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

[tejas710]

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: L_I = (100)(1 + (1.2e-5)($$\Delta$$T)
L_Z = (100)(1 + (3.1e-5)($$\Delta$$T)

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

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.

 

[LowlyPion]

Welcome to PF.

If they give no temperature rise, then leave your answer in terms of ΔT as you have.

 

[tejas710]

Thanks. I guess I will leave it as an expression.

 

[faiyth]

Poptor, eh?

 

[faiyth]

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?

 

[LowlyPion]

The displacement of the end is given by the angle times the radius for small angle displacements.

 

[faiyth]

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.