An aluminum measuring tape is correctly calibrated in metric units at exactly 0 degree Celsius. At is used to measure the distance between two lines on a floor, and the reading is 25.000 meters at a temperature of 30.000 degree Celsius. Determine the actual distance between the lines.
increase of length = L *coefficient of expansion * 30
To determine the actual distance between the lines, we need to consider the expansion or contraction of the aluminum measuring tape due to the change in temperature.
Aluminum has a coefficient of linear expansion, which is a measure of how much it expands or contracts per degree Celsius of temperature change. The coefficient of linear expansion for aluminum is approximately 0.000022 (1/°C).
Given the temperature change from 0°C to 30°C, which is a 30-degree increase, we can calculate the expansion factor:
Expansion factor = coefficient of linear expansion * temperature change
Expansion factor = 0.000022 (1/°C) * 30°C
Expansion factor = 0.00066
(Note: This value indicates the fractional increase or decrease in length for each degree Celsius of temperature change.)
Now, we can calculate the expanded length of the measuring tape at 30°C.
Expanded length = original length * (1 + expansion factor)
Expanded length = 25.000 meters * (1 + 0.00066)
Expanded length = 25.000 meters * 1.00066
Expanded length = 25.0165 meters
Therefore, the actual distance between the lines, accounting for the expansion of the aluminum measuring tape, is approximately 25.0165 meters.