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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?

Respuesta :

Answer:

[tex]F=945\ N[/tex]

Explanation:

Given:

  • shear stress strength of the aluminium, [tex]\tau=210\ MPa[/tex]
  • width of aluminium foil, [tex]w=300\ mm[/tex]
  • thickness of aluminium foil, [tex]t=15\times 10^{-3}\ mm[/tex]

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

[tex]\tau=\frac{F}{A}[/tex]

where:

[tex]A =[/tex] 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.

[tex]210=\frac{F}{15\times 10^{-3} \times 300}}[/tex]

[tex]F=945\ N[/tex]

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