Find the length of a bridge if it is known that the steel in the roadbed expands by 0.52 m when the temperature changes from +2 to +30°C.
The liear expansion coefficient for steel in that temperature range is ab9out 12*10^-6 per degree C change.
Solve this equation for L:
(delta L) = 0.52 m = L*(alpha)*(delta T)
where delta T = 30 - 2 = 28 C
L = 0.52 m/{28 * 12*10^-6)
To find the length of the bridge, we need to determine the linear expansion coefficient of the steel in the roadbed. This coefficient indicates how much the material expands or contracts with a change in temperature.
The formula to calculate the change in length due to thermal expansion is:
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, we know the change in temperature is from +2°C to +30°C, which gives ΔT = 30 - 2 = 28°C. We also know the change in length is 0.52 m.
Now, we need to determine the linear expansion coefficient (α) of the steel. The linear expansion coefficient is typically given in units of per degree Celsius (or per Kelvin). Unfortunately, this value is not provided in the question, so we will need to look it up.
The linear expansion coefficient varies depending on the specific type of steel used. A common average value for steel is around 12 x 10^-6 per degree Celsius (12 × 10^-6/°C).
Using the formula for change in length, we can now find the original length (L):
0.52 = (12 × 10^-6) * L * 28
Next, we isolate L:
L = 0.52 / (12 × 10^-6 * 28)
Calculating this gives us:
L ≈ 1571.43 meters
Therefore, the length of the bridge is approximately 1571.43 meters.