State the expression for change in length of a body due to force acting on it.
Answers
Explanation:
Elasticity: Stress and Strain
LEARNING OBJECTIVES
By the end of this section, you will be able to:
State Hooke’s law.
Explain Hooke’s law using graphical representation between deformation and applied force.
Discuss the three types of deformations such as changes in length, sideways shear and changes in volume.
Describe with examples the young’s modulus, shear modulus and bulk modulus.
Determine the change in length given mass, length and radius.
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
F = kΔL,
where ΔL is the amount of deformation (the change in length, for example) produced by the force F, and k 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 ΔL—it is not constant as a kinetic friction force is. Rearranging this to
\displaystyle\Delta{L}=\frac{F}{k}ΔL=
k
F
makes it clear that the deformation is proportional to the applied force. Figure 1 shows the Hooke’s law relationship between the extension ΔL 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.