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 calculate the space that exists between each rail after the temperature change, we need to take into account the expansion and contraction of the steel railroad rails due to the temperature difference.
First, let's calculate the coefficient of thermal expansion for steel. The coefficient of linear expansion for steel is approximately 0.0000065 per °F.
Next, 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
Now, we can calculate the change in length of each rail due to the temperature change. The formula for calculating the change in length is:
Change in length = Initial length × Coefficient of thermal expansion × Change in temperature
Change in length = 10 meters × 0.0000065 per °F × (-117°F)
Change in length = -0.00007665 meters
Since the change in length is negative, it means that the rails have contracted.
Finally, we can calculate the space that exists between each rail now:
Space between each rail = Change in length / (Number of rails - 1)
Number of rails = 1 (since they are laid end to end)
Space between each rail = -0.00007665 meters / (1 - 1)
Space between each rail = -0.00007665 meters
The space between each rail after the temperature change is approximately -0.00007665 meters (or -0.07665 mm).
To determine how much space exists between each rail, we need to consider the expansion and contraction of the steel railroad rails due to temperature change. Metals expand when heated and contract when cooled.
To calculate the space between each rail, we need to find the change in length of the steel rails from the initial temperature of 115°F to the final temperature of -2°F.
First, let's calculate the linear expansion coefficient of steel. The linear expansion coefficient (α) represents the change in length per unit length of a material per degree of temperature change. For steel, the linear expansion coefficient is approximately 0.000012 per °F.
Next, we need to calculate the change in temperature by subtracting the initial temperature from the final temperature:
Change in temperature = Final temperature - Initial temperature
Change in temperature = -2°F - 115°F
Change in temperature = -117°F
Now, calculate the change in length of the steel rails:
Change in length = Initial length * linear expansion coefficient * change in temperature
Change in length = 10 meters * 0.000012 per °F * -117°F
Calculating this, we get:
Change in length = -0.01404 meters
Note that the result is negative, indicating contraction of the steel rails.
Finally, the space between each rail can be found by dividing the change in length by the number of gaps between the 10-meter long rails. Assuming there are 9 gaps between the 10-meter long rails (10 rails in total), we divide the change in length by 9:
Space between rails = Change in length / Number of gaps
Space between rails = -0.01404 meters / 9
Calculating this, we get:
Space between rails ≈ -0.00156 meters
Therefore, there is approximately -0.00156 meters (or -1.56 millimeters) of space between each rail after the temperature drops from 115°F to -2°F.