The New River Gorge bridge in West Virginia is a 518-m long steel arch. How much will its length change between the temperature extremes of -200C and 350C?
To determine the change in length of the New River Gorge bridge between the temperature extremes of -20°C and 35°C, we need to use the coefficient of linear expansion for steel.
The coefficient of linear expansion represents how much a material expands or contracts per unit length for each degree change in temperature. For steel, the coefficient of linear expansion is typically around 12 x 10^-6 per °C.
To calculate the change in length, we can use the formula:
ΔL = α * L * ΔT
Where:
ΔL is the change in length
α is the coefficient of linear expansion
L is the initial length of the bridge
ΔT is the change in temperature
Given:
L = 518 m (initial length of the bridge)
ΔT = (35°C) - (-20°C) = 55°C (change in temperature)
Substituting the values into the formula:
ΔL = (12 x 10^-6 / °C) * 518 m * 55°C
Calculating the equation:
ΔL = (12 x 10^-6 / °C) * 518 m * 55°C
= (12 x 10^-6) * (518) * (55)
≈ 341 mm
Therefore, the length of the New River Gorge bridge will change approximately 341 mm (or 0.341 meters) between the temperature extremes of -20°C and 35°C.