CBSE Class 11 Physics Mechanics Of Solid And Fluid Notes

MECHANICS OF SOLID AND FLUID

• Deforming force:- A force acting on a body which produces change in its shape of body instead of its state of rest or uniform motion of the body.

• Elasticity:-The property of matter by virtue which it regains its original shape and size, when the deforming forces are removed is called elasticity.

• Plasticity:- The inability of a body to return to its original shape and size, when the deforming forces are removed is called plasticity.

• Hooke’s law:- when a wire is loaded within elastic limit, the extension produced in wire is directly proportional to the load applied.

OR

Within elastic limit stress α strain

Stress / Strain = Constant

• Stress :- Restoring force set up per unit area when deforming force acts on the body

Strain:- The ratio of change in dimension to the original dimension is called strain

Hooke’s L aw:- Within elastic limit, stress α strain

= Constant (Modulus of Elasticity)

Modulus of elasticity are of 3 types.

(1) Young’s Modulus (Y) = Normal stress / Longitudinal Strain

(2) Bulk Modulus (K) =   Normal stress / Volumetric Strain

(3) Modulus of rigidity modulus (ƞ) =  Tangential stress / Shearing Strain

• Compressibility : the reciprocal of bulk modulus of a material is called its

compressibility

Compressibility = 1/K

Stress – Strain- diagram

• Proportionality limit(P) – The stress at the limit of proportionality point P is known as proportionality limit

• Elastic limit - the maximum stress which can be applied to a wire so that on unloading it return to its original length is called the elastic limit

• Yield point(Y)- The stress, beyond which the length of the wire increase virtually for no increase in the stress

• Plastic region- the region of stress- strain graph between the elastic limit and the breaking point is called the plastic region.

• Fracture point or Breaking point(B)- the value of stress corresponding to which the wire breaks is called breaking point

• Work done in stretching a wire per unit volume/energy sored per unit volume of specimen
= ½ x stress x strain

• Elastic after effect:- The delay in regaining the original state by a body after the removal of the deforming force is called elastic after effect.

• Elastic fatigue:- the loss in strength of a material caused due to repeated alternating strains to which the material is subjected.

• Poisson’s ratio(ϭ) :- The ratio of lateral strain to longitudinal strain is called

• Applications of elasticity
1. Metallic part of machinery is never subjected to a stress beyond the elastic limit of material.
2. Metallic rope used in cranes to lift heavy weight are decided on the elastic limit of material
3. In designing beam to support load (in construction of roofs and bridges)
4. Preference of hollow shaft than solid shaft
5. Calculating the maximum height of a mountain

MECHANICS OF FLUID

• Pressure :The force/threat acting per unit area is called pressure S.I Unit of pressure is N/M2 or pascal (Pa)
Dimensional formula (ML^-1T^-2)

• Pascal’s law:- Pressure applied to an enclosed fluid is transmitted to all part of the fluid and to the wall of the container.

• Application of Pascal’s law:-
(1) Hydraulic lift, presses etc.
(2) Hydraulic brakes

• Pressure exerted by liquid column:- P = hρg, where h= depth of liquid,
ρ=density , g=accn. due to gravity.

• Variation of pressure with depth: P = Pa + hρg, where Pa =atmospheric pressure

• Atmospheric pressure:- The pressure exerted by atmosphere is called atmospheric pressure.
At sea level, atmospheric pressure= 0.76m of Hg column
Mathematically 1 atm = 1.013 x 10⁵ Nm^-2

• Archimedes’ principle:- It states that when a body is immersed completely or partly in a fluid, it loses in weight equal to the weight of the fluid displaced by it.
Mathematically: Apparent weight = True weight – Vρg
Where V is volume of fluid displaced, ρ is its density.

• Viscosity:- It is the property of liquid (or gases) due to which a backward dragging force acts tangentially between two layers of liquid when there is relative motion between them.

• Newton’s formula for Viscous force:- the viscous force between two liquid layer each of area A and having a velocity gradient dv/dx is
F = ƞ A (dv/dx) , where ƞ is coefficient of viscosity

• Coefficient of viscosity:- It is define as the tangential viscous force which maintains a unit velocity gradient between two parallel layers each of unit area
S.I unit of coefficient of viscosity is poiseuille or pascal-second

• Poiseuille’s equation:- when a liquid of coefficient of viscosity flows through a tube of length ‘l’ and radius r, then the volume of liquid following out per second is given

V = πPr⁴/8 ƞl ,

Where P is the difference of pressure between the two ends of the tube.

• Stoke’s law: The backward dragging force acing on a small sphere of radius r falling with uniform velocity v through a medium of coefficient of viscosity is given by

F = 6π ƞrv

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