Mechanics 3 Flashcards
Define plastic bodies
Bodies which do not return at all to its original dimensions after removal of deforming force are called plastic bodies/materials.
Define perfectly elastic bodies
Some bodies/materials that return exactly to its original dimensions after removal of external deforming force. They are called perfectly elastic bodies or materials.
Define elasticity
The property by virtue of which material bodies regain their original dimensions on removal of deforming force is called elasticity.
Define plasticity
The property of material to undergo permanent deformation even after removal of external deforming forces is known as plasticity.
Define deformation
The change in shape, size or both of a body arising due to external force is called deformation.
Define deforming force
The force responsible for deformation of a body is called deforming force.
Why is deformation produced in a body?
Deformation is produced in a body due to change in relative positions of molecules within the body due to applied deforming force.
Define Stress
Stress is defined as applied force per unit cross sectional area of the body.
Define longitudinal stress
When applied force/ deforming force produces change in length of a body, the stress associated is called longitudinal stress or tensile stress.
Define volume stress
If a deforming force produces change in volume of a body, the stress associated is called volume stress.
Define shearing stress
If the deforming force produces change in shape of the body, the stress associated with it is called shearing stress.
Define strain
Strain is defined as the change in dimensions per unit original dimensions.
Define longitudinal or tensile stress
Longitudinal or tensile strain is defined as the ratio of change in length to original length.
Define volume strain
Volume strain is defined as the ratio of change in volume to original volume.
Define shearing strain
Shearing strain is defined as the ratio of relative displacement of any layer to perpendicular distance from fixed layer.
State Hooke’s law
Provided the elastic limit is not exceeded, deformation of a material is proportional to the force applied to it,
Define modulus of elasticity
Modulus of elasticity of a material is defined as the slope of stress-strain curve in the elastic deformation region.
Define elastic limit
The maximum value if stress up to which stress is directly proportional to strain is known as the elastic limit.
What is set?
If the elastic limit is exceeded, then the body does not preserve its original dimensions after removal of external, deforming force and acquires a perfect deformation ‘set’.
Define Young’s modulus (elasticity of length)
Young’s modulus is the ratio of longitudinal stress to longitudinal strain.
Why is Young’s modulus of elasticity only a property of solids?
Only solids have length.
Define Bulk modulus (Volume elasticity)
Bulk modulus is defined as the ratio of the volume stress to the volume strain.
Young’s modulus is high for ________.
Materials with strong interatomic bonds.
Define compressibility
The reciprocal of the Bulk modulus of elasticity is called compressibility of the material.
Define modulus of rigidity (elasticity of shape)
Modulus of rigidity is defined as the ratio of shearing stress to shearing strain.
Define Poisson’s ratio
Poisson’s ratio is defined as the ratio of the lateral strain to longitudinal strain.
What is the range of Poisson’s ratio for a homogeneous isotropic material?
-1 <= 0.5
What it the range of Poisson’s ratio in actual practice?
Always positive
0.2 <= 0.4
Experimental Determination of Young’s modulus
Pg 83
Explain Searle’s method
Load applied to wire in steps of half kilogram till wire breaks.
Diagram page 84
E - elastic limit
Beyond E, small increase in strain gives large increase in stress and the graph bends towards strain axis.
Till E’ - becomes set on removal of external deforming force
Yp= yield point - graph becomes parallel to strain axis - increase in strain without increase in stress - plastic flow begins - cross section of wire decreases uniformly upto N.
Later “neck” or constriction begins to form at weak point.
N= breaking stress - maximum stress which the wire can bear.
When is a material brittle, ductile?
Ductile : Plastic region from E’ to N is large.
Brittle : Material breaks soon after elastic limit is crossed.
What are ductile substances?
Substances which lengthen considerably undergo plastic deformation till they break are called ductile substances.
Define Brittle
Substances which break just after elastic limit is reached are called brittle substances.
Define elastometers
Substances which can be stretched to cause large strains are know as elastometers.
