Question

Find out longitudinal stress and tangential stress on the given fixed block.

Answer 1

Hint Longitudinal stress is the kind of stress that acts on a body in the direction of its length. Tangential stress acts inward, towards the surface of the body. We need to find the longitudinal and tangential stress of the block using the formula given below.

Formula used
$\Rightarrow stress = \dfrac{F}{A}$
Where, F is the deforming force and A is the area of the cross section of the given block.

Complete step by step answer
Stress is a property of a body, which describes the magnitude of the force applied on the body and the amount of deformation caused to the body.
Longitudinal stress here, is also the normal stress. We know the formula for stress,
$\Rightarrow stress = \dfrac{F}{A}$
Where, F is the deforming force and A is the area of the cross section.
Here, the longitudinal stress involves the length of the block. Thus, we use the sine function.
$\Rightarrow {\text{longitudinal stress = }}\dfrac{{100\sin {{30}^ \circ }}}{{5 \times 2}}$
We know that sin 30° is $\dfrac{1}{2}$.
Thus, the longitudinal stress becomes,
$\Rightarrow {\text{longitudinal stress = 5 N/}}{{\text{m}}^2}$.
Now, in case of tangential stress, it involves the surface of the block, which eventually implies that we use cos function.
$\Rightarrow {\text{tangential stress = }}\dfrac{{100\cos {{30}^ \circ }}}{{5 \times 2}}$
And the value of cos 30° is √3/2.
Then, the tangential stress becomes,
$\Rightarrow {\text{tangential stress = 5}}\sqrt 3 {\text{ N/}}{{\text{m}}^2}$.

Note
Stress is a quantity that describes the magnitude of force that causes deformation. It is determined by force per unit area of the body. There are six types of stress present. They are:
-Compression
-Tension
-Bending
-Shear
-Torsion
-Volume