Steel expands 11 parts in a million for each 1 degree C change. Consider a 40,000 km steel pipe that forms a ring to fit snugly all around the circumference of the Earth. Suppose people along its length breathe on it so as to raise its temperature 0.80 degree C. The pipe gets longer. It also is no longer snug. How high does it stand above ground level? (To simplify, consider only the expansion of its radial distance from the center of Earth, and apply the geometry formula that relates circumference C and radius r, C = 2 \pi r. The result is surprising!)
delta C = 2*pi*delta r = 2*pi*r*alpha*deltaT
The distance the piper rises is delta r.
delta r = r*alpha*deltaT
=[4*10*7 m/(2pi)]*11*10^-6*0.8 = 56 m
thanks so much!!!!!
To find out how high the steel pipe stands above ground level due to its expansion, we need to consider the change in its radius caused by the increase in temperature.
First, let's calculate the change in radius. We know that steel expands 11 parts in a million for each 1 degree Celsius change. So, for a 0.80 degree Celsius temperature increase, the change in radius can be calculated as follows:
Change in radius = (0.80 degrees Celsius) * (11 parts in a million) * (current radius)
Now, let's consider the current radius of the steel pipe. The pipe forms a ring that fits snugly all around the circumference of the Earth. The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. In this case, the circumference is equal to the Earth's circumference, which is approximately 40,000 km.
So, we can rearrange the formula to solve for the current radius:
current radius = C / (2π)
Substituting the value for C, we get:
current radius = 40,000 km / (2π)
Now, let's put all the values together to calculate the change in radius:
Change in radius = (0.80 degrees Celsius) * (11 parts in a million) * (40,000 km / (2π))
Next, we need to calculate how high the pipe stands above ground level due to this change in radius. To simplify the calculation, we'll consider only the expansion of the radial distance from the center of the Earth.
The height can be found using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is the radius of the Earth plus the change in radius, and one of the sides is the radius of the Earth.
By applying the Pythagorean theorem, we can calculate the height:
Height = √((current radius + change in radius)^2 - current radius^2)
Now, we can substitute the values and calculate the height:
Height = √(((40,000 km / (2π)) + (0.80 degrees Celsius) * (11 parts in a million) * (40,000 km / (2π)))^2 - (40,000 km / (2π))^2)
By plugging in the values and simplifying, we can find the surprising result of how high the steel pipe stands above ground level.