure if that was true or not...

Your value for 'c' should be close to zero as this would represent errors in measurement and so on. So you will not have to figure what qualitatively 'c' represents.