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

• Vibu212
In summary, the conversation discusses a home lab experiment involving a rubber band and coins, and the process of finding the slope and y-intercept of a graph. The question also asks for the uncertainty values in the equation y = mx + b. The conversation includes suggestions for using regression software to find the values, as well as a website that can help with the calculations. The final part of the conversation clarifies the relationship between the slope value and the constant k, as well as the uncertainty in k. Overall, the conversation ends with gratitude for the helpful explanations provided.
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.

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).

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.

Vibu212 said:
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.

~~

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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

Vibu212 said:
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"}

~~

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

## 1. What is the formula for calculating slope?

The formula for calculating slope is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on a line.

## 2. How do you find the y-intercept of a line?

The y-intercept of a line can be found by setting the value of x to 0 in the equation of the line. This will give you the point where the line crosses the y-axis.

## 3. What is Hooke's Law?

Hooke's Law is a principle in physics that states that the force required to stretch or compress a spring is directly proportional to the displacement of the spring from its equilibrium position. It can be mathematically expressed as F = -kx, where F is the force, k is the spring constant, and x is the displacement.

## 4. How do you use Hooke's Law to solve problems?

To solve problems using Hooke's Law, you need to know the values of the force, spring constant, and displacement. Once you have these values, you can plug them into the formula F = -kx and solve for the unknown variable. This can be used to calculate the force, spring constant, or displacement, depending on which variable is unknown.

## 5. What are some real-life applications of Hooke's Law?

Hooke's Law is used in various real-life applications, such as designing and testing springs in mechanical and electrical systems, measuring the elasticity of materials, and understanding the behavior of elastic materials under stress. It is also used in medical devices, such as prosthetics and braces, and in sports equipment, such as tennis rackets and golf clubs.

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