A change in length ratio question

In summary, the conversation discusses the concept of stretching a length and the resulting ratio of change. It is mentioned that under uniform stretching, the ratio remains the same regardless of which portion of the length is examined. This is due to Hookes Law, which states that the ratio is proportional to the pressure in the member.
  • #1
X1088LoD
22
0
This may be common sense, but my brain just isn't working at the moment.

If I am taking a length, L, and effectively stretching it to a new
length, L+dL. I am interested in the ratio dL/L

Let us say for example L is 2 mm long, and a stretched length of 2+0.2
mm is 2.2 mm. The total ratio of change, dL/L, is 0.2/2, or 0.1

If I take a portion of that length, let's say, between 1.2 and 1.6, and
examine only the length where L is now 0.4. If the same stretching is
applied, does the ratio of dL/L remain the same no matter where I am
looking at a portion of the length?

Thanks
 
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  • #2
Probably- yes. It depends on how you stretch the line.

Under a uniform stretch- x'=ax. dx=x'-x=(a-1) x, dx/x=a-1
 
  • #3
If you are looking at this as a physical (Physics - Mechanics) problem then the answer is yes. A thing called Hookes Law states that dL/L is proportional to the pressure (Force per unit CrossSection) in the member. So if the member is of uniform cross-sectional area then the pressure (tensile pressure if stretching and compressive pressure if contracting) is constant along its length and therefore so is dL/L.
 

FAQ: A change in length ratio question

What is a change in length ratio question?

A change in length ratio question is a type of mathematical problem that involves finding the ratio between two lengths before and after a change has occurred. The change could be a stretching or shrinking of an object, or a change in the proportions of an image.

How do I solve a change in length ratio question?

To solve a change in length ratio question, you need to first identify the two lengths that are being compared and determine the change that has occurred. Then, you can set up a ratio using the original length and the changed length. Finally, solve for the missing value using cross-multiplication or equivalent ratios.

What are some real-life applications of change in length ratio questions?

Change in length ratio questions are commonly used in fields such as engineering and architecture to determine the appropriate proportions and dimensions of structures. They can also be used in photography to adjust the aspect ratio of images.

Are there any specific formulas or equations for solving change in length ratio questions?

There are no specific formulas or equations for solving change in length ratio questions. However, understanding the concept of ratios and proportions is essential in solving these types of problems.

Is it necessary to use the same units for both lengths in a change in length ratio question?

Yes, it is important to use the same units for both lengths in a change in length ratio question. This ensures that the ratio is accurate and meaningful. If the lengths are in different units, you can convert them to the same unit before solving the problem.

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