Surface Tension

      
      Surface tension is basically a property of liquid. The liquid surface behave like a stretched elastic membrane which has a natural tendency to contract and tends to have a minimum possible area. This property of liquid is called surface tension.

Inter molecular force

A. Cohesive force :-
       The force acting between the molecules of one type of molecules or molecules of different substance is called adhesive force.

B. Adhesive force :-
       The force acting between different type of molecules or molecules of different substance is called adhesive force.

 * Inter molecular force are different from the gravitational forces          not obey the inverse square low.

* The distance up to which these forces effective, is called molecular range. This distance is nearly 10^-9m. Within these limit this increases very rapidly as the distance decreases.

Property of surface tension :-

* surface tension is a scalar quantity.
* It acts tangential to liquid surface.
* surface tension is always produced due to cohesive force.
* More is the cohesive force, more is the surface tension.
* when surface area of liquid is increased, molecules from the interior of the liquid rise to the surface. For this , work is done against the downward cohesive force.

Dependency of surface tension :-

* On cohesive force :- those factor which increase the cohesive force between molecules increase the surface tension and those which decrease the cohesive force between molecules decrease the surface tension.

* On Impurities :- If the impurity is completely soluble then on mixing it in the liquid, its surface tension increases. E.g., on dissolving ionic salt in small quantities in a liquid, its surface tension increases. If the impurities is partially soluble in a liquid then its surface tension decreases because adhesive force between insoluble impurity molecules and liquid molecules decreases cohesive force effectively, e.g.

A. On mixing detergent in water its surface tension decreases.

B. Surface tension of water is more then ( alcohol + water ) mixture.

* On temperature
      On increasing temperature surface tension decreases. At critical temperature and boiling point it becomes zero.

NOTE :- Surface tension of water is maximum at four degree centigrade.

* On contamination
     The dust particles or lubricating materials on the liquid surface decreases its surface tension.

* On Electrification
     The surface tension of the liquid decreases due to electrification because a force starts acting due to it the outward direction normal to the free surface of liquid.

Definition of surface tension

    The force acting per unit lenght of an imaginary line drawn on the free liquid surface at right angle to the line and in the plane of liquid surface, its define as surface tension.
 For floating needle  2Tlsin Q= mg

* required excess force for lift
- wire  F ex = 2Tl
- for ring  F ex = 4πrt
- square frame F ex =8aT
- Hollow disc F ex = 2πT(r1 + r2 )
- Circular disc F ex = 2πrt
- Square plate F ex = 4at

*  Work = surface energy =4πr^2T
- liquid drop W = 4πr^2T
- Soap bubble W = 8πr^2T

* Excess pressure
P ex = P in - P out

- In liquid drop P ex = 2T / R

- In soap bubble P ex = 4T/R

* Angle of contact :-
    The angle enclosed between the tangent plane at the liquid surface and the tangent plane at the solid surface at the point of contact inside the liquid is defined as the angle of contact.

The angle of contact depends the nature of the solid and liquid in contact.
Angle of contact Q is less than 90° --> concave shape, liquid rise up.

Angle of contact Q is more than 90°--> convex shape, liquid falls.

Angle of contact Q is equal to the 90°--> plane shape, liquid neither rise nor falls.

* Effect of temperature on angle of contact :-

   On increasing temperature surface tension decreases, thus cosxc increases [ cosxc is inversely proportional to the temperature ] and xc decreases. So on increasing temperature, xc decreases.

* Effect of impurities on angle of contact :-

A. Solute impurities increase surface tension, so cosxc decreases and angle of contact xc increases.

B. Partially solute impurities decrease surface tension, so angle of contact xc decreases.

* Effect of water proofing agent =

     Angle of contact increases due to water proofing agent. It gets converted acute to obtuse angle.

* special thank you to ALLEN to provide me content for this blog.

* picture credit goes to google
https://www.researchgate.net/figure/The-ramifications-of-surface-energy-in-the-form-of-surface-tension-are-well-known-from_fig1_331025219

https://www.remet.com/en/insights/an-analysis-into-surface-tension/

VIBRATION

 Vibration is a periodic motion of small magnitude. But for sake of simplicity we can assume that it as simple harmonic motion of small amplitude.

