Calculating Radius of Curvature for Metal Bar

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To calculate the radius of curvature for a metal bar that expands due to a temperature increase, first determine the length of the heated bar using the coefficient of thermal expansion. With a temperature rise of 40 degrees Celsius, the bar's length increases, allowing it to form an arc. The relationship between the arc length, angle, and radius of curvature can be established using the law of sines. The provided hint about small angles can be applied to simplify calculations. Ultimately, the radius of curvature can be derived from these relationships.
brad sue
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Hi guys ,I need help to find the radius of curvature for this exercice:

A metal bar is 1.75m long with a coefficient of thermal expansion of 1.34*10-5K-1. It is rigidly held between two fixed beams. When the temperature rises, the metal bar takes on the shape of the arc of a circle.
What is the radius of curvature of the circle when the temperature rises by 40 degrees celcius?

hint:for small angle: sin(x)=x-x3/6.

thankx for your help!
 
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I'm confident you can find the length of the heated bar. Then, just draw an arc and relate these lengths to the angle of the arc and the radius of curvature. You'll need to use the law of sines, and then you can use the "hint" and solve for the radius.
 
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