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

• tejas710
In summary, the problem involves a bi-metallic strip that curves when heated due to the unequal expansion of iron and zinc. The objective is to calculate the bending angle when the original length of the strip is 100mm and the thickness is 1mm. The attempted solution involved using the linear expansion equation and the formula for displacement of the end, but the lack of given temperatures makes it impossible to find a numerical answer. The appropriate formula for this problem is theta = length / thickness * (a1 - a2)*(T2-T1), where a1 and a2 are the expansion coefficients and T2 and T1 are the temperatures.
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: LI = (100)(1 + (1.2e-5)($$\Delta$$T)
LZ = (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.

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.

1. What is a bimetallic strip bending angle?

A bimetallic strip bending angle is the change in angle between the two layers of metal in a bimetallic strip when exposed to a change in temperature. This angle is important because it allows the strip to bend and can be used in various applications such as thermostats and thermometers.

2. How does a bimetallic strip bending angle work?

A bimetallic strip is made of two different metals with different coefficients of thermal expansion. When exposed to a change in temperature, one metal will expand more than the other, causing the strip to bend. This bending angle is proportional to the difference in expansion between the two metals.

3. What factors affect the bimetallic strip bending angle?

The bimetallic strip bending angle is primarily affected by the difference in thermal expansion coefficients of the two metals used, as well as the thickness and length of the strip. The temperature difference between the two sides of the strip also plays a role in determining the bending angle.

4. How is the bimetallic strip bending angle measured?

The bimetallic strip bending angle can be measured using a protractor or by attaching a pointer to the strip and measuring the deflection with a ruler. The angle can also be calculated using the length and thickness of the strip, as well as the temperature difference and thermal expansion coefficients of the two metals.

5. What are some applications of bimetallic strip bending angle?

Bimetallic strip bending angle has various applications in engineering and science, including in thermostats, thermometers, and heat-sensitive switches. It can also be used in mechanical devices to convert thermal energy into mechanical energy.

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