Two circular rods, both of length L and having the same diameter, are placed end to end between rigid supports with no initial stress in the rods. The coefficient of linear expansion and Young's modulus for rod A are αA and YA respectively; those for rod B are αB and YB respectively. Both rods are "normal" materials with α>0. The temperature of the rods is now raised by ΔT. What is the stress F/A in the rods after heating?Express the stress in terms of ?A, ?B, YA, YB, and ?T.

Explanation:

From the information given.

The formula for Youngs modulus(Y) can be illustrated as follows:

where;

F = force

A = area

ΔL / L = the fraction of the change that occurred in the length.

If we make ΔL / L the subject of the formula, the above expression can be re-written as:

However, the total fractional change that occurred in the length can be computed as:

where;

The area of both rods is said to be equal as well.

Thus;

----- Let this be equation (1)

Recall that:

in which

ΔL = change in length

L = the original length of rod before extension

∝ = coefficient of linear expansion

ΔT = temperature change

Similarly:

The total fractional change in the length is:

The sum of both the thermal and compressive stress of the combined rod is equal to the fractional change.

Mathematically:

where;

∴

From equation (1) & (2)

Making the stress the subject, we get;

answer: the exterior temperature of commercial jet planes as they leave the stratosphere and return to the ground increases steadily.

explanation:

the lower most layer of atmosphere is troposphere which extends from 0 to 12 km above the surface of the earth. the temperature initially decreases as distance is increased from the earth's surface. commercial jets fly in lower part of the stratosphere. the stratosphere extends upto 50 km. the temperature in stratosphere starts rising again due to presence of ozone which traps the uv rays.

thus, when the planes leave the stratosphere and return to the ground, the exterior temperature increases steadily.