NOTE: the formula for converting the
CHANGE in temperature is NOT the same
as simply converting the temperature!
A bridge is made with segments of concrete 81 m long (at the original temperature). If the linear expansion coefficient is 1.2 × 10−5(◦C)−1, how much spacing is needed to allow for expansion for an increase in temperature of 61◦F?
Answer in units of cm
To find the spacing needed for expansion, we need to first convert the change in temperature from Fahrenheit (°F) to Celsius (°C). Then we can calculate the change in length of the concrete segment using the linear expansion coefficient. Finally, we can convert the change in length from meters to centimeters.
Step 1: Convert the change in temperature from °F to °C
To convert Fahrenheit to Celsius, we can use the formula: °C = (°F - 32) * (5/9)
Change in temperature (°C) = (61°F - 32°F) * (5/9)
Change in temperature (°C) = 29°F * (5/9)
Change in temperature (°C) = 16.11°C (rounded to two decimal places)
Step 2: Calculate the change in length of the concrete segment
The change in length of the concrete segment can be calculated using the formula:
Change in length = original length * linear expansion coefficient * change in temperature
Change in length (meters) = 81 m * (1.2 x 10^-5/°C) * 16.11°C
Change in length (meters) ≈ 0.001557108 m (rounded to nine decimal places)
Step 3: Convert the change in length from meters to centimeters
To convert meters to centimeters, we multiply by 100.
Change in length (centimeters) = 0.001557108 m * 100
Change in length (centimeters) ≈ 0.1557108 cm (rounded to seven decimal places)
Therefore, the spacing needed to allow for expansion is approximately 0.1557108 cm.