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Friday, December 23, 2016

Fundamental Physics Quick Revision 11th Standard 101-2b

101-2b
In this section, we cover the fundamental concept of Scalars and Vectors
First off, what is a quantity?
A quantity is a measure of certain physical events or instances that are inherently present in the natural world.
Now to this extent we ask, how do we measure these quantities?
A scalar is a physical quantity that is defined solely based on it's magnitude.A vector is a physical quantity that is defined based on both it's magnitude and it's direction.

A particle moving along a straight line can move in only two directions. We can take its motion to be positive in one of these directions and negative in the other. For a particle moving in three dimensions, however, a plus sign or minus sign is no longer enough to indicate a direction. Instead, we must use a vector.

A vector has magnitude as well as direction, and vectors follow certain (vector) rules of combination, which we examine in this chapter. A vector quantity is a quantity that has both a magnitude and a direction and thus can be represented with a vector. Some physical quantities that are vector quantities are displacement, velocity, and acceleration. You will see many more throughout this book, so learning the rules of vector combination now will help you greatly in later chapters.

Not all physical quantities involve a direction. Temperature, pressure, energy, mass, and time, for example, do not “point” in the spatial sense. We call such quantities scalars, and we deal with them by the rules of ordinary algebra. A single value, with a sign (as in a temperature of 40°F), specifies a scalar.

The simplest vector quantity is displacement, or change of position. A vector that represents a displacement is called, reasonably, a displacement vector. (Similarly, we have velocity vectors and acceleration vectors.) If a particle changes its position by moving from A to B in, we say that it undergoes a displacement from A to B, which we represent with an arrow pointing from A to B. The arrow specifies the vector graphically. To distinguish vector symbols from other kinds of arrows in this book, we use the outline of a triangle as the arrowhead.

The arrows from A to B, from A to B , and from A to B have the same magnitude and direction. Thus, they specify identical displacement vectors and represent the same change of position for the particle. A vector can be shifted without changing its value if its length and direction are not changed.
The displacement vector tells us nothing about the actual path that the particle takes. For example, all three paths connecting points A and B cor- respond to the same displacement vector, that of the Displacement vectors represent only the overall effect of the motion, not the motion itself.

To elaborate, in order for a quantity to be considered a vector, the physical or numerical values considered to define it, it must be accompanied by a secondary set of value that provide the necessary data on the direction or orientation of that quantity in physical space.The fundamental quantities, are all scalar quantities i.e Mass, Length, Time etc.
The derived quantities, such as Force, Displacement, Velocity etc. are vectors.The difference is more imperative when considering specific quantities w.r.t the world co-oordinate systems, so as to improve upon anything physical.

Fundamental Physics Quick Revision 11th Standard 101-2a

101-2a

This part deals with the essentials of the three main kinematic parameters and the equations pertaining to motion.

The world, and everything in it, moves. Even seemingly stationary things, such as a roadway, move with Earth’s rotation, Earth’s orbit around the Sun, the Sun’s or- bit around the center of the Milky Way galaxy, and that galaxy’s migration relative to other galaxies. The classification and comparison of motions (called kinematics) is often challenging. What exactly do you measure, and how do you compare?

Before we attempt an answer, we shall examine some general properties of motion that is restricted in three ways.

1. The motion is along a straight line only. The line may be vertical, horizontal, or slanted, but it must be straight.  

2. Forces(pushes and pulls)cause motion. In this chapter we discuss only the motion itself and changes in the motion. Does the moving object speed up, slow down, stop, or reverse direction? If the motion does change, how is time involved in the change?  

3. The moving object is either a particle (by which we mean a point-like object such as an electron) or an object that moves like a particle (such that every portion moves in the same direction and at the same rate). A stiff pig slipping down a straight playground slide might be considered to be moving like a par- ticle; however, a tumbling tumbleweed would not.  

The three main kinematic parameters are:

Parameter            Standard unit of measure

Displacement                         m
Velocity                                 m/s
Acceleration                          m/s<sup>2</sup>

As you may well know, all three above quantities are vector quantities, meaning that they have both magnitude and direction.

It is also to be noted that all three of these quantities are incremental differentials of the same physical quantity, displacement, with respect to time.

To elaborate,

Displacement is the shortest distance between two points. Its magnitude is in meters, and relative direction can be either along the positive direction on the Cartesian plane or along the negative direction on the Cartesian plane.

It's variation, i.e differential, with respect to time renders the result we call velocity.
The rate of change of displacement with respect to time is therefore what is known as velocity.

The same directional parameters as those of the displacement that determined it, will play a part in determining the direction of the velocity.

The rate of change of velocity, following from the case of velocity will also derive it's direction from the former. This is acceleration.

