How to solve problems in mechanics...??

As we all are aware of how important mechanics is in physics, here are more tips to solve problems further. Though intensive practice is required in mechanics , it is essential to know how to solve the problems too….

Here are few ways to approach problems in mechanics…

In a PLANE :

1. Problems where there is a motion in a Two Dimensional Plane:

In such type of problems, do follow the below:

i. The very first step required is to select a coordinate system and resolve the velocity vector into its individual x and y components.  

ii. Next, find out the respective acceleration in each direction and solve according to the equation of rectilinear motion.

iii. Now, if you find acceleration only in vertical direction, follow the methods for solving constant-acceleration problems to analyze the vertical motion. The motion in x and y have the same time of flight t.

iv. If there is any problem relating to the trajectory, find the motions in x and y direction with respect to time from the previous point and from one equation, find the value of t and substitute that in another equation to find out the equation of the trajectory.

2. Problems which deal with Motion in a Three dimensional Plane :

i. To solve such problems, just select one coordinate system and resolve the velocity into x, y and z directions.

ii. The acceleration in each direction can be found out and solved according to the equation of rectilinear motion.

3. Problems which involve Uniform Circular Motion :

i. To approach any problem, the very first thing needed  to be done is to draw a neat diagram of the system.

ii. Next, consider all the forces and their origin on each object. Find out the forces acting on each object. Note down all the contact forces wherever there is a contact.

iii. Calculate the centripetal force required for the motion which is circular.

The velocity can be found accordingly with the centripetal force = mv2/R.

The frogs and the tower

Here is a short story of a small frog which leaves you inspired and productive...

There once was a bunch of tiny frogs...who arranged a running competition. The goal was to reach the top of a very high tower. A big crowd had gathered around the tower to see the race and cheer on the contestants...

The race began...

Honestly, no-one in the crowd really believed that the tiny frogs would reach the top of the tower. You heard statements such as:

"Oh, WAY too difficult!!"

"They will NEVER make it to the top".

"Not a chance that they will succeed. The tower is too high!"

The tiny frogs began collapsing one by one.

Except for those who in a fresh tempo were climbing higher and higher...

The crowd continued to yell "It is too difficult!!! No one will make it!"

More tiny frogs got tired and gave up.

But ONE continued higher and higher and higher,This one wouldn't give up!

At the end, everyone else had given up climbing the tower. Except for the one tiny frog who, after a big effort, was the only one who reached the top!

THEN all of the other tiny frogs naturally wanted to know how this one frog managed to do it?

A contestant asked the tiny frog how the one who succeeded had found the strength to reach the goal?

It turned out...

That the winner was deaf....!!

Whatever race it may be, believe in yourself and work hard towards your goal in a persistent way..!! You'd definitely be in the top position.

Happy Birthday Robert William Holley..!!

Do you know that today is the birthday of the famous scientist Robert William Holley …??

Robert William Holley was an American biochemist. He shared theNobel Prize in Physiology or Medicine in 1968 (with Har Gobind Khorana and Marshall Warren Nirenberg) for describing the structure of alanine transfer RNA, linking DNA and protein synthesis.

Holley's research on RNA focused first on isolating transfer RNA (tRNA), and later on determining the sequence and structure of alanine tRNA, the molecule that incorporates the amino acid alanine into proteins. Holley's team of researchers determined the tRNA's structure by using two ribonucleases to split the tRNA molecule into pieces. Each enzyme split the molecule at location points for specific nucleotides. By a process of "puzzling out" the structure of the pieces split by the two different enzymes, then comparing the pieces from both enzyme splits, the team eventually determined the entire structure of the molecule.

The structure was completed in 1964, and was a key discovery in explaining the synthesis of proteins from messenger RNA. It was also the first nucleotide sequence of a ribonucleic acid ever determined

Hargobind Khorana was an Indian-American biochemist who shared the 1968 Nobel Prize for Physiology or Medicine with Marshall W. Nirenberg and Robert W. Holley for research that helped to show how the order of nucleotides in nucleic acids, which carry the genetic code of the cell, control the cell’s synthesis of proteins. Khorana and Nirenberg were also awarded the Louisa Gross Horwitz Prize from Columbia University in the same year.

