Physics Vector Calculator

Introduction to physics vector calculator:

Vector calculation problems in physics are those problems that require the application of vectors and operations on vectors. Many complex calculator problems in physics are solved easily by using vectors. Since vectors are different from scalar quantities in that they have direction as well as magnitude, even the basic arithmetic operations on vectors are different from those on scalars.

Addition, subtraction and multiplication of vectors, all have different methods than those of simple algebra.

In this short tutorial, we deal with physics vector problems that are solved using these operations on vectors.

Physics Vector Application Problems and Solutions

A river flows at 3 m/s and is 300 m wide. A man swims across the river with a velocity of 2 m.s directed always perpendicular to the flow of current. Find the magnitude of the resultant velocity of the man under the effect of the stream?

Given :

Velocity of river `vecVr` = 3 m/s

Width of river, `W` = 300 m

Velocity of swimmer, `vecVs` = 2 m/s

Angle between velocity of river and velocity of swimmer, `theta` = 90°

The following diagram illustrates the given situation:

In the above diagram, velocity '`vecV` ' is the resultant velocity of the man under the influence of the stream.

Since the resultant velocity of the swimmer (`vecV` ) is the result of the combined velocities of the river and the swimmer, therefore

`vecV = vecVs + vecVr`

By applying the vector addition formula derived from triangle law of vector addition, we get

`vecV = sqrt((Vs)^2 + (Vr)^2 + (Vs)(Vr)*costheta)`

`vecV = sqrt((2)^2 + (3)^2 + (2)(3)*cos90)`

`vecV = sqrt(4 + 9)`

`vecV = sqrt(13) = 3.6 m/s`

Thus, the resultant velocity of the swimmer under the action of the stream is 3.6 m/s.

Explanation to above Physics Vector Application Problem

In the above question, find the direction of the resultant velocity `vecV` of the swimmer with respect to the shore of the river.

Let the angle of inclination of resultant velocity vector `vecV` to the velocity of the river `vecVr` be `alpha` °.

We know that angle between velocity of river and that of swimmer, `theta = 90` °

Thus applying the formula for velocity of resultant vector,

`tan(alpha) = (Vb sintheta)/(Va - Vbcostheta)` , where `Vb` is the velocity of swimmer and `Va` the velocity of river.

`tan(alpha) = (Vs sintheta)/(Vr - Vscostheta)`

`tan(alpha) = (2 sin90)/(3 - 2cos90)`

`tan(alpha) = 2/3 = 0.66`

By referring to the trigonometric table for tangent, we get `alpha = 33.7` ° (approx).

Thus, the velocity of the swimmer has a direction of 33.7° inclination to the shore of the river.

Specific heat

Specific heat(c) is the heat-energy required to change the temperature of a body of unit mass by 1 degree Celsius. The temperature change can be positive or negative. If the temperature is reduced then HT(heat) is released or lost by the body. Usually specifc ht is used for raise in temperature. Specifc ht is also known as specifc ht capacity. Both have same meanings only terms used are different. One term that is confused with specifc ht capacity or specifc ht is ht capacity. Ht capacity is different from the former two terms. Ht capacity (C) is that amount of ht that is needed to raise the temp of a body by a given amount. Note that here temperature is not raised by one degree Celsius. Also mass of the body is not unit mass.
Specific Heat Formula is given as:
Q= M c ∆T
Q here is ht required to change the temperature of a body of mass M by some temperature.
∆T is the change in temperature which is difference between final and initial temperatures.
SI Unit of Q is joule, of mass is gram and of temp is Celsius so SI unit of specifc ht or specifc ht capcity is J/ gm oC. other derived Units for Specific Heat are kJ/kg K, cal/g K, cal/g oC, kJ/kg oC and many more.
I like to share this 2nd Law of Thermodynamics Definition with you all through my article.
Ht capacity is given by C = Q/∆T
Unit of ht capacity is J per K or J/K.
Ht capacity per unit mass per degree Celsius is specifc ht capacity. Also ht capacity per unit mole per degree Celsius is known as molar ht capacity J/ moleoC, and per unit volume is volumetric ht capacity (J / m3 oC).
Different materials have different value of specifc ht. Metals have usually low specifc hts than liquids. Like Specific Heat of Tin is 0.21kJ/kg K. This means that 1 kg of tin if heated to change its temperature by 1 kelvin then it will need 0.21 kilo joules of heat-energy. Specific Heat Capacity of Copper is 0.385 J/g oC (1 gram of copper needs 0.385 joules of energy to raise its temp by 1 degree Celsius)
Specific Heat of Glass is 0.84 J per gram OCelsius.
While specifc heat capacity of H2O is 4.18 J/g oC. If we compare this value with metals’ specifc ht we will get to know that it is very high. So, water needs very high energy or enthalpy to change its temperature by one unit. This high enthalpy helps it in maintaining aquatic life.

Si System of Measurement

Introduction to S.I. systems of measurement:

The eleventh general conference of weights and measures which held in oct, 1960 recommended a unified systematically constituted system of fundamental, supplementary and derived units, called the ‘International system of units’. This system is abbreviated as the SI, system international d’ units. Fundamentally, SI units is an absolute MKS system of units with addition to three more basic fundamental units, namely- ampere(A) for current, Kelvin(K) for temperature and candela (Cd) for luminous intensity. All these units are called fundamental or base units.

