Suppose that the 1.3 km span of the Golden Gate Bridge had no expansion joints. Calculate how much longer the bride would be if the temperature of the bridge increases by 35°C.
214.5
To calculate the change in length of the bridge due to a temperature increase, we can use the linear coefficient of thermal expansion (α) and the 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
ΔT is the change in temperature
The linear coefficient of thermal expansion for steel, which is the material the Golden Gate Bridge is made of, is approximately 12 x 10^(-6) per °C.
Given:
Original length (L) = 1.3 km = 1300 m
Change in temperature (ΔT) = 35°C
Substituting these values into the formula, we get:
ΔL = (12 x 10^(-6) / °C) * (1300 m) * (35°C)
Calculating the expression:
ΔL = 0.000012 * 1300 * 35
ΔL = 0.546 m
Therefore, if the temperature of the bridge increases by 35°C, the bridge would be approximately 0.546 meters longer.
To calculate the change in length of the Golden Gate Bridge due to temperature increase, we need to use the coefficient of linear expansion. The coefficient of linear expansion (α) represents the fractional increase in length per degree Celsius.
First, we need to find the coefficient of linear expansion (α) for the material used in the bridge. The Golden Gate Bridge is primarily made of steel, so we'll use the coefficient of linear expansion for steel, which is approximately 12 x 10^-6 per degree Celsius.
Next, we calculate the change in length (ΔL) using the formula:
ΔL = α * L * ΔT
Where:
ΔL = Change in length
α = Coefficient of linear expansion
L = Original length
ΔT = Change in temperature
Given:
L = 1.3 km (1300 m)
ΔT = 35°C
Now, we can substitute the values into the formula to calculate the change in length:
ΔL = (12 x 10^-6) * (1300 m) * (35°C)
To perform this calculation:
- Convert the length from kilometers to meters: 1.3 km = 1300 m
- Substitute the values into the formula:
ΔL = (12 x 10^-6) * (1300 m) * (35°C)
Evaluating the calculation:
ΔL = (12 x 10^-6) * (1300) * (35)
= 0.054 m
Therefore, the bridge would be approximately 0.054 meters longer if the temperature of the bridge increases by 35°C, assuming there are no expansion joints.