Solve Home Lab Questions: Slope & y-Intercept, Hooke's Law

[Vibu212]

Ok I got couple of home labs to do...but in few of them i m stuk at the end. Plz answer any question that you know of.

1. In this home lab, I did an experiment about strech (of a rubber band) vs weight (of coins attached to it). Then plotted a graph and found slope and y int as the question requested. However, the question ends like this...

...find the slope and y intercept. These values can be used to represent the uncertainities (delta)m, and (delta)b in y = mx + b. By comparing the best fit leanear equation (which is y = mx + b) to the predictions of Hooke's law, find

k +/1 (delta)k

- Now, it somewat seems easy to me, but no matter how many times i use the table (that i used for graphing) I just couldn't find the solution. Even after using equations such as F = kx or KE = 1/2mx(square). Any help is appriciated.

 

[whozum]

Im assuming that says

k\ \ plus \ or \ minus \ \ \Delta k

Also

KE = \frac{1}{2} mv^2

But for the question, if you know how to do curve fits curves in excel (linear fit), just do that and find a regression value, which will tell you how well the curve fits (your data's relative error to the theoretical value).

 

[juvenal]

You should have a table with two columns of values: one is your force measurement, F, and the other is your displacement measurement, x, where x=0 when there are no coins attached. Therefore you are fitting F = kx + b. Your fit should give you b=0 within one or two standard deviations of the fit error for b. k and its error should also come out of the fit as the previous poster mentioned.

 

[xanthym]

Ok I got couple of home labs to do...but in few of them i m stuk at the end. Plz answer any question that you know of.

1. In this home lab, I did an experiment about strech (of a rubber band) vs weight (of coins attached to it). Then plotted a graph and found slope and y int as the question requested. However, the question ends like this...

...find the slope and y intercept. These values can be used to represent the uncertainities (delta)m, and (delta)b in y = mx + b. By comparing the best fit leanear equation (which is y = mx + b) to the predictions of Hooke's law, find

k +/1 (delta)k

- Now, it somewat seems easy to me, but no matter how many times i use the table (that i used for graphing) I just couldn't find the solution. Even after using equations such as F = kx or KE = 1/2mx(square). Any help is appriciated.

If you have no regression software available, the Web Site below computes Linear Regression Slope and Intercept with corresponding error values for each. Scroll down page to use, input (x,y) data into individual boxes provided, type "0.95" for "confidence level", and click "calculate". Computed values are displayed in boxes below the "calculate" button.
http://home.ubalt.edu/ntsbarsh/Business-stat/otherapplets/Regression.htm


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[Vibu212]

http://img75.echo.cx/img75/1497/untitled5rm.png


actually I do have a software...and this is the graph and this is what i get by doing a linear fit. How which value is related to k? how is it determined (so that i can find delta k too)

ty for those who answered :p

 

[xanthym]

http://img75.echo.cx/img75/1497/untitled5rm.png


actually I do have a software...and this is the graph and this is what i get by doing a linear fit. How which value is related to k? how is it determined (so that i can find delta k too)

ty for those who answered :p

The value of slope "m" corresponds to the value of "k". You are essentially fitting {F = k*x + b}, where "k" is the slope, "x" the displacement, and "b" the intercept ("b" should be close to 0). The value of {"Std Dev of Slope"} given by the regression corresponds to the "uncertainty Δk" in "k" which the lab exercise required.
k = Slope "m"
Δk = {"Std Dev of Slope"}

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[Vibu212]

THANK YOU for explaining the usefulness of the linear fit! You all are very helpfull