Question

One of the most important properties of materials in many applications is strength. Two of the qualitative measures of the strength of a material are tensile strength and shear strength. The tensile strength of a material is the amount of force needed to pull the material apart perpendicular to a cross section, such as pulling on a rope. The shear strength is the amount of force needed to rupture the material when a force is applied parallel to the cross section, such as breaking a pencil overhanging a table edge. Both tensile strength and shear strength have units of pressure because they represent the force that must be applied per unit area in order to break the material.

The importance of knowing the tensile strength and shear strength of a material is evidenced by the number of machines and companies specializing in determining these properties. Many types of materials and objects are tested, from fabric and metal to nuts and bolts. It is always comforting to know that the tensile strength of the rope holding you above the ground can support your weight. Shear strength needs to be found for bridges, the floors of multilevel buildings, and the joints where the wings join the body of an airplane. Without the experimental determination of these properties, trial and error would be the only other method of determining these values, a process that would be dangerous to life and limb.
A typical machine tests the tensile strength of a sheet of material cut into a standard size of 5.00 centimeters wide by10.0 centimeters long. The machine consists of one clamp that holds the entire width (5.00 centimeters) so that it hangs vertically. A second clamp is placed on the lower end of the object, to which a variable downward force is applied. The force is slowly increased until the object ruptures, and the breaking force is recorded.

A strip of aluminum foil with a thickness of15.0 micrometers and matching the size recommendations of the machine is placed in the machine and tested. The force needed to rupture the foil is found to be 233 newtons.

1)What is the tensile strength of the aluminum foil sample?( Express your answer in megapascals to three significant figures. )

2) Given that the tensile strength of aluminum foil is 311 megapascals, its thickness is approximately 15.0 micrometers, and a roll of household aluminum foil is30.0 centimeters wide, how much force F is needed to pull off a sheet to use?

Assume that the force is applied equally along the whole width of the foil and that you are trying to pull perpendicular to the cross section.

Express your answer in newtons to three significant figures.

3)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 30.0centimeters wide and its thickness is approximately 15.0micrometers, how much shear force is needed to pull off a sheet?

Assume that the force is applied equally along the whole width of the foil. (Express your answer in newtons to three significant figures.)

Answer 1

1)

Tensile Strength = Force/Area

= 233 N/ 7.50*10^-7 = 3.106 x 10^8 Pa = 311 MPa

2)

3)

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

just find the area or the cross-section again.

0.000015 x 0.300 = 0.0000045

210000000 = F/0.0000045

F = 945.000 N

Answer 2

(A) The tensile strength is, Tensile strength== 233 7.5x 10-7 = 3.10666x10Pa =3.11x108 Pa =3.11 MPa