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

Conduction

conduction,
transfer of heat or electricity through a substance, resulting from a difference in temperature between different parts of the substance, in the case of heat, or from a difference in electric potential, in the case of electricity. Since heat is energy associated with the motions of the particles making up the substance, it is transferred by such motions, shifting from regions of higher temperature, where the particles are more energetic, to regions of lower temperature. The rate of heat flow between two regions is proportional to the temperature difference between them and the heat conductivity of the substance. In solids, the molecules themselves are bound and contribute to conduction of heat mainly by vibrating against neighboring molecules; a more important mechanism, however, is the migration of energetic free electrons through the solid. Metals, which have a high free-electron density, are good conductors of heat, while nonmetals, such as wood or glass, have few free electrons and do not conduct as well. Especially poor conductors, such as asbestos, have been used as insulators to impede heat flow (see insulation). Liquids and gases have their molecules farther apart and are generally poor conductors of heat. Conduction of electricity consists of the flow of charges as a result of an electromotive force, or potential difference. The rate of flow, i.e., the electric current, is proportional to the potential difference and to the electrical conductivity of the substance, which in turn depends on the nature of the substance, its cross-sectional area, and its temperature. In solids, electric current consists of a flow of electrons; as in the case of heat conduction, metals are better conductors of electricity because of their greater free-electron density, while nonmetals, such as rubber, are poor conductors and may be used as electrical insulators, or dielectrics. Increasing the cross-sectional area of a given conductor will increase the current because more electrons will be available for conduction. Increasing the temperature will inhibit conduction in a metal because the increased thermal motions of the electrons will tend to interfere with their regular flow in an electric current; in a nonmetal, however, an increase in temperature improves conduction because it frees more electrons. In liquids and gases, current consists not only in the flow of electrons but also in that of ions. A highly ionized liquid solution, e.g., saltwater, is a good conductor. Gases at high temperatures tend to become ionized and thus become good conductors, although at ordinary temperatures they tend to be poor conductors.



Heat Transfer

Objectives:

1. Describe how heat energy causes molecules to move.

2. List examples of heat energy transfer by conduction, convection, and radiation.

Notes:

Heat:

Heat energy is created due to the internal motion of molecules in a substance. Heat can more correctly be explained as the amount of kinetic energy in a substance. Therefore, the amount of heat in a substance depends on the mass of the object. Heat transfer is defined as the movement of heat from a warmer substance to a cooler one. This is technically known as moving down a temperature gradient. There are three types of heat transfer.

A. Conduction

Transferred by direct contact of molecules
Molecules in hot substances move fast
Collide with cooler, slower molecules and transfer energy

· Conductors – transfer heat well (metals: silver, copper, aluminum, iron)

· Insulators – bad conductors of heat (nonmetals: glass, wood, rubber, & plastics)

B. Convection

Liquids & gases
The molecules in heated gas or liquid move farther apart and become less dense.
The less dense gas of liquid rises
Created a circular current

C. Radiation
Heat transferred through empty space via infrared radiation

Measuring Heat

Can measure temperature not heat
Unit is the calorie (cal) or joule (J)
1cal = 4.19J
a cal is the amount of heat needed to raise 1g of water 1 degree

The specific heat of a substance is the amount of heat (cal) needed to raise a substance 1oC .

Can be used to calculate the amount of heat gained or lost by a substance

measured using a bomb calorimeter

Is the ability of a substance to absorb heat

High specific heat – slow to heat up and slow to cool down (& visa versa)
Can be measured using a calorimeter Mass · DT · Specific heat



Reaction:

Newton's Laws of Motion

Newton's first law
-an object at rest will remain at rest; an object in motion will continue with the constant velocity unless forces acted upon it. this is called as the law of inertia.

Newton's second law
-according to Newton, an object accelerate if acted on by an unbalanced force. This acceleration depends on two factors.
1. the resultant force acting on the object, and
2. the mass or amount of matter of which the object is made.

