Wednesday, January 14, 2015

Quiz on Dynamics



Test Your Knowledge
This is a test of your knowledge. You’ll find the answers at the end of the quiz.
Fill in the blanks.
1. Newton's laws are valid in --- frame of reference.
2. --- force is a pull on the body towards the centre of the circle.
3. Circular motion is a special case of ---- motion.
4. In a uniform circular motion --- is constant.
5. Centrifugal force means ---- force
6. Centre seeking force is called ---
7. If the string of Whirling stone is cut, the stone moves in ---- direction.
8. Satellite communications use --- waves
9. Centripetal acceleration, a = ----
10. The angle subtended by an arc of unit length on a circle of unit radius is called ---
11. In SHM, the acceleration of the particle is directly proportional to ---
12. A body executing oscillatory motion comes to rest at ----
13. Periodic motion is also called as ---
14. If a particle in periodic motion moves back and forth over the same path, its motion is called ----.


Answers:
1) inertial         
2) Centripetal           
3) Rotatory         
4) Angular Velocity        
5) Fictitious
6) Centripetal force    
7) Straight line or tangential to the circle     
8) Microwaves  
9) a =  v2/r
10)  a radian            
11)  Its displacement                
12) The equilibrium position
13) Harmonic motion                       
14)  Oscillatory or Vibratory motion.

Simple Harmonic Motion and its Characteristics

Simple Harmonic Motion: 
The to and fro motion of a particle about a mean position on a fixed path such that the acceleration of the particle is always directed to the mean position and is directly proportional to the displacement of the particle from its mean position is called Simple harmonic motion.

Characteristics of SHM:
1. A constant time period (T) (or) a constant frequency υ = 1/T
2. An amplitude (A)
3. A constant mechanical energy which is the sum of potential energy and Kinetic energy at every point in the path of oscillation.

Centrifugal Force


Centrifugal Force:
1. It acts normally on the same particle executing uniform circular motion.
2. It is directed radially away from the centre of the circle.
3. It cannot be associated with any agent.
4. It is a fictitious force in an inertial frame of reference.
5. It is the tendency of the body to fly away from the centre of the circle.
6. It comes in to play in a rotating frame of reference.
7. In a uniform circular motion, its magnitude is constant and equal to that of the centripetal force.
8. Centrifugal force depends on mass 'm'. Hence bodies of higher mass rotate on a circle of higher radius (principle of centrifuge).

Centripetal Force



Centripetal Force:
1. It acts normally on a particle executing a uniform circular motion.
2. It is always directed radically towards the centre of the circle.
3. It is associated with an external agent.
4. It is a real force in an inertial frame of reference.
5. It is a pull on the body towards the centre on a curved path.
6. It is necessary to make a body to travel on a curved path.
7. In a uniform circular motion, its magnitude is constant.
8. Centripetal force depends on mass of a body in a circular motion with speed V.

Centrifuge and Laundry Drier



Centrifuge:
1. A centrifuge is a machine used to separate particles of higher mass from those of lower mass in a given mixture.
2. A centrifuge consists of a cylindrical vessel rotated about its own axis at high speed with the help of an electric motor.
3. When milk is poured into the cylindrical vessel of the centrifuge and rotated with high speed, the particles of higher mass (skimmed milk) are thrown away from the centre due to greater centrifugal force and lower-mass cream particles collect at the centre, that is, near the axle.

Laundry Drier:
1. The wet clothes are dropped into a cylindrical vessel containing holes.
2. When the vessel is rotated, the wet clothes get struck to the walls of the vessel.
3. The centrifugal force pushes the water molecules out from the clothes through the holes.
4. In this way the clothes are dried.

Principal of Artificial Satellites and their Uses


Principle of Orbiting Satellite:
1. A satellite is a natural or artificial body orbiting around another body of larger mass and larger radius.
2. Moon is a natural satellite of earth.
3. When a sufficient horizontal speed is imparted to a body it revolves round the earth. This is the principle of launching an artificial satellite.