Definition of Fundamental Si Units

Universally accepted SI system defines some quantities as fundamental or base units that are as follows:

1. Metre (m): It is the unit of length. Metre is the length equal to 1,650,763.73 wavelength in vaccum of radiation corresponding to the transition between the energy levels 2p10 and 5d5of the krypton 86 atom.

2. Kilogram (kg): It is the unit of mass. A kilogram is equal to the mass of the international prototype which is in custody of the International bureau of weights and measures at Severs, near Paris, France. This prototype is a cylinder of the Platinum Irridium alloy.

3. Second (s): It is the unit of time. A second is defined as the duration of 9,192,631,770 periods of radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.

4. Ampere (A): It is the unit of electric current. Ampere is that constant current which if maintained in two parallel conductors of infinite length, of negligible circular cross section and placed at a distance of one metre apart in vaccum, would produce between these conductors a force equal to 2 × 107 N/m length.

5. Kelvin (K): It is the unit of temperature. Kelvin is expressed as the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.

6. Candela (Cd): It is the unit of luminous intensity. It is the luminous intensity, in a perpendicular direction, of a surface of 1/600,000 square metre of a blackbody at the temperature of freezing platinum under a pressure of 101,325 newton per square metre.

Advantages of Si System of Measurement:

The main advantages of SI system are

i. It is a metric system.

ii. It is more comprehensive because it defines the units of both primary fundamental as well as auxillary fundamental quantities.

iii. It is a rationalized system of units, acceptable to both magnetism and electricity.

iv. It is a non-gravitational system of units. It clearly distinguishes between the units of mass and weight which are kilogram and newton respectively.

Rising Stars

Introduction for rising stars:

Rising stars are born with a special abilities,where we can see mysterious light appering in the sky.The stars which shine highly in the sky,those are the rising stars. I like to share this Calculate the Wavelength of Light with you all through my article.

Stars are celestial bodies that continuously emit light and heat. Thus ,the sun is also a star. It appears large as compared to other stars because they are very far away from us, through many of them are much larger than the sun. Some of you may think that the stars appear in the sky only at night. It is not so. The stars are not visible during the day becaouse of the glare og bright sunlight.

Distance of Rising Stars in Light Years

Most of the stars are so far away that even light from them takes millions of years to reach the earth. The distance of the stars are ,therefore,expressed in terms of light year.one light year is the distance travelled by light in the one year at the speed of light which is about 300 000 kilometers per second. Light year is a unit of distance and is equal to 3 00 000 x 365 x 24 x 60 x 60 km,which is equal to 9 460 000 000 000 km or 9.46 x 1012 kilometers. The approximate distance of the sun from the earth is 150 000 000 km,which means that light takes about 8 Minutes 20 sec to reach the earth from the sun. The stars nearest to the earth after the sun is Alpha centauri, which is at a distance of about 4.3 light year. Please express your views of this topic Physics Formula by commenting on blog.

All stars including  the sun move around some celestial body or a group of bodies with high speeds. How ever, when viewed from the earth the distance between any two stars does not seem to change in spite of their great speeds. This is so, because the stars are so far away from us that any changes in distance between them do not become perceptible in a few years or even during one's lifetime.

Constellations

Many a time, a group of stars,as seen from earth ,appears to form some kind of a pattern. Our ancestors imagined some known shapes formed by many groups of stars and gave them specific names.such a group of stars is known as a constellation.We can easily identify some constellations even with naked eyes.However, you should know how a particular  constellation looks like and where to look for it in the night sky. Some easily identifiable constellations are uras major or vrihat saptarshi,ursa minor or laugh saptarshi and orion or mriga.

The most prominent group of stars that form a part of the constellation uras major or vrihat saptarshi is know as Big Dipper. The Big Dipper is a group of many stars of which seven are comparatively brighter and are easily visible. It appears like a big ladle or a question mark. The two stars at the top of the ladle is called pointers as the line joining them points to the direction of the pole star.How ever,it constellation uras major ,which is also know as Great Bear.

Uses of Capacitors

Introduction to uses of capacitors:

Every conducting material has a capacity to hold charge. The shape, size and surroundings of the conductor have an influence on the amount of charge a particular conductor can hold. The quantity of charge that a conductor holds is linearly proportional to the potential difference between ends of a conductor. The capacity of material to hold charge is termed as conductance.

For any conductor, when the charge on the conductor is increased, its potential also increases. The charge on the conductor is directly proportional to the potential difference applied to the conductor.

Q a V

Q = CV

Here C is proportionality constant called as capacitance. So capacitance is

C = Q / V

Capacitance: It is the ratio of the magnitude of the charge on conductor to the magnitude of the potential difference between the ends of the conductor.

Unit of capacitance is coulomb / volt or farad.

Uses of Capacitors:

Storing Energy: In a small volume, capacitors can create a strong electric field. They are used to store large amount of energy. The best example is the Camera flash circuits that make uses of capacitor to store large amount of  energy and discharge when needed.