The acceleration is directly proportional to the resultant force acting on the object's mass. If a group of forces act on an object of mass m. the vector of these forces F causes the object to have an acceleration a given by:

a= F/m or F = m a

the direction of a is in the direction of the resultant force.

Newton's second law is often written as F = m a. the force of F on the left side of the equation, however, represents the net or resultant force acting on the object.

Units for Newton's second law of motion
the unit of acceleration in SI system is the meter/second2 (m/s2). for the mass is the kilogram, and the force is the Newton(N)

1 N = (1 kg) (1 m/s2)

Newtons third law
for every force exerted is an equal oppositely directed force actong on some other body. this is often called the law of action and reaction
Newton indicated in this law that forcwa come in pairs. the action force is the force exerted by one object on another. the reaction force is the force exerted by the other object on the first.

Tension in a string
Tension in a srting is a particular case of Newton's third law of motion. this is back pulling or reaction exerted by a mass on the strong because of its resistance of motion.

Law of universal Gravitation
the gravitational force exerted by a mass m1 on a nother mass m2 is proportional to the product of their masses and the inversely proportional to the square of their separation r.

F = G m1 m2 / r2

where G is a constant called the universal gravitational constant equal to:

G = 6.6 x 10 Nm2 / kg2


Reaction:
Sir Isaac Newton first presented his three laws of motion in the "Principia Mathematica Philosophiae Naturalis" in 1686. His third law states that for every action (force) in nature there is an equal and opposite reaction. In other words, if object A exerts a force on object B, then object B also exerts an equal and opposite force on object A. Notice that the forces are exerted on different objects.

For aircraft, the principal of action and reaction is very important. It helps to explain the generation of lift from an airfoil. In this problem, the air is deflected downward by the action of the airfoil, and in reaction the wing is pushed upward. Similarly, for a spinning ball, the air is deflected to one side, and the ball reacts by moving in the opposite direction. A jet engine also produces thrust through action and reaction. The engine produces hot exhaust gases which flow out the back of the engine. In reaction, a thrusting force is produced in the opposite direction.
FOR EVERY ACTION, THERE IS AN EQUAL AND OPPOSITE REACTION

Kinematics

kinematics is defined as the quantitative description of an object's motion.

kinds of Motion motion may be simple if is due to a single forces; or compound, if it is the combined effect of several forces.

Uniform Motion this motion is due to an instantaneous force. it is characterized by a constant velocity, that is, the moving body will pass over equal distance per unit time.
S=vt
where S is the total space or distanced travelled; v, the constant velocity and t, the time.

Steps in Solving Problems in Kinematics

1. illustrate the situation described in the problem. include in the diagram a coordinate axis; the values of known quantities represented in terms of appropriate symbols; a symbol for the unknown quantity you wish to determine.
2. divide the problem in to parts. each part can often be solved with relative ease even though the original problem might have seemed impossibly complicated.
3. fond one of the equation listed earlier in which the only unknown quantity in the equation is the one whose value you wish to calculate.
4. rearrange the equations so that the unknown appears alone on the left and the known quantities on the right.
5. check your work.

GRAVITATIONAL ACCELERATION
-caused the vertical motion of objects thrown into air or of the objects falling through the air. if not for the resistive force of the air on these objects, this acceleration would be constant. this acceleration is caused by the gravitational force of the earth pulling down on objects.
the magnitude of this acceleration has a value at the earth's surface of 9.8m/s2.
g=9.8m/s2
=980cm/s2
=32ft/s2

