Ten meter long steel railroad rails are laid end to end, with no space between, on a hot day when the temperature is 115°F. Six months later the temperature has dropped to -2°F.How much space now exists between each rail?
To determine the amount of space that exists between each rail now, we need to consider the expansion and contraction of the steel rails due to the change in temperature.
First, let's calculate the change in temperature:
Change in temperature = Final temperature - Initial temperature
Change in temperature = -2°F - 115°F
Change in temperature = -117°F
Next, we need to find the coefficient of linear expansion for steel. The coefficient of linear expansion for steel is typically around 0.0000065 per degree Fahrenheit (°F).
Now, we can calculate the change in length for each rail due to the change in temperature:
Change in length = Initial length * Coefficient of linear expansion * Change in temperature
Change in length = 10 meters * 0.0000065 (1/°F) * -117°F
Calculating the value:
Change in length = 10 meters * 0.0000065 (1/°F) * -117°F
Change in length ≈ -0.0076 meters
Since the rails were initially laid with no space between them, the negative change in length means that there will now be a small gap between each rail. The approximate amount of space now existing between each rail is 0.0076 meters (or 7.6 millimeters).
To determine the space between each rail after the temperature change, we need to consider the concept of thermal expansion. Steel expands when heated and contracts when cooled.
First, let's calculate the change in temperature:
Change in temperature = Final temperature - Initial temperature
Change in temperature = -2°F - 115°F
Change in temperature = -117°F
Next, we need to find the coefficient of linear expansion for steel. This value represents the amount of expansion or contraction per degree of temperature change. Let's assume the coefficient of linear expansion for steel is 12 x 10^-6 per °F.
Now we can calculate the change in length of each rail:
Change in length = Initial length * Coefficient of linear expansion * Change in temperature
Change in length = 10 meters * 12 x 10^-6 per °F * (-117°F)
Calculating this equation will give us the change in length. Let's perform the calculation:
Change in length = 10 meters * 12 x 10^-6 per °F * (-117°F)
Change in length ≈ -1.404 meters
Since the length change is negative, it means the rails have contracted. Therefore, there will be a reduction in the total length of the laid rails.
To find the space between each rail, we need to divide the change in length by the number of spaces (one less than the number of rails laid end to end). In this case, we have one space less since the rails are laid end to end.
Number of spaces = Number of rails - 1
Number of spaces = 1 rail - 1
Let's calculate the space between each rail:
Space between each rail = Change in length / Number of spaces
Space between each rail = -1.404 meters / 0 spaces
Space between each rail is undefined (since there are no spaces when rails are laid end to end)
Therefore, in this scenario, there is no space between each rail after the temperature change from 115°F to -2°F.