![5.7.1. The pendulum
A pendulum is a heavy bob suspended by a light thread. The length [L] of the
pendulum is measured from the point of suspension or pivot to the centre of gravity
of the bob. When the pendulum is displaced from the centre position and released, it
begins to swing to and fro. One complete to and fro motion is called an oscillation. The
maximum displacement of the bob from the mean position is called the amplitude of
the oscillation. The time taken for one oscillation is called the time period
of the pendulum (T).
The time period of the pendulum:
ƒƒ * It does not depend on the amplitude and this can be verified
experimentally. i s proportional to the square root of the length of the pendulum.
[ Tα√L].
ƒƒi s inversely proportional to the square
root of the acceleration due to gravity.
[ Tα ].
Putting both together along with the
constant of proportionality, 2π, we get the
final form of the formula:](https://image.slidesharecdn.com/measurements-161104124131/85/Measurements-57-320.jpg)
Measurements
- 2. Measurement
- 3. Measurement Physics can also be defined as the branch of science dealing with the study of properties of materials. To understand the properties of materials, measurement of physical quantities such as length, mass, time etc., are involved. The uniqueness of physics lies in the measurement of these physical quantities.
- 4. Fundamental quantities and derived quantities Physical quantities can be classified into two namely, fundamental quantities and derived quantities. Fundamental quantities are quantities which cannot be expressed in terms of any other physical quantity. For example, quantities like length, mass, time, temperature are fundamental quantities. Quantities that can be expressed in terms of fundamental quantities are called derived quantities. Area, volume, density etc. are examples for derived quantities
- 5. Unit To measure a quantity, we always compare it with some reference standard. To say that a rope is 10 metres long is to say that it is 10 times as long as an object whose length is defined as 1 metre. Such a standard is called a unit of the quantity. Therefore, unit of a physical quantity is defined as the established standard used for comparison of the given physical quantity. The units in which the fundamental quantities are measured are called fundamental units and the units used to measure derived quantities are called derived units.
- 6. Physical quantity Unit Symbol Fundamental quantities Length Mass Time Electric current Temperature Luminous intensity Amount of substance metre kilogram second ampere kelvin candela mole m kg s A K cd mol Supplementary quantities Plane angle Solid angle radian steradian rad sr
- 7. SI standards
- 8. Length
- 9. Length Length is defined as the distance between two points. The SI unit of length is metre. One standard metre is equal to 1 650763.73 wavelengths of the orange − red light emitted by the individual atoms of krypton − 86 in a krypton discharge lamp.
- 10. Mass
- 11. Mass Mass is the quantity of matter contained in a body. It is independent of temperature and pressure. It does not vary from place to place. The SI unit of mass is kilogram
- 12. Time
- 13. Time Until 1960 the standard of time was based on the mean solar day; In 1967, an atomic standard was adopted for second, the SI unit of time. One standard second is defined as the time taken for 9 192 631 770 periods of the radiation corresponding to unperturbed transition between hyperfine levels of the ground state of cesium − 133 atom. Atomic clocks are based on this. In atomic clocks, an error of one second occurs only in 5000 years.
- 14. ELECTRIC CURRENT
- 15. Ampere The ampere is the constant current which, flowing through two straight parallel infinitely long conductors of negligible cross-section, and placed in vacuum 1 m apart, would produce between the conductors a force of 2X10-7 newton per unit length of the conductors.
- 16. Temperature
- 17. Kelvin It is the primary unit of temperature. The Kelvin is the fraction of 1 / 273.16 of the thermodynamic temperature of the triple point of water*.
- 18. Temperature Freezing point of water is 0° C in celcius scale but at 0° C, water molecules do not come to rest. -273° C molecules come to rest. -273° C is absolute zero and it is taken as null point for Kelvin scale. -273° C = 0 k 273 k = 0° C The usage of negative values in celcius scale can be avoided by using Kelvin scale.
- 20. Candela The candela is the luminous intensity in a given direction due to a source, which emits monochromatic radiation of frequency 540×1012 Hz and of which the radiant intensity in that direction is 1 / 683 watt per steradian
- 22. Mole The mole is the amount of substance which contains as many elementary entities as there are atoms in 0.012 kg of carbon-12.
- 23. Rules and conventions for writing SI units and their symbols
- 24. 1. The units named after scientists are not written with a capital initial letter. For example : newton, henry, watt
- 25. 2. The symbols of the units named after scientist should be written by a capital letter. For example : N for newton, H for henry, W for watt
- 26. 3. Small letters are used as symbols for units not derived from a proper name. For example : m for metre, kg for kilogram
- 27. 4. No full stop or other punctuation marks should be used within or at the end of symbols. For example : 50 m and not as 50 m.
