Question

A 30 m segment of railroad track is clamped to the ground at both ends when the temperature outside is 0C by strong steel pins. Thermal expansion is α=10 x 10-6 /C, Young’s Modulus Y is 1011 Pa. The temperature is then increased by an amount ΔT. A. The pressure is Y B. The pressure is 0 C. The pressure depends on the cross-sectional area of the tracks D. The pressure is Yα ΔT E. The pressure is Y????∆T Lo Lo+∆T????L�

Answer 1

Answer:

The pressure due to thermal expansion on the segment of rail is

$Stress = Y(\alpha\Delta T)$

Explanation:

As we know by law of thermal expansion the increase in length due to temperature change is given as

$\Delta L = L_o \alpha \Delta T$

so we can find the thermal strain as

$\frac{\Delta L}{L} = \alpha \Delta T$

Now by law of elasticity we know that

$Elasticity = \frac{Stress}{Strain}$

So we have

$Stress = Y(strain)$

from above equation of strain we have

$Stress = Y(\alpha\Delta T)$

So above is the pressure due to thermal expansion on the segment of rail

Answer 2

The pressure due to thermal expansion on the segment of rail is

Stress is = Y(αΔΤ)

The correct option is 'D' The pressure is Yα ΔT

What is a Thermal expansion?

When we know that according to the law of thermal expansion the increase in length due to temperature change is given as

ΔLis = L₀ₐΔT

Then we can find the thermal strain as:

ΔL/L is = αΔΤ

After that by the law of elasticity we know that is:

Then The Elasticity is = stress/strain

Now, we have

Stress is = Y (strain)

from The above equation of strain we have is:

Then Stress is = Y(αΔΤ)

Hence proof above is the pressure due to thermal expansion on the segment of rail.

Therefore, The correct option is 'D' The pressure is Yα ΔT

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