Examples of elastometers
Tissue of aorta, rubber etc
Explain elastometers
Although elastic region is very large, they do not obey Hooke’s law over most of the region. Hence no well defined plastic regions. Hence can be stretched to cause large strains.
Force exerted by rod due to heating
Yα δ* θ*A
Application of elastic behavior of materials
Design of buildings Architecture Suspension bridges Beams Cranes - factor if safety
How much is the factor of safety?
10
How is flexibility of rope managed?
Ultimate stress= 10(10^4)/πr2
A >_ 3.3333333 * 10^(-4)
r>_ 1 cm
In order to have flexibility of rope, made up of a large number of thin wires braided together
How do suspension bridges and arched bridges support their load?
Suspension bridge : supports its load through tension in cables and compression in towers
Arched bridge : supports its load primarily through compression
What happens when a beam sags?
Top under compression, bottom under tension.
How can sag be minimized?
Giving top and bottom of beam larger cross-section, neither compression nor tension along centre line of beam, so it has smaller cross section.
Also by using material with large Y, small l, and large d and b.
Equation for sag
δ= W*(l^3) / (4b(d^3)Y)
What does sag depend on?
Inversely proportional to d cube
Inversely proportional to b
Directly proportional to l cube
Inversely proportional to Y
What is buckling?
If the load is placed exactly at the centre of the beam and depth of the box is increased, then beam will bend as shown and this is called buckling.
How can buckling be reduced?
By using an I-beam.
What are the advantages of I-beam?
Minimizes both weight and stress
I beam can be much lighter but almost as strong for bending
Large load bearing surface which reduces buckling and is enough to prevent too much buckling
Provides high bending moment and a lot of material is saved. #Puneri
Define strain energy
Strain energy is defined as the elastic potential energy gained by a wire during elongation by a stretching force.
Equation for strain energy
1/2 * S * E * V
Or
1/2 * F * l
Expression for longitudinal stress
Mg/ π(r*r)
Expression for shearing strain
Tan θ= θ ( in rad)
Expression for Bulk modulus
-V* (dp/dv)
Expression for modulus of rigidity
η= F/(A*θ)
Expression for Poisson’s ratio
σ= (d-δ(d))/(l-δ(l))
Give reasons : rain drops, soap bubbles and small droplets of mercury take spherical shape
Surface tension
Rain water does not pass through tiny holes in the fabrics of umbrellas, tents, raincoats. Why?
Al203 coating?
Surface tension
Give reasons: water spiders are able to walk on the surface of water and while they walk their feet produce dimples on the surface without rupturing the film.
Surface Tension
What are two characteristics of intermolecular forces?
Short range forces
Do not obey inverse square law
Define Cohesive force.
The force of attraction between two molecules of the same substance is known as cohesive force.
Short note on cohesive force
Definition
Definite shape and rigidity of solid body due to cohesion
Strongest in solids
Eg: between two air molecules and between two water molecules
Define Adhesive force
The force of attraction between two molecules of different substances is called adhesive force.
Define Range of Molecular force
The maximum distance between the molecules up to which the intermolecular forces are effective is called range of molecular attraction.
Define Sphere of influence
An imaginary sphere drawn, with molecule as centre and radius equal to molecular range is called sphere of influence.
Define surface film
The layer of surface of liquid whose thickness is about equal to range of molecular attraction is called surface film.
Explain the cause of surface tension
Pg 94
Where do molecules in water have maximum PE?
At the surface
Define surface energy per unit area
The potential energy per unit area of liquid surface under isothermal conditions is called surface energy per unit area.
Define surface
The force per unit length acting at right angles to and imaginary line drawn on the free surface of a liquid is known as surface tension.
Expression for ‘T’
T = F/l
Applications of surface tension
Tooth paste - contains soap, reduces surface tension, spreads more freely
Detergent - surface tension of water reduces, increases area of contact
Mosquito eggs - float on water due to surface tension of water. Kerosene is sprayed and ST is lowered and eggs go down inside water and stops breeding of Mosquitos.
