A steel measuring tape is calibrated at 20 degrees Celsius. A reading of 32.10m is measured when it is used to find the length of a building. If the temperature is 5degrees Celsius, what is the actual length of the building at that temperature?

The coefficient of linear expansion for steel is 12*10^-6

Does the building expand also? What is its coefficent of linear expansion?

It just says to take into consideration the measuring tape and not the building.

To find the actual length of the building at 5 degrees Celsius, we need to take into account the expansion of the steel measuring tape due to the change in temperature.

The formula for linear expansion is given by:
ΔL = L₀ * α * ΔT

Where:
ΔL is the change in length
L₀ is the original length
α is the coefficient of linear expansion
ΔT is the change in temperature

Given:
L₀ = 32.10 m (the reading obtained at 20 degrees Celsius)
ΔT = 5 - 20 = -15 degrees Celsius (change in temperature)
α = 12 * 10^-6 (the coefficient of linear expansion for steel)

Substituting these values into the formula, we get:
ΔL = 32.10 m * 12 * 10^-6 * (-15)

Calculating this, we find:
ΔL ≈ -0.07254 m

The negative sign indicates that the steel tape has contracted due to the decrease in temperature.

To find the actual length of the building at 5 degrees Celsius, we need to subtract the contraction from the original length:
Actual Length = L₀ + ΔL
Actual Length = 32.10 m + (-0.07254 m)
Actual Length ≈ 32.02746 m

Therefore, the actual length of the building at 5 degrees Celsius is approximately 32.02746 meters.

You can get the length of the tape at 5C by

deltaL=32.10*12E-6*(15)then subtracting deltaL from that L.

Opps, add delta L to L. The tape shrinks, so the measurement of the building is longer.