Uses of Artificial Satellites:
1. Artificial satellites help to develop reliable communication links over the entire globe.
2. They are used to the 'Weather Prediction'.
3. Satellites and space stations are used for the study of astronomy.
4. The artificial satellites are used for remote sensing.
5. Telephones, Fax, Internet are some examples for global communications.
6. Artificial satellites are also used for spying in the defense service.

Quiz on Screw Gauge




Test Your Knowledge
This is a test of your knowledge. You’ll find the answers at the end of the quiz.
Fill in the blanks.
1. Least count of an ordinary scale is .......
2. Screw gauge works on the principle of a ............
3. The scale marked on the index of a screw gauge is called ...............
4. Screw gauge consist of ...........and........
5. The distance traveled by the tip of a screw for one complete rotation of its head is called......
6. If the zeroth division of the head scale is below the index line of the pitch scale, the error is said to be ............ and the correction is ................
7. If the zeroth division of the head scale is........ , the index line of the pitch scale, the error is said to be negative and the correction has to be........
8. In the screw gauge the other end of the barrel is tapered and has 100 (or) 50 equal divisions on it, is called the ...........

Answers:
1. 1 mm       
2. Screw in a net        
3. Pitch scale
4. Head scale , Pitch scale         
5. The pitch of the screw             
6. Positive, negative    
7. Above, positive       
8. Head scale

Uses of a Screw Gauge


Uses of a screw gauge:
  • The thickness of a metal sheet is expressed in gauge number. By finding the thickness of a metal sheet in m.m. by using a screw gauge, we can know its gauge number. For example, if the thickness of a sheet is 5.16 m.m., then the gauge number will be 6. If the thickness of a sheet is 0.953 mm, then the gauge number will be 10. To know gauge number for various thickness use a conversion table.

  • The diameter of a wire is expressed in American wire gauge size. By finding the diameter of a wire after removing the insulation of the wire in mm by using a screw gauge, the gauge size can be obtained. For example, if the metric size of a wire is 52 mm, then A.W.G. size will be '0'. If the metric size of a wire is 5 mm, then A.W.G., size will be 10. To know A.W.G. size for various metric sizes of a wire use a conversion table.
  • Screw gauge is used to find the diameter of a steel rod that is used in the construction of a building.
  • It is used in the industry to manufacture components of a machine with required measurements.
  • As this instrument is used to measure the gauge of a metal sheet or a wire, it is named as screw gauge.

Zero Errors of a Screw Gauge



Zero errors of a screw gauge:
    Some times the zeroth division of the head scale does not coincide with the index line but lies below or above the index line, when S1 and S2 are in contact. This happens due to a fault in the instrument while manufacturing it or by the frequent use of the instrument. This error is known as zero error.

Suppose 2nd division of the head scale coincides with the index line when S1 and S2 are in contact. The zeroth division of the head scale lies 2 divisions below the index line. So the observed head scale reading (HSR) will be 2 divisions more than the correct reading. This error is known as positive zero error. To get correct HSR, 2 divisions should be subtracted from the observed HSR so the zero correction is negative.

     Suppose 98th division of a head scale coincides with the index line when there are 100 divisions on the head scale. The zeroth division of the head scale lies 2 divisions above the index line. The observed HSR will be 2 divisions less than the correct reading. So this error is known as negative zero error. To get correct HSR, 2 divisions should be added to the observed HSR. So the zero correction is positive.

To derive a formula for the thickness of a glass plate:
    When the given object is fixed between S1 and S2, the screw moves backward, a distance equal to the thickness of the object. This distance is noted from the pitch scale. If the edge of the head scale coincides with a division on the pitch scale and zeroth division of head scale coincides with the index line, then that reading can be taken as the thickness of the object, when there is no zero error. Some times the edge of the head scale lies in between two divisions of the pitch scale. The division that just precedes the edge is taken as pitch scale reading (PSR). The thickness of the object will be equal to PSR + distance between PSR and the edge. The division of the head scale that coincides with the index line gives the head scale reading (HSR). We know that the rotation of one division of head scale makes the screw to move a distance equal to the least count. So the product of HSR and L.C. gives the distance between P.S.R. and the edge.

