The New River Gorge bridge in West Virginia is a 518-m-long steel arch. How much will its length change between temperature extremes −17°C and 30°C?
change in L=a*L*change in T
you are missing the a but the formula would look like
Change in L=a*518*47
To find the change in length of the New River Gorge bridge between temperature extremes of -17°C and 30°C, we can use the linear thermal expansion formula:
ΔL = α * L * ΔT
Where:
ΔL is the change in length
α is the linear coefficient of thermal expansion
L is the original length of the bridge
ΔT is the change in temperature
To proceed, we need to determine the linear coefficient of thermal expansion for the steel material used in the bridge. The linear coefficient of thermal expansion for steel typically ranges from 10 to 13 × 10^(-6) °C^(-1).
Let's assume a value of α = 12 × 10^(-6) °C^(-1) for the steel material in the New River Gorge bridge.
Given:
Original length (L) = 518 m
Change in temperature (ΔT) = (30°C) - (-17°C) = 47°C
Linear coefficient of thermal expansion (α) = 12 × 10^(-6) °C^(-1)
Now, we can calculate the change in length (ΔL) using the formula:
ΔL = α * L * ΔT
ΔL = (12 × 10^(-6) °C^(-1)) * (518 m) * (47°C)
Simplifying the expression:
ΔL = 0.000012 * 518 * 47
≈ 0.286 m
Therefore, the length of the New River Gorge bridge will change by approximately 0.286 meters (or 286 millimeters) between temperature extremes of -17°C and 30°C.