Youngs Modulus & Spring Constant Experiment

[kingstar]

Homework Statement

I've been asked to find the stiffness constant of a rubber band and young's modulus.
To do this I created the experiment like this http://www.gcsesciencemethods.co.uk/2012/05/hookes-law-1.html and then i put all the values in a table. I plotted a graph of extension vs weight (i was asked), and found the spring constant.

The examiner doesn't really care about the value's its more to demonstrate my understanding.

Now i have a table with the:
Weight, original length, length (with weight added), extension.
My question is how do i find Youngs Modulus from this?

(I know the area, 2.93x10^-3m^2)

Homework Equations

F = -kx

YM = Stress/Strain

The Attempt at a Solution

I attempted to find the stress and strain at each weight.
Example: For one of the extensions i used a weight of 0.1N, so i used that data to find Youngs Modulus, but when i did it for 0.2N it wasn't the same.
This has left me so confused! :<

 

[kingstar]

anyone?! :(

 

[PhanthomJay]

Homework Statement

I've been asked to find the stiffness constant of a rubber band and young's modulus.
To do this I created the experiment like this http://www.gcsesciencemethods.co.uk/2012/05/hookes-law-1.html and then i put all the values in a table. I plotted a graph of extension vs weight (i was asked), and found the spring constant.

The examiner doesn't really care about the value's its more to demonstrate my understanding.

Now i have a table with the:
Weight, original length, length (with weight added), extension.
My question is how do i find Youngs Modulus from this?

(I know the area, 2.93x10^-3m^2)

Homework Equations

F = -kx

YM = Stress/Strain

The Attempt at a Solution

I attempted to find the stress and strain at each weight.
Example: For one of the extensions i used a weight of 0.1N, so i used that data to find Youngs Modulus, but when i did it for 0.2N it wasn't the same.
This has left me so confused!

Within the proportional limit and accuracy of the lab data (and applicabilty of Hooke's law for the spring), you should get a straight line relationship of force versus displacement, where the slope of the graphed line is the spring constant, k. In calculating strain, where strain is the displacement divided by the original length, you can do a bit of algebraic manipulation of your stress-starin equation to to conclude that k = AE/L, where L is the original length of the spring, not the stretched length.

 

[kingstar]

Thank you. I've got it.

 

[Nickie]

As a scientist, it is important to understand the purpose and limitations of an experiment. In this case, the experiment is attempting to find the stiffness constant and Young's modulus of a rubber band. The stiffness constant is a measure of how easily a material can be stretched, while Young's modulus is a measure of a material's stiffness or ability to resist deformation.

The experiment you conducted is a simple way to determine the stiffness constant of a rubber band. By plotting a graph of extension vs weight, you were able to calculate the slope of the line, which represents the stiffness constant. This value may vary slightly depending on the specific rubber band used and the accuracy of your measurements.

However, finding Young's modulus from this experiment is not as straightforward. As you mentioned, Young's modulus is calculated using the formula Stress/Strain. In this experiment, the stress would be the weight added to the rubber band, and the strain would be the extension of the rubber band. However, in order to accurately calculate Young's modulus, you would need to know the initial cross-sectional area of the rubber band, as well as the amount of strain at each weight. This information is not provided in the experiment.

It is also important to note that Young's modulus is a constant for a specific material, while the stiffness constant can vary depending on the dimensions and shape of the material. So even if you were able to calculate Young's modulus from this experiment, it may not be an accurate representation of the true value.

In summary, while the experiment you conducted may have given you an estimate of the stiffness constant of the rubber band, it is not a reliable method for determining Young's modulus. For a more accurate measurement, you would need to conduct a more controlled experiment, taking into account the initial dimensions of the rubber band and measuring the strain at each weight.