Give the expression for relation between surface energy and surface tension.
dw=T*dA
Define angle of contact
When liquid is in contact with a solid, the angle between the tangent drawn to the free surface of the liquid and the surface of the solid measured inside the liquid is known a the angle of contact.
Characteristics of angle of contact
For a given solid-liquid pair, angle of contact is constant.
Value of angle if contact depends on the nature of liquid and solid in contact.
Depends upon the medium which exists above the free surface of liquid.
Changes due to impurity.
Changes with temperature.
Explain angle of contact
Pg 97
Gravity and adhesion with air can be neglected.
(i) partially wets the solid: adhesive stronger than cohesive
(ii) does not wet the solid: adhesive weaker than cohesive
(iii) completely wets the solid: adhesive very strong, cohesive can be neglected.
When is angle of contact acute?
Liquid partially wets the solid. Eg: Kerosene
When is the angle of contact obtuse?
Liquid which does not wet the solid
Eg: Mercury
When is the angle of contact zero?
When liquid completely wets the solid.
Eg: pure water and clean glass
Explain shape of a liquid drop
Cos(θ)= (T1-T2)/T3 Where, T1- force due to ST at solid-liquid interface T2- at air-solid interface T3- at air-liquid interface
If T2>T1 : theta acute
If T21 : no drop formed
Why are small drops spherical and large drops flattened?
Small drop : gravitational P.E. very small, may be neglected
Large drop : energy due to gravity dominates to make P.E. minimum, tries to bring C.G. as low as possible and drop flattens
Laplace law derivation
Equate dW from TdA and dW from excess pressure*area
Laplace law of a spherical membrane
For liquid drop: Pi-Po= 2T/r
Expression for excess pressure in a soap bubble
Pi-Po=4T/r
Expression for excess pressure in a liquid drop
Pi-Po=2T/r
Give reasons: treads of raincoat are coated with water-proofing agents like resin etc.
This is as they have very small force of adhesion with water and so they become waterproof.
Define capillary
A glass tube having a very fine bore is called a capillary.
Define Capillarity
The phenomenon of rise or fall of liquid in inside a capillary tube when it is dipped in the liquid is known as capillarity.
Applications of capillarity
Sap and water rises upto the topmost leaves of trees
Water rises up in the crevices in rocks
Cloth rag soaks water
Blotting paper absorbs ink
Ink rises in a pen
Oil rises up the wick of lamp on account of capillarity
What is the relation between pressure in concave and convex side?
The pressure in the concave side is greater than the pressure on the convex side.
Explain capillary action
Pg 101
Height of liquid column in capillary tube
h= 2Tcos(θ)/(rρg)
Why should height be corrected in a capillary?
Some water above meniscus.
What is the correction for height of liquid in a capillary?
h+(r/3)
What will happen to liquid rise in capillary in the absence of gravity?
Rise will be upto the top as length is insufficient
What is the effect of highly soluble impurity (eg common salt) on surface tension?
ST increases
Sparingly soluble impurity like phenol or alcohol is dissolved in water. What is the influence on surface tension?
Decreases
What is the effect of insoluble impurity on surface tension of water?
Decreases
What does oil sprinkled in the sea do?
Decrease in surface tension
Waves calm down
Height of water waves reduced
What is the effect of temperature on surface tension?
In most liquids except molten copper or molten cadmium, as temperature increases, ST decreases.
T at θdegC To at 0degC alpha- constant depends on nature of the liquid Then over a certain range, T=To(1-(α*θ))
What is the effect of temperature on surface tension on molten copper or cadmium?
Increase in ST with increase in temperature
Define critical temperature of a liquid
The temperature at which ST of a liquid becomes zero is called the critical temperature if the liquid.
What is the effect if contamination on surface tension?
Presence of dust particles or lubricating materials on the liquid surface decreases its surface tension.
