hi

i am trying to solve this question for someone, i think its calc. but i am have some problems, if you can help me out I would really appreciate.

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- May 31st 2009, 10:10 AM #1

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- Jun 1st 2009, 12:10 PM #2

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## This is a physics problem

By increasing in temperature, the steel expanded from 85 meters to S meters. Finding S given this increase in temperature is a physics problem. But here is the math:

Suppose the track follows the curve of a circle of radius R, and central angle between the fixed point of the rail and the midpoint of the rail is $\displaystyle \theta$. Then S/2=R$\displaystyle \theta$. Similarly, $\displaystyle 85/2=R\sin\theta$. Solving this system of equations gives you all the information you need to find X. The vertical distance D between the ground and the center of the circle is $\displaystyle D=R\cos\theta$ and $\displaystyle X=R-D$.

Say for example, the rail expanded from 85m to 90m. Then the solution to $\displaystyle \frac{90}{85}=\frac{\theta}{\sin\theta}$ is $\displaystyle \theta=33.36^\circ$. So the radius of the circle is 77.28m and the distance from the circle's center to the ground is 64.55m. Thus, the rail is sitting 12.72m off the ground. (Obviously, a realistic value of its expansion of a few millimeters will cause it to rise only a few centimeters.)