He was born in Raipur, British India (today Tehsil Kabirwala Punjab Pakistan) and became a naturalized citizen of the United Statesin 1966, and subsequently received the National Medal of Science. He served as MIT's Alfred P. Sloan Professor of Biology and Chemistry, Emeritus and was a member of the Board of Scientific Governors at The Scripps Research Institute

Ribonucleic acid (RNA) with three repeating units (UCUCUCU → UCU CUC UCU) produced two alternating amino acids. This, combined with the Nirenberg and Leder experiment, showed that UCU codes for Serine and CUC codes for Leucine. RNAs with three repeating units (UACUACUA → UAC UAC UAC, or ACU ACU ACU, or CUA CUA CUA) produced three different strings of amino acids. RNAs with four repeating units, including UAG, UAA, or UGA, produced only dipeptides and tripeptides thus revealing that UAG, UAA and UGA are stop codons.

 With this, Khorana and his team had established that the mother of all codes, the biological language common to all living organisms, is spelled out in three-letter words: each set of three nucleotides codes for a specific amino acid. Their Nobel lecture was delivered on December 12, 1968. Khorana was the first scientist to chemically synthesize oligonucleotides.

MyRank wishes a very happy birthday to Robert William Holley, who is the main person behind the structure of RNA and protein synthesis...

Real Gases

As you are heading towards the end of january,  you might be in need of many important tips for your revision process...

Here are few such in the topic Real Gases.

Gases that don’t obey    equation are known as “Real gas”.

Compression factor = (Z) = 

For ideal gas, Z = 1 and for non-ideal gas  .

If Z < 1, there exists net attraction between gas molecules

If Z > 1, there exists net repulsion between the gas molecules.

Vander waal’s equation: The gas which obeys Boyle’s law, charle’s  law for all values of temperatures and pressure is “Ideal gas”. But no gas is ideal or perfect in nature. So, for real gas this theory was given.

Where a and b are characteristics constants of a real gas.

pressure correction

volume correction

Volume correction:

Vander waal’s assumed that molecules of real gas are rigid spherical particles which posses a definite volume. Thus, the volume of real gas i.e., volume available for compression or movement is actual volume minus volume occupied by gas molecule.

Note:

As i.e., at very high temperature and very low pressure, a non-ideal gas becomes  an ideal gas.

If 'b' is effective volume of the molecules per mole of the gas, the ideal volume for the equation is  not V.

Corrected volume  = V – b for 1 mole of a gas for n moles, corrected volume = .

Where, r is the radius of gas molecule

N = Avogadro number

Pressure correction:

A molecule in the interior of the gas is attracted by other molecules on all sides. A gas molecule which is just going to strike the wall of the vessel experiences an inward pull due to attractive forces.

Hence, it strikes the wall with  less momentum and the observed pressure will be less than the ideal pressure.

P' is the pressure correction 

.

Therefore, after this two corrections, we get,

This equation is called real gas equation depending on a and b the gas behavior changes.

Units of a and b:-

1. Pressure correction

    .

     

Units of a :-

S.I. units of a  .

 Unit of b:-

Volume correction.

Unit of b.

PAIR OF STRAIGHT LINES

Are you already tensed by knowing that you are hardly left with two more months of preparation..? Now, its the time for you to give up your old practice methods and to make a perfect move..!!

Whenever you start any topic and learn it, make sure you note all the important formulae and shortcuts to make your revision more effective.

Here are few such tips on the topic Pair of Straight Lines.

  ü  Joint equation of the straight lines,   is 

  ü  If a,b,h are real then is called a homogenous equation of degree 2 

  ü  If a,b,h are not all 0 then the equation represents straight lines iff

  ü  If,lines are coincident.

  ü  If then we can writeso that

  ü  If H=0 represents a pair of straight lines and b is not equal to zero, if m1, m2  are slopes of lines.          Then 

              

          , .

  ü  The equation to the pair of lines passing through origin and perpendicular to pair of lines  is  is .

*** The product of perpendicular let fall from the point (x1, y1) upon the lines is  is .

**** Angle between pair of lines   is 

 And .

*** If the  lines are coincident then 

     

     

      If  the lines are perpendicular then 

   

 

 

*** Bisectors of the Angle between the lines by a Homogenous equation

ü  The joint equation of the bisectors of the angles between the lines represented by the equation  is .

**** The necessary and sufficient condition forto represent a pair of straight lines is that

 and .

**** Equations of bisectors:

** The equations of the bisectors of the angles between the lines represented byare given by .

Where (x1, y1) is the point of intersection of lines represented by given equations.

*** If   represents a pair of parallel straight lines then and distance between those parallel lines is

** If the equation  represent pair of straight lines then they intersect at point .

 **** if the equation  represents two straight lines then the product of perpendicular drawn from origin to these lines is 

.

** Area formed by lines represented  and axis of x is 

**** Lines joining origin to the point of intersection of curve:

The combined equation of the straight lines joining the origin to the points of intersection of a second degree curve   and a straight line  is  is 

** Area of triangle formed by=0 and  is is