Elasticity: Stress and Strain Quiz

PDF page 238: We now move from consideration of forces that affect the motion of an object (such as friction and drag) to those that affect an object’s shape. If a bulldozer pushes a car into a wall, the car will not move but it will noticeably change shape. A change in shape due to the application of a force is a deformation. Even very small forces are known to cause some deformation. For small deformations, two important characteristics are observed. First, the object returns to its original shape when the force is removed—that is, the deformation is elastic for small deformations. Second, the size of the deformation is proportional to the force—that is, for small deformations, Hooke’s law is obeyed. In equation form, Hooke’s law is given by 5.26 where is the amount of deformation (the change in length, for example) produced by the force , and is a proportionality constant that depends on the shape and composition of the object and the direction of the force. Note that this force is a function of the deformation —it is not constant as a kinetic friction force is. Rearranging this to

PDF page 238: We now move from consideration of forces that affect the motion of an object (such as friction and drag) to those that affect an object’s shape. If a bulldozer pushes a car into a wall, the car will not move but it will noticeably change shape. A change in shape due to the application of a force is a deformation. Even very small forces are known to cause some deformation. For small deformations, two important characteristics are observed. First, the object returns to its original shape when the force is removed—that is, the deformation is elastic for small deformations. Second, the size of the deformation is proportional to the force—that is, for small deformations, Hooke’s law is obeyed. In equation form, Hooke’s law is given by 5.26 where is the amount of deformation (the change in length, for example) produced by the force , and is a proportionality constant that depends on the shape and composition of the object and the direction of the force. Note that this force is a function of the deformation —it is not constant as a kinetic friction force is. Rearranging this to

PDF page 238: We now move from consideration of forces that affect the motion of an object (such as friction and drag) to those that affect an object’s shape. If a bulldozer pushes a car into a wall, the car will not move but it will noticeably change shape. A change in shape due to the application of a force is a deformation. Even very small forces are known to cause some deformation. For small deformations, two important characteristics are observed. First, the object returns to its original shape when the force is removed—that is, the deformation is elastic for small deformations. Second, the size of the deformation is proportional to the force—that is, for small deformations, Hooke’s law is obeyed. In equation form, Hooke’s law is given by 5.26 where is the amount of deformation (the change in length, for example) produced by the force , and is a proportionality constant that depends on the shape and composition of the object and the direction of the force. Note that this force is a function of the deformation —it is not constant as a kinetic friction force is. Rearranging this to

PDF page 238: We now move from consideration of forces that affect the motion of an object (such as friction and drag) to those that affect an object’s shape. If a bulldozer pushes a car into a wall, the car will not move but it will noticeably change shape. A change in shape due to the application of a force is a deformation. Even very small forces are known to cause some deformation. For small deformations, two important characteristics are observed. First, the object returns to its original shape when the force is removed—that is, the deformation is elastic for small deformations. Second, the size of the deformation is proportional to the force—that is, for small deformations, Hooke’s law is obeyed. In equation form, Hooke’s law is given by 5.26 where is the amount of deformation (the change in length, for example) produced by the force , and is a proportionality constant that depends on the shape and composition of the object and the direction of the force. Note that this force is a function of the deformation —it is not constant as a kinetic friction force is. Rearranging this to

PDF page 239: makes it clear that the deformation is proportional to the applied force. Figure 5.11 shows the Hooke’s law relationship between the extension of a spring or of a human bone. For metals or springs, the straight line region in which Hooke’s law pertains is much larger. Bones are brittle and the elastic region is small and the fracture abrupt. Eventually a large enough stress to the material will cause it to break or fracture. Tensile strength is the breaking stress that will cause permanent deformation or fracture of a material.

PDF page 239: makes it clear that the deformation is proportional to the applied force. Figure 5.11 shows the Hooke’s law relationship between the extension of a spring or of a human bone. For metals or springs, the straight line region in which Hooke’s law pertains is much larger. Bones are brittle and the elastic region is small and the fracture abrupt. Eventually a large enough stress to the material will cause it to break or fracture. Tensile strength is the breaking stress that will cause permanent deformation or fracture of a material.

PDF page 239: The proportionality constant depends upon a number of factors for the material. For example, a guitar string made of nylon stretches when it is tightened, and the elongation is proportional to the force applied (at least for small deformations). Thicker nylon strings and ones made of steel stretch less for the same applied force, implying they have a larger (see Figure 5.12). Finally, all three strings return to their normal lengths when the force is removed, provided the deformation is small. Most materials will behave in this manner if the deformation is less than about 0.1% or about 1 part in .

PDF page 239: The proportionality constant depends upon a number of factors for the material. For example, a guitar string made of nylon stretches when it is tightened, and the elongation is proportional to the force applied (at least for small deformations). Thicker nylon strings and ones made of steel stretch less for the same applied force, implying they have a larger (see Figure 5.12). Finally, all three strings return to their normal lengths when the force is removed, provided the deformation is small. Most materials will behave in this manner if the deformation is less than about 0.1% or about 1 part in .

PDF page 240: We now consider three specific types of deformations: changes in length (tension and compression), sideways shear (stress), and changes in volume. All deformations are assumed to be small unless otherwise stated.

PDF page 240: A change in length is produced when a force is applied to a wire or rod parallel to its length , either stretching it (a tension) or compressing it. (See Figure 5.13.)

PDF page 240: FIGURE 5.13 (a) Tension. The rod is stretched a length

PDF page 240: that depends on the substance, is the cross-sectional area, and is the original length. Table 5.3 lists values of for several materials—those with a large are said to have a large tensile stiffness because they deform less for a given tension or compression.