Question

As stated in the introduction, shear strength is another measure of the strength of a material. A shear force is a force that acts parallel to the plane in the material that breaks. A good example of a shear is that of a martial arts expert breaking boards or bricks with her hands. Other applications in which shear forces and shear strength need to be known are geology, for studying earthquakes and landslides; fluid dynamics; and structural engineering. Aluminum has a shear strength of 210 megapascals. When you bend aluminum foil around an edge (i.e., the edge of the box) and pull, you are effectively applying a shear force along the bent edge of the foil. If a roll of household aluminum foil is 30.0 centimeters wide and its thickness is approximately 15.0 micrometers, how much shear force is needed to pull off a sheet?

Answer 1

Answer:

$F=945\ N$

Explanation:

Given:

• shear stress strength of the aluminium, $\tau=210\ MPa$

• width of aluminium foil, $w=300\ mm$

• thickness of aluminium foil, $t=15\times 10^{-3}\ mm$

We know the relation between shear force and shear stress as:

$\tau=\frac{F}{A}$

where:

$A =$ area subjected to the force F

Here the area subjected under the shear force is the bent part of the aluminium foil whole along the width.

$210=\frac{F}{15\times 10^{-3} \times 300}}$

$F=945\ N$