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Stress, strain, elasticity and pressure

Pressure :

Pressure is defined as force acting normally on unit area of the surface.
Pressure (P)  =  image001
SI unit of pressure is N/m2 also called pascal (Pa), it is an scalar quantity.
Atmospheric Pressure :
Atmospheric pressure is that pressure which is exerted by a mercury column of 76 cm length at 0°C at 45° latitude at the sea-level. It is equal to weight of 76 cm column of mercury of cross-section area 1 cm2. Generally it is measured in bar. 1 bar = 105 N/m2
Atmospheric pressure 1 atm = 1.01 bar = 1.01 x 105 N/m2 = 760 torr
One torr is the pressure exerted by a mercury column of 1 mm length.
  • Atmospheric pressure decreases with the increase of heigh,
  • It is difficult to cook on the mountain as the pressure is low on mountain in comparison to planes
  • The fountain pen of a passenger leaks in aeroplane at height due to reduction in atmospheric pressure.
  • We can measure atmospheric pressure with the help of barometer.
  • Sudden fall in barometric reading is the indication of storm.
  • Slow fall in barometric reading is the indication of rain.
  • Slow rise in the barometric reading is the indication of clear weather.
Pressure in fluid:
Force exerted on unit area of wall or base of the container by the molecules of fluid is the pressure of liquid.
The pressure exerted by liquid at depth h below the surface of liquid is given as p = hdg where d is the density of liquid.
  • Some important point in connection to fluid pressure
  • In a static liquid at same horizontal level, pressure is same at all points.
  • Pressure at a point in a static liquid has same value in all directions.
  • Pressure at a point in a liquid is proportional to the depth of the point from the free surface.
  • Pressure at a point in a liquid is proportional to the density of the liquid.
Pascal law for pressure:
The pressure exerted anywhere at a point of confined fluid is transmitted equally and undiminished, in all directions throughout the liquid.
  • If gravitational attraction is negligible, in equilibrium condition, pressure is same at all points in a liquid.
  • If an external pressure is applied to an enclosed fluid, it is transmitted undiminished to every direction.
  • Hydraulic lift, hydraulic press, Hydraulic brake work on Pascal law.
Effect of pressure on Melting Point and Boiling Point
(i) The M.P. of substances which expands on fusion increases with the increase in pressure; for example - wax
(ii) The M.P. of substances which contracts on fusion decreases with the increase in temperature for example – ice.
(iii) Boiling point of all the substances increases with the increase in pressure.

Flotation:

Buoyant Force:
  • When a body is immersed partially of wholly in a liquid, a force acts on the body by the liquid in the upward direction. This force is called Buoyant force or force of buoyancy or up thrust.
  • It is equal to the weight of liquid displaced by the  submerged part of the  body and acts at the centre of gravity of displaced liquid.
  • The buoyant force acts at the centre of gravity of the liquid displaced by the submerged part of the body which is called centre of buoyancy.
Archimedes Principle:
  • When a body is immersed partly or wholly in a liquid, there is an apparent loss in the weight of the body which is equal to the weight of liquid displaced by the body.
  • If w1 is the weight and V is the volume of a body in air and its weight becomes win a liquid of density p then, loss in weight =w1-w2
Law of Floatation:
A body floats in a liquid if
  • density of material of body is less than or equal to the density of liquid.
  • If density of material of body is equal to density of liquid, the body floats fully submerged in liquid in neutral equilibrium.
  • When body floats in neutral equilibrium, the weight of the body is equal to the weight of displaced liquid.
  • The centre of gravity of the body and centre of gravity of the displaced liquid i.e. centre of buoyancy  should be in one vertical line.
Some important points:
  • Ice  and large iceberg float on water surface as its density is lesser than the density  of water.
  • When a piece of ice floats on water, its 11/12th part submerged in water and 1/12th part is outside the water.
  • In sea water 1/9th part is outside the water during floating.
  • It is easier to swim in sea water than in a river as density of sea water is greater than the density of river water and in sea water buoyant force is greater than in river system.
  • The density of human body is less than the density of water but the density of human head is greater than the density of water, therefore during swimming a person displaces the liquid with hands and legs and total weight of displace liquid becomes equal to the weight of the body.
Meta Centre: When a floating body is slightly tilted from equilibrium position, the centre of buoyancy shifts. The point at which the vertical line passing through the new position of centre of buoyancy meets with the initial line is called Meta centre.
Conditions for stable equilibrium of Floating body
(i) The Meta centre must always be higher than the centre gravity of the body.
(ii) The line joining the centre of gravity of the body and centre of flotation should be vertical.
Density: Density is defined as mass per unit volume.   image002
Its SI unit is kg/m3.
Relative density = image003
Since relative density is a ratio, it is unitless.
  • Relative density is measured by Hydrometer.
  • The density of sea water is more than that of normal water. This explains why it is easier to swim in sea water.
  • If ice floating in water in a vessel melts, the level of water in the vessel does not change.
  • Purity of milk is measured by lactometer.

Elasticity:

Elasticity is the property of material of a body by virtue of which the body acquires its original shape and size after the removal of deforming force.
Elastic Limit: it is the limit of stress and strain upto which a wire remains elastic i.e. when the  stretching force is removed the wire acquire its natural length.
Stress: The internal restoring force per unit area set up inside the body subjected to deforming force is called stress. Stress are of two types :
  • Normal stress
  • Tangential stress
Strain: The fractional change in configuration i.e. length, volume and shape is called strain, it has no unit.
Stain is of three types:
  • Longitudinal strain
  • Volume strain
  • Sheering strain
Hooke's law: Under elastic limit, stress is proportional to strain.
i.e. stress is directly proportional to  strain or image005= E
E is called elastic constant or modulus of elasticity. Its value is different for different material. Its SI unit is Nm-2 also called pascal.
  • Young's modulus of elasticity
image006
  •  Bulk modulus of elasticity
image007
  • Rigidity modulus
(η)image009
  • The torque required to produce a twist in a hollow cylinder is greater than that required to produce the same twist in a solid cylinder, therefore hollow shaft is stronger than a solid shaft.
  • Springs are made of steel not of copper as young’s modulus of elasticity of steel is more than that of copper.