How to Calculate Actual Length of a Measured Distance Using Thermal Expansion Formula

What is the actual length of the distance measured using a stainless steel measuring tape calibrated to be 100.000 m long at 20 ∘C?

Option 1: 99.999 m

Option 2: 100.001 m

Option 3: 100.002 m

Option 4: 100.003 m

Final answer:

The actual length of the measured distance is 100.017 m.

To calculate the actual length of the distance measured using the stainless steel measuring tape calibrated at 100.000 m, we need to consider thermal expansion. The linear coefficient of thermal expansion for stainless steel is typically around 17 x 10-6 ℃-1.

By applying the thermal expansion formula ΔL = L0 × α × ΔT, where ΔL is the change in length, L0 is the initial length, α is the linear coefficient of thermal expansion, and ΔT is the change in temperature, we can calculate the change in length.

Given that the tape was used to measure a distance of 100 m at a temperature of 30 ∘C, we can plug in the values: ΔL = 100.000 m × 17 x 10-6 ℃-1 × (30 ℃ - 20 ℃). This calculation results in ΔL = 0.017 m.

Therefore, the actual length of the measured distance is 100 m + 0.017 m = 100.017 m.

It's essential to consider thermal expansion when precise measurements are required, especially when working with materials like stainless steel. Understanding the principles of thermal expansion can help ensure accurate measurements in various applications.