Revision: 11th Std >> Friction in Solids and Liquids MAH-MHT CET (PCM/PCB) Friction in Solids and Liquids

"The change in shape or size or both of a body due to an external force is called deformation."

The change in shape or size or both of a body due to an external force is called deformation.

"When a force is applied to a solid (which is not free to move), the size or shape, or both, change due to changes in the relative positions of molecules. Such a force is called a deforming force."

A body that regains its original shape and size completely and instantaneously upon removal of the deforming force is said to be perfectly elastic.

If a body regains its original shape and size after removal of the deforming force, it is called an elastic body and the property is called elasticity.

A body that regains its original shape and size after removal of the deforming force is called an elastic body, and the property is called elasticity.

OR

The property by which a body returns to its original shape after the removal of a deforming force is called elasticity.

A body that does not regain its original shape and size and retains its altered shape or size upon removal of the deforming force is called a plastic body, and the property is called plasticity.

The permanent deformation in substances (like putty and mud) that do not return to their original shape after the deforming force is removed is called plastic deformation (or plasticity).

When a solid is deformed and returns to its original shape upon removal of the force, the deformation is called elastic deformation.

The angular displacement of the surface in direct contact with the applied shear stress from its original position is called shear strain: τ = W/L = tan ⁡θ.

When there is an increase in the length or extension of the body in the direction of the applied force, the stress produced is called tensile stress.

When there is a decrease in the length or compression of the body due to the applied force, the stress produced is called compressive stress.

When equal normal forces are applied on every surface of a body causing a change in volume, the restoring force opposing this change per unit area is called hydraulic stress (also called volume stress).

The strain is defined as the ratio of change in dimensions of the body to its original dimensions.

Strain = `"change in dimensions"/"original dimensions"`

The ratio of change in volume of the body to its original volume is called volume strain: ΔV/V.

The internal restoring force per unit area of a body is called stress.

OR

The internal restoring force acting per unit area of a deformed body is called stress.

• SI Unit: N/m² (pascal, Pa)
   Dimensions: [M¹L⁻¹T⁻²]

Strain is defined as the ratio of the change in dimensions of the body to its original dimensions.

OR

The ratio of change in configuration to the original configuration is called strain.

• It has no unit and no dimensions (pure ratio).

The ratio of change in length of the body to its initial length is called longitudinal strain: ε = ΔL/L.

The modulus of elasticity of a material is the ratio of stress to the corresponding strain. It is defined as the slope of the stress-strain curve in the elastic deforming region and depends on the nature of the material.

\[\frac {stress}{strain}\] = Constant

The constant is called the modulus of elasticity.

OR

The constant ratio of stress to strain within the elastic limit is called the Modulus of Elasticity.

"Young’s modulus is the ratio of longitudinal stress to longitudinal strain."

OR

The ratio of tensile (or compressive) stress to the longitudinal strain is called Young's Modulus of Elasticity, denoted by Y.

A graph drawn by taking tensile strain along the x-axis and tensile stress along the y-axis, obtained by gradually increasing the load on a metal wire suspended vertically from a rigid support until the wire breaks, and measuring the elongation produced during each step.

In case of some materials like vulcanized rubber, when the stress applied on a body decreases to zero, the strain does not return to zero immediately. The strain lags behind the stress. This lagging of strain behind the stress is called elastic hysteresis.

The elastic potential energy gained by a wire during elongation by a stretching force is called as strain energy.

Hardness is the property of a material that enables it to resist plastic deformation.

"This mechanical force between two solid surfaces in contact with each other is called the frictional force."

The property which resists the relative motion between two surfaces in contact is called friction.

"The property which resists the relative motion between two surfaces in contact is called friction."

The mathematical expression for Young's modulus (Y) is:

Y = \[\frac{MgL}{\pi r^2l}\] or \[\frac {FL}{AΔL}\]

Where:

• Y = Young’s Modulus
• M = Mass of the load attached
• g = Acceleration due to gravity
• L = Original length of the wire
• r = Radius of the wire cross-section
• l = Extension or elongation produced in the wire

W = \[\frac {1}{2}\]Fl

Where:

• W = Work done (Strain energy)
• F = Stretching force applied
• l = Extension/elongation produced
• Y = Young's modulus
• Stress = Force per unit area = \[\frac {F}{A}\]
• Strain = Change in length per unit length = \[\frac {l}{L}\]

Hooke's Law was discovered by English scientist Robert Hooke in 1660. He first stated it as a Latin anagram: "As the extension, so the force."

Statement: For small deformations, stress is directly proportional to strain, within the elastic limit.

Key Points:

• Hooke's Law is a measure of elasticity.
• It is valid only up to the elastic limit. Beyond this, the material does not return to its original shape and Hooke's Law no longer applies.
• In springs: The force needed to extend or compress a spring by distance x is proportional to that distance → F = −kx (where k is the spring constant).
• Hooke's Law is applicable only in the case of elastic deformation.

• OA (Proportional Region): Stress ∝ Strain; material behaves elastically; Hooke's Law valid.
• Point A: Proportional limit — end of Hooke's Law.
• Region AB: Non-linear elastic region; material still returns to original shape.
• Point B (Elastic/Yield Limit): End of elastic behavior; start of plastic deformation.
• Region BD: Permanent (plastic) deformation; material does not return to original shape.
• Point D: Ultimate Tensile Strength — maximum stress the material can bear.
• Point E: Fracture point — material breaks.