By what amount will a 178 m long concrete slab on the Mackinac Bridge contract when going from +39C to -35C? The linear expansion coefficient is 10-5 per C.
deltaL = a*L*deltaT
where deltaL is the change in length, a s the linear expansion coefficient, L0 is it's initial length, deltaT is the final temperature
deltaL = 10^-5*178*(-35 - 39)
To calculate the amount by which the concrete slab on the Mackinac Bridge will contract, we need to use the formula for linear expansion:
ΔL = α * L * ΔT
where:
ΔL is the change in length
α is the linear expansion coefficient
L is the original length
ΔT is the change in temperature
In this case, the original length (L) is given as 178 meters, the linear expansion coefficient (α) is given as 10^-5 per degree Celsius, and the change in temperature (ΔT) is -35°C (-35 degrees Celsius is colder than +39 degrees Celsius).
Now, let's calculate the change in length (ΔL):
ΔL = (10^-5 per C) * (178 m) * (-35C - (+39C))
First, let's simplify the difference in temperatures:
ΔL = (10^-5 per C) * (178 m) * (-74C)
Next, we calculate the change in length:
ΔL = -0.00001 * 178 * (-74)
ΔL ≈ -0.131972 meters
Therefore, the concrete slab on the Mackinac Bridge will contract by approximately 0.131972 meters (or about 13.2 centimeters) when going from +39°C to -35°C.