Steel railroad tracks of length L = 18.30 m are laid at 10.0° C. How much space should be left between the track sections if they are to just touch when the temperature is T = 49.0° C? mm
Please help. I have tried this
L° α Δt = 18.3 * 13 10^-6 * (49 -10) = .92781cm which equals to 9.2681 mm I think but its wrong. please help.
I have 12 * 10^-6 for the thermal expansion coef of steel
meters in --> meters out
18.3 * 12 * 10^-6 * (39) = 8564*10^-6 m
= .008564 m = 8.564 mm
Thank you so much Damon :)!
To calculate the space that should be left between the track sections, you need to consider the expansion of the steel track with temperature change.
The formula to calculate the change in length of an object due to temperature change is:
ΔL = L * α * (Tf - Ti),
Where:
ΔL is the change in length,
L is the original length,
α is the linear expansion coefficient of the material, and
Tf and Ti are the final and initial temperatures, respectively.
In this case, the temperature change is from Ti = 10.0°C to Tf = 49.0°C, and the original length is L = 18.30 m.
You have correctly identified the linear expansion coefficient of steel (α) as 13 * 10^(-6) (°C)^(-1).
Let's calculate ΔL:
ΔL = L * α * (Tf - Ti)
= 18.30 m * 13 * 10^(-6) (°C)^(-1) * (49.0°C - 10.0°C)
Calculating the numerical value:
ΔL = 18.3 * 13 * (49 - 10) * 10^(-6) m
= 18.3 * 13 * 39 * 10^(-6) m
≈ 9.5924 * 10^(-3) m
≈ 9.5924 mm
Therefore, the correct amount of space that should be left between the track sections is approximately 9.5924 millimeters.
To solve this problem, you need to consider the coefficient of linear expansion for steel and use it in the formula to calculate the change in length of the railroad tracks.
The formula for linear expansion of a material is given by:
ΔL = α * L * ΔT
Where:
ΔL is the change in length of the railroad tracks
α is the coefficient of linear expansion for steel
L is the original length of the railroad tracks
ΔT is the change in temperature
In this case, you have the original length (L = 18.30 m), the change in temperature (ΔT = 49.0°C - 10.0°C = 39.0°C), and you need to find the change in length (ΔL) to determine the space that should be left between the track sections.
Now, you mentioned that you used the formula: L° α Δt = 18.3 * 13 10^-6 * (49 - 10) = .92781cm. However, it seems that you made a mistake in converting the units. Let's correct that:
Using the correct units, the calculation should be as follows:
α = 13 * 10^-6 (per °C) (coefficient of linear expansion for steel)
L = 18.30 m (original length of the railroad tracks)
ΔT = 39.0°C (change in temperature)
Now, substitute these values into the formula:
ΔL = α * L * ΔT
ΔL = (13 * 10^-6) * (18.30) * (39.0)
ΔL = 0.0090474 m
To convert the result to millimeters (mm), multiply by 1000:
ΔL = 0.0090474 m * 1000 = 9.0474 mm
Therefore, the correct change in length is approximately 9.0474 mm. This represents the amount of space that should be left between the track sections for them to just touch when the temperature is 49.0°C.