Uniform Strong Electric Field:  in some basic electrical appliances, there is a need of  electric field to interact with magnetic field. In such situation capacitors are used to create large electric field in a small volume.  The best example is electric motors and ceiling fans which require electric field to do mechanical work. Thus capacitors give the necessary torque to  start and also keep the motor rotate continuously.

Filters: Capacitor blocks direct current and allows alternating current. So they are used as filters in the circuit.

More Uses of Capacitors:

Tuning circuits: Tuning circuits are used in communication system to catch and transmit  electromagnetic waves. of certain frequency. For a tuning circuit, capacitors along with inductor  is connected in series are used.  A tuning circuit allows catching a particular radio frequency. Radio, TV receivers uses this principle.

Oscillating circuit and Amplifier circuit: Capacitors are used in production of AC signal or in timer circuits. The oscillating circuits has a capacitor connected either with resistor or inductor. capacitors are used as components in  all types of amplifier circuit to increase the given input signal.

Power supplies: Capacitors are used to reduce voltage fluctuations in electric power supplies as filters, to transmit regulated pulsed signal and to provide necessary time delay.

Niels Bohr Atomic Theory

Introduction to Neils Bohr atomic theory energy resource conservation
A Danish physicist Niels Henrik David Bohr was gave the atomic theory which is used now these days. Niels Bohr lived from 7 October 1885 to 18 November 1962. He was the founder of atomic structure and the quantum mechanics. Niels Bohr got the Nobel Prize in 1922 for the atomic theory. Niel Bohr married in 1912 with Margrethe Norlund and her son Aage Bohr also got the Nobel Prize in 1975 . I like to share this Atomic Number and Atomic Mass with you all through my article.

Neils Bohr Atomic Theory:

The most important and the main features of the atomic and the molecular structure was given by the Nile Bohr in 1915, so this picture which explains the atomic and the molecular structure is called as the Bohr’s model. The atomic theory given by the Niels Bohr states that the matter is made by the elementary and the discrete units called as atom. The word atom comes from the Greek word atomos, which meant indivisible. After the further researches the atom is not indivisible, it is divisible in the fundamental particles named as protons, electrons and the neutrons. These particles are called the elementary particles. These elementary particle rare further discovered by the various scientists. In this theory the electrons exhibits the property of both as a wave and as a particle meant that, it can be refracted like a wave and has some little mass like a particle. There is a consequence that the electron shows dual nature at a single time means the electron have some momentum and the position at the same time. The Bohr’s model describes that there is a possibility not sure that we find the electron in any particular circular orbit. Is this topic Formula for Mass hard for you? Watch out for my coming posts.

Conclusion on Neils Bohr Atomic Theory:
As according to the Rutherford atom model, all the electrons revolve around the nucleus. But he did not explain then why not all the electrons falls into the nucleus after spending the energy. This fact was completely explained by the Niels Bohr and stated that the electrons revolve around the nucleus in the fixed orbits only. The in that fixed orbits the angular momentum of the electrons is equal to the multiple integral of nh / 2`Pi` .

Silver Valence Electrons

Introduction to silver valence electrons:

Number of valence electrons in a silver atom is strongly dependent upon how one is defining valence electrons. There are multiple ways one can look at valence electrons. If one were to treat electrons in the outermost Having problem with De localization of Electrons keep reading my upcoming posts, i will try to help you.

It is common for students in the initial stages to begin to equate number of valence electrons with the group number in the periodic table to which the element belongs. The formula does work for some elements of group 1 and 2, e.g. Li, Na, Be etc. It fails miserably for other elements, e.g. Fe, Co and Ni are placed in group VIII and clearly it is impossible for each of them to have 8 valence electrons.

Valency and Valence Electrons:

A large number of elements display multiple valencies arising due to differing behavior of valence electrons. If all the valence electrons were to come into play every time then formation of multiple compounds like CO and CO2 would never have been possible.

Multiple valencies are best explained by theories of electron configuration and energy levels provided by quantum mechanics. It identifies valence electrons as ones with the highest principal quantum number (Shells of the earlier theory put forth by Bohr). Electron configuration of Carbon is (1s)2(2s)2(2p)2, which leaves four electrons in the n=2 shell, which become valence electrons for C. However, two electrons in 2s being in a relatively more stable energy level makes it possible for C to depict a valency of 2 with formation of compounds such as CO. Is this topic specific heat practice problems hard for you? Watch out for my coming posts.

Valence Electrons for Silver:

The theory described explains neatly the valence electrons for main group elements but again tends to fail as we move up towards elements with higher atomic numbers. The essence of it is that a theory exists but a simple (or even algebraic) formula cannot be given to determine valence electrons, which would explain all the elements.

There is only one electron in the n=5 shell of a silver atom. Fortunately silver displays only a single valency of one unlike its group neighbors Cu and Au, which display multiple valencies while reacting with other elements and forming compounds. Hence, replying to a question on number of valence electrons in silver with an answer of one valence electron would make all concerned happy at the school level and get full marks to students.