Equilibrium

Equilibrium state of balance. When a body or a system is in equilibrium, there is no net tendency to change. In mechanics, equilibrium has to do with the forces acting on a body. When no force is acting to make a body move in a line, the body is in translational equilibrium; when no force is acting to make the body turn, the body is in rotational equilibrium. A body in equilibrium at rest is said to be in static equilibrium. However, a state of equilibrium does not mean that no forces act on the body, but only that the forces are balanced. For example, when a lever is being used to hold up a raised object, forces are being exerted downward on each end of the lever and upward on its fulcrum, but the upward and downward forces balance to maintain translational equilibrium, and the clockwise and counterclockwise moments of the forces on either end balance to maintain rotational equilibrium. The stability of a body is a measure of its ability to return to a position of equilibrium after being disturbed. It depends on the shape of the body and the location of its center of gravity (see center of mass). A body with a large flat base and a low center of gravity will be very stable, returning quickly to its position of equilibrium after being tipped. However, a body with a small base and high center of gravity will tend to topple if tipped and is thus less stable than the first body. A body balanced precariously on a point is in unstable equilibrium. Some bodies, such as a ball or a cone lying on its side, do not return to their original position of equilibrium when pushed, assuming instead a new position of equilibrium; these are said to be in neutral equilibrium. In thermodynamics, two bodies placed in contact with each other are said to be in thermal equilibrium when, after a sufficient length of time, their temperatures are equal. Chemical equilibrium refers to reversible chemical reactions in which the reactions involved are occurring in opposite directions at equal rates, so that no net change is observed.


Reaction:
Equilibrium is achieved when the forward rate of a reaction is equal to the reverse rate of a reaction. This very simple principle can be observed in a closed container of liquid. In the container the liquid has vapor pressure that is influenced by the pressure above the liquid. In the closed container the pressure above the liquid will raise until it reaches equilibrium vapor pressure. At that time the amount of molecules leaving the liquid is equal to the amount of molecules entering the solution. This equilibrium reaction displays the quality of a reversible reaction.

water D water vapor

Rolling Friction

Rolling friction is the resistive force that slows down the motion of a rolling ball or wheel. This frictional force is typically a combination of several friction forces and is at the point of contact with the ground or other surface. When the materials are both hard, static friction and molecular friction slow down the rolling. When the wheel or tire is soft, its distortion slows down the motion. When the other surface is soft, the plowing effect is a major force in slowing the motion. The coefficient of rolling friction is determined experimentally.

static friction
The surface of the wheel and what it is rolling on are not perfectly smooth. They have irregularities. In sliding friction, this surface roughness is the reason for the static and kinetic resistance to motion. Although the wheel is not sliding, the surface roughness causes a "jiggle" when the wheel is rolling. The resistance from this movement is close to the point where static friction transitions to kinetic friction.
Treads
If the wheel or tire has treads or grooves with sharp edges, those edges add to the static friction when they come into contact with the ground or other surface. Treads can help to prevent spinning the tire when the force from the torque becomes larger than the static friction. They also help prevent skids when braking.
Molecular friction
Molecular friction is caused by the molecular attraction or adhesion of the materials. It is like a "stickiness" factor. When materials are pushed together, molecular forces try to prevent them from being pulled apart. This can be seen in highly polished metals and certain materials such as rubber. As an extreme example, you could put double-sided tape on the rim of a wheel and see the resistance to rolling from the sticky tape.
Wheel is soft
When a wheel or tire is relatively soft and can be easily deformed, the resulting friction is a form of plowing friction. The deformation of the tire takes up energy that would be used to roll the wheel. Deformation is the greatest factor in rolling friction of tires or wheels made of soft materials.
Increasing tire pressure is a way to reduce rolling friction in an automobile or bicycle.
Surface is soft
When the ground or other surface is relatively soft, the major source of friction comes from the plowing effect. The wheel sinks into the soft material and must push or plow its way through. Although rolling is more effective than sliding an object in a soft material, it still requires a substantial effort.
Trying to ride a bicycle through soft dirt is an example of the effect of rolling friction on a soft surface.
Although treads on the wheel or tire will help to move the tire through the soft material, they do not contribute much rolling friction force in resisting the motion.
Both are soft
Interestingly, you can drive a vehicle through soft dirt easier if its tires have less air. The deformation of the tire improves traction.

Reaction:
Rolling friction is the force that slows down the motion of a rolling wheel. This frictional force is typically a combination of several friction forces at the point of contact with the ground. When the materials are both hard, static friction and molecular friction slow down the rolling. When the wheel or tire is soft, its distortion slows down the motion. When the other surface is soft, the plowing effect is a major force in slowing the motion. draft