Suppose that the 1.3 km span of the golden gate bridge had no expansion joints. Calculate how much longer the bridge would be if the temperature of the bridge increases by 35 degrees celsious
Assume the bridge is made of steel. The coefficient of thermal expansion of steel is 11*10^-6 degC^-1
A 35 degree C will expand the length by an amount
35*11^10^-6 = 3.85*10^-4
of the original length. That would be about 0.50 meters
Oh boy, it sounds like the Golden Gate Bridge could be in for a stretch! Well, let's crunch some numbers and see how much longer it would get.
To calculate the change in length, we can use the thermal expansion coefficient of steel, which is about 12 x 10^-6 per degree Celsius. Multiply this by the original length of 1.3 km and the temperature change of 35 degrees Celsius, and we get:
(12 x 10^-6) x (1.3 km) x (35 degrees Celsius) = 0.00546 km
This means that the Golden Gate Bridge would stretch by approximately 0.00546 km (or 5.46 meters) if the temperature increased by 35 degrees Celsius.
So, if you plan to measure the length of the bridge on a hot day, make sure to account for its newfound stretchiness!
To calculate the change in length of the bridge, we need to use the coefficient of linear expansion. The coefficient of linear expansion for steel, which is the material used in the Golden Gate Bridge, is approximately 12 x 10^(-6) per degree Celsius.
Given:
Length of the bridge span = 1.3 km = 1300 m
Change in temperature = 35 degrees Celsius
We can use the formula:
Change in length = Original length * Coefficient of linear expansion * Change in temperature
Change in length = 1300 * (12 x 10^(-6)) * 35
Calculating, we get:
Change in length = 546 meters
Therefore, if the temperature of the Golden Gate Bridge increases by 35 degrees Celsius without any expansion joints, the bridge would become approximately 546 meters longer.
To calculate how much longer the Golden Gate Bridge would be if its temperature increased by 35 degrees Celsius, we need to consider the coefficient of thermal expansion for the material the bridge is made of. The coefficient of thermal expansion quantifies how much a material expands or contracts with temperature changes.
Assuming the Golden Gate Bridge is made of steel, we can find the coefficient of linear expansion for steel, which is typically around 11.7 x 10^-6 per degree Celsius.
To calculate the change in length, we can use the formula:
ΔL = L * α * ΔT
Where:
ΔL is the change in length
L is the original length
α is the coefficient of linear expansion
ΔT is the change in temperature
In this case:
L = 1.3 km = 1300 m
α = 11.7 x 10^-6 per degree Celsius
ΔT = 35 degrees Celsius
Plugging in these values into the formula, we get:
ΔL = 1300 m * 11.7 x 10^-6 per degree Celsius * 35 degrees Celsius
Calculating this, we find:
ΔL = 0.05355 meters or 53.55 mm
Therefore, if the temperature of the Golden Gate Bridge increased by 35 degrees Celsius, the bridge would be approximately 53.55 millimeters longer.