steel train rails are placed end to end with space in between on a day where a temperature is 30 degrees. How much stress will be build if the temperature is increase to 150 degrees .assume that the original is 1.5m
To calculate the stress that will be built in the steel train rails due to a temperature increase, we need to consider the concept of thermal expansion and the coefficient of linear expansion.
The coefficient of linear expansion (α) represents how much a material expands or contracts per unit length when its temperature changes by 1 degree Celsius.
First, we need to determine the change in temperature (ΔT) by subtracting the initial temperature from the final temperature:
ΔT = 150 degrees - 30 degrees = 120 degrees
Next, we'll use the coefficient of linear expansion for steel, which is approximately 12 x 10^(-6) per degree Celsius.
The change in length (ΔL) can be calculated using the formula:
ΔL = α * L * ΔT
where:
ΔL is the change in length
α is the coefficient of linear expansion
L is the original length of the steel rail
ΔT is the change in temperature
Given that the original length (L) is 1.5m, we can substitute these values into the formula:
ΔL = (12 x 10^(-6) per degree Celsius) * (1.5m) * (120 degrees)
Simplifying the equation:
ΔL = 1.728 millimeters
Thus, the change in length of the steel train rails will be 1.728 millimeters when the temperature increases to 150 degrees. This change in length causes stress to build up in the rails.
If you want to calculate the stress (σ) that will result from this change in length, you will need to know the mechanical properties of the steel, such as Young's modulus, tensile strength, or yield strength. These properties are required to determine how the change in length affects the stress in the rails.