There are 4 fundamental equations of motion connecting the three quantities and time:

Where v is final velocity, u is initial velocity, a is acceleration, s is displacement and t is time

Thursday, December 22, 2016

Fundamental Physics Quick Revision 11th Standard 101-1a

101-1a

Here are some fundamental mathematical basics of 11th Standard Physics for your quick reference

This one 101-1a will cover all the basic formulae you will need to solve your Kinematics problems and some for basic unit conversions.

SI Prefixes*

Factor Prefix Symbol
1024    yotta        Y
1021    zetta         Z
1018    exa           E
1015    peta    P
1012    tera          T
109      giga G
106      mega       M
103      kilo      k
102    hecto    h
101      deka        da

Factor   Prefix    Symbol
10–1       deci        d
10–2       centi       c
10–3       milli       m
10–6       micro     mu
10–9   nano       n
10–12   pico        p
10–15   femto      f
10–18     atto         a
10–21     zepto      z
10–24     yocto      y

*In all cases, the first syllable is accented, as in ná-no-mé-ter.

Trigonometric Identities:

Reciprocal identities
displaymath161

Pythagorean Identities

Quotient Identities

Co-Function Identities
displaymath164

Even-Odd Identities

Sum-Difference Formulas
displaymath166

Double Angle Formulas
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Power-Reducing/Half Angle Formulas
displaymath167

Sum-to-Product Formulas
displaymath168

Product-to-Sum Formulas
displaymath169

Basic Derivatives and Integrals:

Newton's generalized binomial theorem

In this generalization, the finite sum is replaced by an infinite series. In order to do this, one needs to give meaning to binomial coefficients with an arbitrary upper index, which cannot be done using the usual formula with factorials. However, for an arbitrary number r, one can define

{r \choose k}={\frac {r\,(r-1)\cdots (r-k+1)}{k!}}={\frac {(r)_{k}}{k!}},

where

(\cdot )_{k}

is the Pochhammer symbol, here standing for a falling factorial. This agrees with the usual definitions when r is a nonnegative integer. Then, if x and y are real numbers with |x| > |y|, and r is any complex number, one has

{\begin{aligned}(x+y)^{r}&=\sum _{k=0}^{\infty }{r \choose k}x^{r-k}y^{k}\\&=x^{r}+rx^{r-1}y+{\frac {r(r-1)}{2!}}x^{r-2}y^{2}+{\frac {r(r-1)(r-2)}{3!}}x^{r-3}y^{3}+\cdots .\end{aligned}}

When r is a non negative integer, the binomial coefficients for k > r are zero, so this equation reduces to the usual binomial theorem, and there are at most r + 1 nonzero terms. For other values of r, the series typically has infinitely many nonzero terms.
For example, with r = 1/2 gives the following series for the square root:

{\sqrt {1+x}}=\textstyle 1+{\frac {1}{2}}x-{\frac {1}{8}}x^{2}+{\frac {1}{16}}x^{3}-{\frac {5}{128}}x^{4}+{\frac {7}{256}}x^{5}-\cdots

Taking

r=-1

, the generalized binomial series gives the geometric series formula, valid for

|x|<1

(1+x)^{-1}={\frac {1}{1+x}}=1-x+x^{2}-x^{3}+x^{4}-x^{5}+\cdots

More generally, with r = −s:

{\frac {1}{(1-x)^{s}}}=\sum _{k=0}^{\infty }{s+k-1 \choose k}x^{k}\equiv \sum _{k=0}^{\infty }{s+k-1 \choose s-1}x^{k}.

So, for instance, when

s=1/2

{\frac {1}{\sqrt {1+x}}}=\textstyle 1-{\frac {1}{2}}x+{\frac {3}{8}}x^{2}-{\frac {5}{16}}x^{3}+{\frac {35}{128}}x^{4}-{\frac {63}{256}}x^{5}+\cdots

Vector Product of Vectors

The vector product and the scalar product are the two ways of multiplying vectors which see the most application in physics and astronomy. The magnitude of the vector product of two vectors can be constructed by taking the product of the magnitudes of the vectors times the sine of the angle (<180 degrees) between them. The magnitude of the vector product can be expressed in the form:

and the direction is given by the right-hand rule. If the vectors are expressed in terms of unit vectors i, j, and k in the x, y, and z directions, then the vector product can be expressed in the rather cumbersome form:

Vector Product, Determinant Form

The vector product is compactly stated in the form of a determinant which for the 3x3 case has a convenient evaluation procedure:

Once the scheme for determinant evaluation is familiar, this is a convenient way to reconstruct the expanded form:

Fundamental Physics Quick Revision 11th Standard 101-1b

101-1b

This part of the portion covers a summary of the fundamentals of units and measurements.