                    Thickness = P.S.R. + H.S.R. × L.C.

    If there is zero error, then thickness = P.S.R.+C.H.S.R. × L.C., where C.H.S.R. is the corrected head scale reading.

Tuesday, January 13, 2015

Derive Formulas of Screw Gauge


To derive a formula of pitch of a screw:
   The distance covered by the screw when its head makes a complete rotation = 1 × pitch of the screw.
   The distance covered by the screw when its head makes 10 complete rotations = 10 × pitch of the screw
   The distance covered by the screw when its head makes 'n' complete rotations (x) = n × pitch of the screw
  Pitch of the screw = The distance covered by the screw (x) /No. of complete rotations
made by the head (n).
     


To derive a formula for the least count of a screw gauge:
    The distance covered by the screw when its head makes a complete rotation
    = 1 × pitch of the screw
    The distance covered by the screw when its head makes 1/10 of a complete rotation
    = 1/10 × pitch of the screw.
    Out of N divisions of the head scale, if only one division crosses the index line then the head of the screw makes 1/N of a complete rotation.
    The distance covered by the screw when its head makes 1/N of a complete rotation
    = 1/N × pitch of the screw
    This distance is the smallest distance that can be measured accurately, by the screw gauge when the head contains N divisions on it. So this can be considered as the least count of the screw gauge.
                


   Generally the L.C. of a screw gauge will be 0.01 mm or 0.001 cm. So it is also known as micrometer screw gauge.

Measurement of Length-Screw Gauge


How do you find the gauge of a metal sheet? How do you find the gauge of a wire that is used in electrical appliances? How do you find the diameter of a steel rod that is used in the construction of buildings? Which measuring device is used in the manufacture of some of small components of machine with accurate measurements?

You get answers to the above questions and learn some other concepts:
          Our daily life starts with measurements. We purchase milk in liters (volume) and vegetables in kg (mass). We try to reach the school in time. Measurement of physical quantities play an important role in physics. A physical quantity cannot be understood completely, by describing it or by knowing its qualities. It is better to know its 'measurement' along with the above two factors to understand it completely. If there were no measurements in physics, it would not have been developed to this extent. Physics is otherwise known as science of measurements.


          Some times very accurate measurements of some physical quantities are essential. For example, very accurate measurements of mass of the ingredients are required in the  preparation of a drug. Very accurate measurements of components of a car are required to assemble it. So very sensitive instruments are required to measure some physical quantities. The sensitivity of an instrument depends on its least count. An instrument is said to be more sensitivity if the least count of the instrument is minimal.


A number of instruments are used to measure length or distance. To measure very small  length like thickness of a thin plate or diameter of a thin wire, an instrument called screw gauge  is used.





  • A screw gauge consists of mainly, a screw and a nut. When the head of the screw is rotated in a nut, the screw moves forward or backward depending on the direction of rotation of the head. The distance travelled by a screw is equal to its pitch, if the head of the screw makes one complete rotation. When the head of the screw is rotated by a small fraction of a complete rotation, the screw moves a distance equal to a small fraction of the pitch of the screw.
 
  • Sometimes this distance becomes the smallest distance that can be measured accurately by using a screw and a nut. This principle is used in the construction of a screw gauge.
 
  • A screw gauge consists of two scales. A pitch scale with an index line is used to measure the distance moved by the screw. A head scale is used to know the number of rotations made by the head of the screw or a portion of the complete rotation made by the head of the screw. The head scale is a circular scale with equally spaced divisions on the head of the screw. Observe the line diagram of a screw gauge and its parts.

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