Some important term of vibration :-

Period :- It is a time taken by a motion to repeat itself, and it is measure in seconds.

Cycle :- It is the motion completed during one time period.

Frequency :- frequency is the number of cycles of motion completed in one second. It is expressed in hertz (Hz) and is equal to one cycle per second.

Resonance :When the frequency of the external force is the same as that of the natural frequency of the system, a state of resonance is said to have been reached. Resonance results in large amplitude of vibrations and this may be dangerous.


TYPE OF VIBRATION :-

 Free vibration :- Elastic vibration in which there are no friction and external forces after the initial release of the body, are known as free or natural vibrations.

Forced vibrations :- When a repeated force continuously acts on a system, the vibrations are said to be forced vibration. The frequency of the vibrations is that of

the applied force and is independent of there own natural frequency of vibrations.

Damped vibration :- When the energy of the vibrating system is gradually dissipated by friction and other resistance the vibrations are said to be damped vibration.

Un-damped vibration :- When there is no friction and resistance present in system to contaract vibration then body execute un-damped vibration.

Longitudinal vibration :- If the shaft is elongate and shortened so that the same moves up and down resulting in tensile and compressive stresses in the shaft, the vibration are said to be longitudinal.

Transverse vibration :- When the shaft is bent alternately and tensile and compressive stresses due to bending results, the vibration are said to be transverse vibration.

Torsional vibration :- When the shaft is twisted and untwisted alternately and torsional shear stresses are induced. the vibrations are known as torsional vibration.

CAM

                                                                  
          A cam is mechanical member used to import desire motion to a follower by direct contact. The cam may be rotating or reciprocating whereas follower may be rotating, reciprocating or oscillating.

It is used in automatic machine, IC engine , mechanical tool, printing control mechanisms.

Element of Cam :-

A driver member known as the Cam
A driven member known as the follower
A frame which support the cam and guides the follower.

Point of remember :-
A cam and follower combination belongs to the category of higher pair.

Type of cam :-

1. according to the shape -

  * wedge and flat cam :-
      a wedge cam has a transitional motion, the follower can either translate or oscillate.

  * Radial and disc cam
       The cam in which the follower moves radially from the center or rotation of the cam is knows as the a radial or disc cam.

  * Spiral cam
        A spiral cam is a face cam in which a groove is cut in the form of spiral. it is used in computer.



  * Cylindrical cam
        In a cylindrical cam, a cylinder which has a circumferential contour cut in surface, rotate about its axis. it also known as barrel and drum cams.

  * Conjugate cams
        it is a double disc cam and preferred when the requirements are low wear, low noise , better control of the follower, high speed, high dynamic load etc.

  * Globoidal cams
        it has two type of surface i.e convex or concave. it is used when moderate speed and the angle of oscillation of follower is large.


2. According to the follower movement :-

  * Rise-Return-Rise (RRR) 
       In this there is alternate return and rise of the follower with no period of dwells. The follower has a linear or a angular displacement.

  * Dwell-Rise-Return-Dwell (DRRDS)
       In this cam, there is rise and return of the follower after the dwell.

  * Dwell-Rise-Dwell-Return-Dwell (DRDRD)
         The dwelling of the cam is followed by rise and dwell and subsequently by return and dwell. In case the return of the follower is by a fall, The motion may be known as Dwell-Rise-Dwell (DRD).

Network diagram

      It is a graphical representation of the logical sequence. In which different activities are interrelated to each other while completing the project.

Rules for network diagram :-
1. An activity can only be started when all the activities earlier to it are completed.

2. No two or more activities may have same head and tail event.

  

    In this condition to represent the same logic we need to use dummy activities.

Dummy activity :- an activity which only shows the relation and logic and dependency of one activity over the another but doesn't consume only time or resource for its completion is termed as dummy activity. It represent as dotted line.

  

                        -------------->

3. Intersecting of activities are represented by

     

4. Dummy activities should only the used when it is very necessary but their is no restriction on the number of dummy activities used.

5. There should be no looping and dangling in  the network diagram.

Dangling :- when activity other then the final activity do not have any successor activities then the situation are called dangling.

Example :-

      Draw a network diagram from the set of activities ?

A      -

B     A

C     B

D     A

E     D

F      C,E

Answer :-  see in image.