Units and measurements form the backbone of all things Physics as they provide both the qualitative and quantitative aspects of Physics meaning and understanding.

Facts considered, there are 7 fundamental quantities, i.e

Mass

Length

Time

Temperature

Current
Amount of substance

Luminous intensity

Each of these have their own SI unit, namely

Mass - Kilogram (kg)

Length - Meter (m)

Time - Second (s)

Temperature - Degree Kelvin (K)

Current - Ampere (A)

Amount of substance - Avogadro Mole (mol)

Luminous intensity - Candela (c)

In this section, we discuss the fundamental quantities necessary for basic statics and kinematics, i.e

Length, Time and Mass.

Length

The meter came to be defined as the distance between two fine lines engraved near the ends of a platinum – iridium bar, the standard meter bar, which was kept at the International Bureau of Weights and Measures near Paris. Accurate copies of the bar were sent to standardizing laboratories throughout the world. These secondary standards were used to produce other, still more accessible standards, so that ultimately every measuring device derived its authority from the standard meter bar through a complicated chain of comparisons.

The meter was redefined as the distance traveled by light in a specified time interval.
In the words of the 17th General Conference on

Weights and Measures:

This time interval was chosen so that the speed of light c is exactly c 299 792 458 m/s.
Measurements of the speed of light had become extremely precise, so it made sense to adopt the speed of light as a defined quantity and to use it to redefine the meter. Table 1-3 shows a wide range of lengths, from that of the universe (top line)

The meter is the length of the path traveled by light in a vacuum during a time interval of 1/299 792 458 of a second.

Time

Time has two aspects. For civil and some scientific purposes, we want to know the time of day so that we can order events in sequence. In much scientific work, we want to know how long an event lasts. Thus, any time standard must be able to answer two questions: “When did it happen?” and “What is its duration?”

To meet the need for a better time standard, atomic clocks have been developed.

The 13th General Conference on Weights and Measures in 1967 adopted a standard second based on the cesium clock:

One second is the time taken by 9 192 631 770 oscillations of the light (of a specified wavelength) emitted by a cesium-133 atom.

Atomic clocks are so consistent that, in principle, two cesium clocks would have to run for 6000 years before their readings would differ by more than 1 s. Even such accuracy pales in comparison with that of clocks currently being developed; their precision may be 1part in 1018—that's, 1 in 1x1018 s(which is about 3x1010 y).

Mass

The SI standard of mass is a platinum–iridium cylinder (Fig. 1-3) kept at the International Bureau of Weights and Measures near Paris and assigned, by international agreement, a mass of 1 kilogram. Accurate copies have been sent to standardizing laboratories in other countries, and the masses of other bodies can be determined by balancing them against a copy. Table 1-5 shows some masses expressed in kilograms, ranging over about 83 orders of magnitude.

Friday, October 14, 2016

Physics - Heat

Today let’s see few little facts of Physics. Physics on the whole is quite a big subject, I will try to gather everything in detail and I am picking up “Heat”. I have taken due care to ensure that the information provided below are correct. However, in any case, if it is found incorrect, please refer your books. To make thing easy I am giving in small paragraph points.

I had a very hard time remembering Physics even though I was a science student. I wrote UGC - NET exam but fail to pass because of all the common terms not by the formulae. Formulae is much easier than the common terms which I am trying to get down from different books. This are common terms which may sound easy but forgets very easily.

Heat is the energy that spontaneously passes between a system and its surroundings in some way other than through work or the transfer of matter. Below are few points which is I thought worth reading. Give me feedback so I can improve the next time.

HEAT

Temperature is a relative measure, or indication of hotness or coldness.

Heat is the form of energy transferred between two (or more) systems or a system and its surroundings by virtue of temperature difference. The SI unit of heat energy transferred is expressed in joule (J) while SI unit of temperature is kelvin (K), and °C is a commonly used unit of temperature.

Thermometer is a device used for measuring temperatures. The two familiar temperature scales are the Fahrenheit temperature scale and the Celsius temperature scale. The Celsius temperature (°C) and the Fahrenheit temperature (°F) are related by: °F = (9/5) °C + 32

In principle, there is no upper limit to temperature but there is a definite lower limit- the absolute zero. This limiting temperature is 273.16° below zero on the Celsius scale of temperature.

Clinical thermometer is used to measure our body temperature. The range of this thermometer is from 35°C to 42°C. For other purposes, we use the laboratory thermometers. The range of these thermometers is usually from – 10°C to 110°C. The normal temperature of the human body is 37°C.

The heat flows from a body at a higher temperature to a body at a lower temperature. There are three ways in which heat can flow from one object to another. These are conduction, convection and radiation.

