When railroad tracks are installed, gaps are left between the rails. Each steel rail is 8.0m long and has a cross-sectional area of 0.0020m^2. On a hot day, each rail thermally expands as much as 4.0mm. If there were no gaps between the rails, what would be the force on the ends of each rail?

[Y=20x10^10 N/m^2]

To find the force on the ends of each rail, we can use the equation for thermal expansion:

ΔL = α * L * ΔT

Where:
ΔL is the change in length of the rail
α is the coefficient of linear expansion
L is the original length of the rail
ΔT is the change in temperature

In this case, we are given:
ΔL = 4.0 mm = 0.0040 m (since 1 mm = 0.001 m)
L = 8.0 m (original length of the rail)
α = ?
ΔT = ?

We need to find the coefficient of linear expansion α and the change in temperature ΔT to proceed.

To find α, we can rearrange the equation:

α = ΔL / (L * ΔT)

Now, let's find ΔT:

To find ΔT, we need to know the temperature change. The problem statement mentions that the rails expand on a hot day, but it does not specify a numerical value for the temperature change. Therefore, we cannot proceed with the calculation without the specific temperature change.

Assuming we have the temperature change, we can use the equation above to find α, and then calculate the force on the ends of each rail using the following equation:

Force = Stress * Area

Where:
Force is the force on the ends of each rail
Stress is the stress in the rail (given by Y * α * ΔT)
Area is the cross-sectional area of the rail (given as 0.0020 m^2)
Y is the Young's modulus, given as 20 × 10^10 N/m^2

Please provide the specific temperature change or any other missing information to proceed with the calculation.