How Do You Calculate the Bending Angle of a Bimetallic Strip?

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Homework Help Overview

The discussion revolves around a thermodynamics problem involving the calculation of the bending angle of a bimetallic strip made of iron and zinc, which curves upon heating due to differing thermal expansion rates. The original poster presents the problem context, including the dimensions of the strip and the coefficients of linear expansion for both metals.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply the linear expansion equation and relates the bending angle to the displacement using the formula s = rθ. However, they express uncertainty about how to proceed without specific temperature values. Other participants question the relevance of certain formulas and seek clarification on the definitions and assumptions involved, particularly regarding the radius in the context of the problem.

Discussion Status

The discussion is ongoing, with some participants suggesting that leaving the answer in terms of ΔT is acceptable due to the lack of specific temperature rise information. There is a recognition of differing interpretations of the problem and the formulas involved, indicating a productive exploration of the topic.

Contextual Notes

Participants note the absence of specific temperature values, which complicates the ability to provide a numerical answer. There is also a mention of potential gaps in logic regarding the application of certain formulas, highlighting the need for further clarification on the relationships between the variables involved.

tejas710
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Hi! There is a thermodynamics problem which I seem to be able to understand, yet unable to solve. If someone can me with it I would appreciate it.

Homework Statement


A Bi-metallic strip is straight at T= T0. It curves as it is heated up due to unequal expansion of two metals. The strip is made up of iron (a = 1.2e-5) and zinc (a = 3.1e-5). The question asks to calculate the bending angle when the original length of the strip is 100mm and with thickness of 1 mm.


Homework Equations


The linear expansion equation: L = L0(1 + a(T2 - T0))


The Attempt at a Solution


The substituted equations: LI = (100)(1 + (1.2e-5)(\DeltaT)
LZ = (100)(1 + (3.1e-5)(\DeltaT)

From here I use the formula s = r\theta
and get \theta = (3.8e-3)(\DeltaT)

I am not sure how to proceed from here because the question asks for a numerical answer but that seems impossible without the temperatures given.
 
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Welcome to PF.

If they give no temperature rise, then leave your answer in terms of ΔT as you have.
 
Thanks. I guess I will leave it as an expression.
 
Poptor, eh?
 
Sorry for the double-post, but also.. I don't understand your solution.

What does s=r*Theta have to do with this question.. and how does that lead to your solution?
 
The displacement of the end is given by the angle times the radius for small angle displacements.
 
Oh.. what exactly is the radius in this question?
I guess it's just that he said:

3. The Attempt at a Solution
The substituted equations: LI = (100)(1 + (1.2e-5)(LaTeX Code: \\Delta T)
LZ = (100)(1 + (3.1e-5)(LaTeX Code: \\Delta T)

From here I use the formula s = rLaTeX Code: \\theta
and get LaTeX Code: \\theta = (3.8e-3)(LaTeX Code: \\Delta T)


I sense a really big logic gap missing..

Otherwise, I thought the appropriate formula was:

Theta = length / thickness * (a1 - a2)*(T2-T1)

Where a1 and a2 are the expansion coefficients, and T2 and T1 are temperatures.

Excuse my ignorance, and thanks for the help.
 

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