The process by which heat is transferred from the hotter end to the colder end of an object is known as conduction. In solids, generally, the heat is transferred by the process of conduction.

The materials which allow heat to pass through them easily are conductors of heat. For examples, aluminum, iron and copper. The materials which do not allow heat to pass through them easily are poor conductors of heat such as plastic and wood. Poor conductors are known as insulators.

In convention heat is carried from one place to another by the actual movement of liquid and gases. In liquids and gases the heat is transferred by convection

The people living in the coastal areas experience an interesting phenomenon. During the day, the land gets heated faster than the water. The air over the land becomes hotter and rises up. The cooler air from the sea rushes in towards the land to take its place. The warm air from the land moves towards the sea to complete the cycle. The air from the sea is called the sea breeze. At night it is exactly the reverse. The water cools down more slowly than the land. So, the cool air from the land moves towards the sea. This is called the land breeze.

The transfer of heat by radiation does not require any medium. It can take place whether a medium is present or not.

Dark-colored objects absorb radiation better than the light-colored objects. That is the reason we feel more comfortable in light-colored clothes in the summer. Woolen clothes keep us warm during winter. It is so because wool is a poor conductor of heat and it has air trapped in between the fibers.

A change in the temperature of a body causes change in its dimensions. The increase in the dimensions of a body due to the increase in its temperature is called thermal expansion. The expansion in length is called linear expansion. The expansion in area is called area expansion. The expansion in volume is called volume expansion.

The amount of heat energy required to raise the temperature of 1g of a substance through 1° is called specific heat capacity of the substance. The S.I. Unit of specific heat capacity is( J/kg)K. Water has the highest specific heat capacity which is equal to 4200 (J/kg)K.

The specific heat capacity is the property of the substance which determines the change in the temperature of the substance (undergoing no phase change) when a given quantity of heat is absorbed (or rejected) by it. It is defined as the amount of heat per unit mass absorbed or rejected by the substance to change its temperature by one unit. It depends on the nature of the substance and its temperature.

The amount of heat energy required to raise the temperature of a given mass of substance through 1° is called heat capacity or thermal capacity of the substance. Its S.I. Unit is (J/K).

Calorimetry means measurement of heat. When a body at higher temperature is brought in contact with another body at lower temperature, the heat lost by the hot body is equal to the heat gained by the colder body, provided no heat is allowed to escape to the surroundings. A device in which heat measurement can be made is called a calorimeter.

CHANGE OF STATE: Matter normally exists in three states: solid, liquid, and gas. A transition from one of these states to another is called a change of state. Two common changes of states are solid to liquid and liquid to gas (and vice versa). These changes can occur when the exchange of heat takes place between the substance and its surroundings.

The change of state from solid to liquid is called melting and from liquid to solid is called fusion. It is observed that the temperature remains constant until the entire amount of the solid substance melts. That is, both the solid and liquid states of the substance coexist in thermal equilibrium during the change of states from solid to liquid.

The temperature at which the solid and the liquid states of the substance in thermal equilibrium with each other is called its melting point. It is characteristic of the substance. It also depends on pressure. The melting point of a substance at standard atmospheric pressure is called its normal melting point.

The change of state from liquid to vapor (or gas) is called vaporization. It is observed that the temperature remains constant until the entire amount of the liquid is converted into vapor. That is, both the liquid and vapor states of the substance coexist in thermal equilibrium, during the change of state from liquid to vapor.

The temperature at which the liquid and the vapor states of the substance coexist is called its boiling point. At high altitudes, atmospheric pressure is lower, reducing the boiling point of water as compared to that at sea level. On the other hand, boiling point is increased inside a pressure cooker by increasing the pressure. Hence cooking is faster.

The boiling point of a substance at standard atmospheric pressure is called its normal boiling point.

However, all substances do not pass through the three states: solid-liquid-gas. There are certain substances which normally pass from the solid to the vapor state directly and vice versa. The change from solid state to vapor state without passing through the liquid state is called sublimation, and the substance is said to sublime. Dry ice (solid CO2) sublimes, so also iodine. During the sublimation process both the solid and vapor states of a substance coexist in thermal equilibrium.

Certain amount of heat energy is transferred between a substance and its surroundings when it undergoes a change of state. The amount of heat per unit mass transferred during change of state of the substance is called latent heat of the substance for the process.

The amount of heat energy supplied to a solid at its melting point, such that it changes into liquid state without any rise in temperature is called latent heat of fusion and that for a liquid-gas state change is called the latent heat of vaporization.

Newton’s Law of Cooling says that the rate of cooling of a body is proportional to the excess temperature of the body over the surroundings.