Elasticity

Concepts of Elasticity
Is the tendency of a substance to regain its original form or volume when external force that deformed it, is removed; or the property by virtue of which a body resists and recovers from a deformation performed by an external force.

Elasticity Limit
The property of elasticity however, works only within certain limits. The smallest value of the stress required to produced a permanent distortion in a body is called the Elastic Limit. When=a stress in excess of this limit is applied, the body will not return to its original state after the stress is removed.\

Stress
Is a measure of the strength of the agent that is causing deformation. Precisely, if a force F is applied to a surface of area A then,

Stress = force / area = F / A

Strain
Is a measure of the deformation.

Strain = change in dimension / original dimension

Hooke’s Law
States that the strains (deformation) are proportional to the stresses that produce them. We then define a constant, called modulus of elasticity by the relation:

Modulus of elasticity = stress / strain

Young’s Modulus
Young’s modulus (Y) is the proportionality constant that relates the compressive or tensile stress and the strain of a particular type of material.

Stress = applied force / cross section = F / A

Strain = elongation / original length =L / L

Bulk Modulus
The bulk modulus (B) is due to a compressing stress, and it is particularly applied to liquids and gasses which cannot be subjected to tensile stress. Since in liquids and gasses the stress is numerically equal to the pressure, we have

B = pressure change / volume strain = - P / V / V

Shear Modulus : Modulus of Rigidity
The modulus of rigidity is due to a shearing stress. If you place your hand on the top over of a book and gently push it to the side, tour hand generates a shear stress. The resulting distortion of the book as the pages slide across each other is a shear strain. If the object being sheared is elastic, there is proportionality between the shear strain and the shear stress. The proportionality constant that relates the shear stress and strain is called the shear moduls. Thus, for shearing stress (S) of elastic materials:

Shear stress = shear modulus x shear strain
S = FL / A x


Referrence:
page 104 Physics Committee
Far Eastern University
2004

Simple Machines

Simple Machine
Is a device by which the magnitude, direction or method of application of a force is changed for the sake of gaining some practical advantage.

Principle of Work
An ideal or frictionless machine, the work done by the machine (output) is equal to the work done upon the machine or the energy applied to it (input). Otherwise the useful wprk output diminished is due to the work done by the friction.

Work Input = useful work + friction work

Efficiency
Is the ration of the output to the input.

Efficiency = work output / work input = power output / power input

Actual Mechanical Advantage
The AMA (Actual Mechanical Advantage) of a machine is

AMA = force ration = force exerted by machine on load / force used to operate machine

Ideal Mechanical Advantage The IMA (ideal mechanical Advantage)

IMA = distance ratio = distance moved by input force/ distance moved by load

Since friction is always present IMA is always greater than the AMA.

Kinds of Simple Machine

a. lever – is a rigid bar, straight and or curved, which rotated about a fixed point called the fulcrum.

b. Wheel an axle- is consist of a large and a small wheel rigidity joined to the same axle. The rope to which the is applied is wound around the large wheel while the rope that carries the weight is around the smaller but in opposite sense, so that the unwinding of the results in the winding of the second.


c. Pulley – is a wheel with a grooved rim through which a rope or cord passes. The effort (pulling) and the resistance (weight) are applied to either end of the rope.

d. Inclined plane – when a body rests on an inclined plane, the weight of the body acts vertically while the reaction of the plane is perpendicular to its surface, the angle between two forces being t the angle between the plane and the horizontal.

e. Screw – is a metal cylinder, grooved in and advancing spiral to its outer surface. From the point of view of Physics, this is a combination of the inclined plane and the lever. If p is the pitch of the screw, that is the distance from one thread to the next, to the work done in complete revolution will be\
R x p


Referrence:
page 69 Physics Committee book
Far Eastern University
2004