A surveyor has a steel measuring tape that is calibrated to be 100.000 m long (i.e., accurate to ±1 mm) at 20°C. If she measures the distance between two stakes to be 65.175 m on a 3°C day, does she need to add or subtract a correction factor to get the true distance? How large, in mm, is the correction factor?

Key Concepts

Thermal Expansion

Thermal expansion refers to the tendency of materials to change in size or volume in response to changes in temperature. For metals like steel, this means that as the temperature decreases, the material contracts, leading to a shorter length. Understanding this concept is crucial for determining how much the measuring tape's length will change when the temperature drops from 20°C to 3°C.

Calibration and Measurement Accuracy

Calibration is the process of adjusting the precision of a measuring instrument to ensure accurate readings. The steel measuring tape is calibrated to be accurate at 20°C, meaning its length is defined at this temperature. When measuring at a different temperature, it is essential to account for any discrepancies that arise due to thermal expansion or contraction, which can affect the accuracy of the measurement.

Correction Factor

A correction factor is a numerical adjustment applied to a measurement to account for systematic errors or deviations from the true value. In this scenario, the correction factor will be calculated based on the change in temperature and the coefficient of linear expansion for steel. This factor will indicate whether the measured distance should be increased or decreased to reflect the true distance between the stakes.