Each Steel Rail is 8.0 m long and has a cross sectional area of .0025msquared. on a hot day, each rail thermally expans as musch as 3.0 X 10EE-3. if there were no gaps between the rails, what would be the force on the ends of each rail?
Cant
To find the force on the ends of each rail, we need to calculate the change in length due to thermal expansion and use Hooke's Law.
Hooke's Law states that the force (F) exerted on an object is equal to the product of its stiffness (k) and the change in length (ΔL).
The formula for thermal expansion is given by:
ΔL = α * L0 * ΔT,
Where ΔL is the change in length, α is the coefficient of linear expansion, L0 is the original length, and ΔT is the change in temperature.
In this case, we know that ΔL = 3.0 × 10^-3 m, L0 = 8.0 m, and α is the coefficient of linear expansion.
To find the coefficient of linear expansion (α):
α = ΔL / (L0 * ΔT).
Let's calculate α:
α = (3.0 × 10^-3 m) / (8.0 m * ΔT).
Now we need to calculate the force (F) using Hooke's Law:
F = k * ΔL,
However, we do not know the value of the stiffness (k). But we can use Young's Modulus (Y) and the formula:
k = Y * A / L0,
Where Y is Young's Modulus, A is the cross-sectional area, and L0 is the original length.
Using this formula, we can calculate k:
k = Y * A / L0.
Finally, we can substitute the values of k and ΔL into Hooke's Law to calculate the force (F):
F = k * ΔL.
To summarize, the steps to find the force on the ends of each rail are as follows:
1. Calculate the coefficient of linear expansion (α): α = (3.0 × 10^-3 m) / (8.0 m * ΔT).
2. Calculate the stiffness (k) using Young's Modulus (Y): k = Y * A / L0.
3. Substitute the values of k and ΔL into Hooke's Law: F = k * ΔL.