Hello everyone in this article we are going to discuss the important property of solids. We know that there are mainly two types of substances are present viz,
- Elastic substance: In which deformation due to external force is takes place and regains the shape and size after removal of forces. E.g. Rubber, metal etc
- Plastic substance: In which deformation due to external force is takes place and regains the shape and size after removal of forces. E.g. polythene bag, chewing gum etc.
When external forces are applied to body, the body is deformed. Due to this deformation, internal forces are set up within the body these forces are termed as restoring forces. The regain in shape or size is takes due to present of restoring force in the substance throughout its surface area. Restoring forces acts against the deforming forces which causes change in shape/size or both of objects. This restoring force produces stress in substance.
Let’s define the concept now….!
The internal restoring force per unit area is called stress.
∴ Stress = (Internal restoring force)/area
Stress = F/A
The internal restoring force is equal to the applied force
∴ Stress = (Applied force)/area = F/A
The Dimensions of stress are [M1 L-1 T-2]
SI unit of stress is Or N/m2 Or Pascal.
Since the deformation due to external forces can be takes place in length, volume and shape, thus there are three types of stress.
Types of stress:
Tensile stress (Longitudinal stress):
When the deformation consists of a change in the length of the body, the stress in it is called tensile stress or longitudinal stress.
Consider a thin uniform rod of radius ‘r’, length ‘L’ is suspended from rigid support and a load is attached to its lower end, then the during extension produced in the wire stress produced in the wire can be given as,
Longitudinal stress is defined as the internal restoring force per unit area.
∴ Tensile stress = (internal restoring force)/area
∴Tensile stress = F/A = Mg/πr2
Volume stress:
When deformation consists of a change in the volume of a body, the stress in it is called as volume stress.
Consider a cubical object of volume ‘V’ and surface area ‘A’, subjected to external force ‘F’, then the volume stress is given as,
Volume stress is defined as the applied force per unit area.
Volume stress = (Applied force)/(Surface area) = F/A
During change in volume due to external force, pressure of object changes, hence volume stress is also termed as change in internal pressure of substance.
∴Volume stress = Change in pressure = dp
Shearing stress:
When deformation consists of a change in the shape of a body, the stress in it is called as shearing stress.
Consider a cube of surface area as shown in fig below. Let the tangential force applied on the top surface from left to right as shown in fig, then the shape of cube is changed to cuboidal, then shearing stress is given as,
Tangential applied force per unit area is known as shearing stress.
∴ Shearing stress = (Tangential Applied force)/(Area.)
∴ Shearing stress =F/A
Some important points to note……!
- The stress is dimensionally equivalent to pressure.
- Stress depends upon eternal force and surface area.
- Longitudinal stress and shearing stress is applicable to solids only, whereas volume stress can be applicable to all three states of matter.
Let’s discuss describe the concept with the help of following numerical….!
Ex: 1) A rod of length 2 m and radius 0.5 cm is suspended from rigid support and the load of mass 10 kg is attached to its lower end. Find the stress acting on the wire.
Solution:
Here, L= 2 m, r= 0.5 cm=5×10-3 m, m= 10 kg.