Finding Young’s modulus by bending a beam

In summary, the conversation discusses using an end-loaded cantilever beam to find the Young's modulus of a rod. The experiment must be set up correctly with a more rigid holding system and a more accurate deflection measurement method. The equation for Young's modulus can be derived using the Euler-Bernoulli beam theory. It is recommended to use a longer thin rectangular strip as the test object and clamp it tightly to a solid bench for more accurate results.
  • #1
Fraser MacDonald
11
1
I have a question regarding finding the Young’s modulus of a rod by loading a weight to the end and measuring the change in displacement.
The experiment is part of my advanced higher physics project on Young’s modulus however it is the only experiment that I’m doing that the book “Tyler” does not cover, and so I am slightly confused as to how I actually derive the relationship through this method.
IMG_8397.JPG
IMG_8397.JPG

I know it isn’t a great set up but it’s all I can do with the equipment I have.

So my question is how do I calculate it via this method?
Thanks
 

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  • #3
Not with the set up shown though . The holding system needs to be much more rigid and the rod needs to be set horizontal .There also needs to be a more accurate deflection measurement method employed .

If you have some freedom to design this experiment properly then I suggest that you use a much longer thin rectangular strip as the test object . Clamp one end of this tightly to the edge of a solid bench and - if nothing better is available - use a metre rule to measure the deflection . The rule being held in a retort stand sitting on the floor . The much larger deflection for given loads and the improved rigidity of the set up should allow you to get better results and a reasonably accurate value for Young's modulus .
 
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  • #4
Once the experiment is set up correctly would the equation to find Young’s modulus be y=(4mgl^3)/(bd^3 δ) and if so, how do I derive this?
 
  • #5
Fraser MacDonald said:
how do I derive this?
The equation you need is:

b2c4731cd266ae5023e98fd55e105409a13d51d0

Where ##E## is what you are looking for and is the only unknown in your case.

It can be derived from this equation:

5c32a9812311ffed238176820bd8c4863bcc5ae1

Both of these equations can be found in the links from my previous post and since it seems to be part of school work, I will let you do some reading to find out the meaning of the variables and the derivation. If you have questions along the way, show your work and ask a specific question.
 
  • #6
IMG_8505.JPG

Is this the correct derivation?
 

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  • #7
The image is too blurry to read it. But if you begun with the initial equation and ended up with the last one, chances are you are correct.
 

1. What is Young's modulus?

Young's modulus, also known as the elastic modulus, is a measure of the stiffness of a material. It represents the amount of stress or force required to produce a given amount of strain or deformation in the material. It is denoted by the symbol E and is measured in units of pressure, such as Pascals or pounds per square inch.

2. Why is it important to find Young's modulus by bending a beam?

Bending a beam is a common method used to determine the Young's modulus of a material. By applying a known force to a beam and measuring the resulting deflection or bending, we can calculate the modulus of the material. This information is important in engineering and construction to ensure the structural integrity and stability of materials and structures.

3. How is Young's modulus calculated from bending a beam?

Young's modulus can be calculated using the equation E = (M * L^3) / (4 * W * D^3), where M is the applied bending moment, L is the length of the beam, W is the width of the beam, and D is the deflection or bending of the beam. This equation is based on the theory of beam bending and can be used to determine the modulus of elasticity for different materials.

4. What are some factors that can affect the accuracy of the Young's modulus calculation?

There are several factors that can affect the accuracy of the Young's modulus calculation when bending a beam. These include the quality and uniformity of the material, the dimensions and shape of the beam, the accuracy of the applied force and measurement of deflection, and any external factors such as temperature or moisture. It is important to control and account for these factors in order to obtain an accurate measurement of Young's modulus.

5. Can Young's modulus be different for different materials?

Yes, Young's modulus can vary for different materials. It is a material property that is specific to each type of material and is influenced by factors such as the atomic structure and bonding. For example, metals generally have a higher Young's modulus than polymers, meaning they are stiffer and more resistant to deformation. This is an important consideration when selecting materials for different applications.

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