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.
looks to me like
(-35-39)°C * 10^-5 m/°C = -74*10^-5 m
always keep track of the units; that will help set up the calculation
I got .13172 m is that correct?
it is delta L/L
(-35-39)*10^-5 nothing/degC *178
or -13172*10^-5 or -.132 m or -13 cm
Yes Riley
boy, I guess I blew that one!
Guess I'll leave the physics to Damon.
To calculate the amount by which the concrete slab will contract when going from +39°C to -35°C, we can use the formula:
ΔL = L * α * ΔT
Where:
ΔL is the change in length
L is the original length of the concrete slab (178 m)
α is the linear expansion coefficient (10^-5 per °C)
ΔT is the change in temperature (final temperature - initial temperature)
Let's plug in the given values and calculate:
ΔT = (-35°C) - (+39°C) = -74°C
ΔL = (178 m) * (10^-5 per °C) * (-74°C)
= -0.01854 m
Therefore, the concrete slab will contract by approximately 0.01854 meters (or 18.54 millimeters) when going from +39°C to -35°C.