- 28. 5. The symbols of the units do not take plural form. For example : 10 kg not as 10 kgs
- 29. 6. When temperature is expressed in kelvin, the degree sign is omitted. For example : 273 K not as 273° k (If expressed in Celsius scale, degree sign is to be included. For example 100° C and not 100 C)
- 30. 7. Use of solidus is recommended only for indicating a division of one letter unit symbol by another unit symbol. Not more than one solidus is used. For example : m s−1 or m / s, J / K mol or J K-1 mol-1 but not J / K / mol.
- 31. 8. Some space is always to be left between the number and the symbol of the unit and also between the symbols for compound units such as force, momentum, etc. For example, it is not correct to write 2.3m. The correct representation is 2.3 m; kg m s–2 and not as kgms-2
- 32. 9. Only accepted symbols should be used. For example : ampere is represented as A and not as amp. or am ; second is represented as s and not as sec.
- 33. 10. Numerical value of any physical quantity should be expressed in scientific notation. For an example, density of mercury is 1.36 × 104 kg m−3 and not as 13600 kg m−3.
- 34. S.No PSR (mm) HSC (div) HSR=HSC XLC CHSR = HSR+_ ZC TR= PSR+ CHSR To Find the thickness “d” of the bar using screw gauge L.C=0.01 mm Z.E= Z.C=
- 35. To Find the breadth of the bar ‘b’ using vernier caliper : L.C=0.01 cm S.No MSR (cm) VSC VSR = VSCX LC (cm) TR= MSR + VSR (cm)
- 36. Importance Of Accurate Measurements Human beings are able to make more accurate measurements. A lot therefore depends on the instruments that are used to make the measurements.
- 37. THREE CHARACTERISTICS OF MEASURING INSTRUMENTS There are three important characteristics of measuring instruments that one must be familiar with. They are: ƒƒ Least Count ƒƒ Range ƒƒ Zero Error
- 38. ƒƒLeast Count The smallest value that any instrument can measure is called the least count of the instrument. For example, if you use a scale then the smallest division is one millimeter. It is the smallest value that the scale can measure and is called the least count of the scale.
- 40. Range The values between the minimum measurable value and the maximum value that can be measured is called the range of the instrument. For example, the range of the scale is zero centimeter to thirty centimeters. Usually, we state the maximum value as the range since the minimum value is generally zero. When we say, the range of the metre scale is 100cm, we mean that the range is from zero to 100cm.
- 41. There are, however, special instruments that are designed to measure from a specific minimum value to a maximum value. In such cases we say the range of the instrument is from such and such value to such and such value. For example, if you had a Voltmeter that reads from 150V to 250V, then we say that the range of the Voltmeter is from 150V to 250V. Usually such instruments are built for a specific purpose and optimized to give accurate readings within the design range and the designer expects that the value will not go outside the design range.
- 42. Zero Error Often instruments do not read zero at the minimum position. For example, the needle of an Ammeter may read 0.02 amperes when it is not connected to the circuit. Such an error is called zero error, since the needle at the minimum position is not reading zero. While using the instrument, one has to apply a correction to the reading to obtain the real value. The value that is read off the instrument is called the observed value to which we apply the zero error correction and obtain the measured value.
- 43. MEASURING LENGTH Vernier caliper The vernier caliper is a device that is used a great deal in engineering work and in workshops which manufacture things. It is an ingenious device where two scales with fairly large least counts are used in conjunction with one another to measure very small values of length. The auxiliary scale, now called the Vernier scale after the inventor, is used nowadays in almostn every instrument meant for accurate measurement such as the barometer, the microscope, etc.
- 44. The principle of the vernier The principle of the Vernier is delightfully simple. Let us say, you have two scales, one with a least count of 1.0mm(main scale) and the other with a least count of 0.9mm (auxiliary or Vernier scale) you can then measure an object whose length is 0.1mm quite easily. Refer to the diagram alongside; by aligning the left edge of the object with the zero of the main scale and butting the edge of the auxiliary scale to the edge of the object, you would find that the first marking of the auxiliary scale would exactly coincide with the first marking of the main scale (object length, 0.1mm + vernier division, 0.9mm = 1.0mm, the first main scale division). Going the other way around, if we did not know the size of the object and we found that the first vernier division coincided with the first main scale division, we could state that the size of the object must be 0.1mm, since:- object length, 0.1mm = 1.0mm, the first main scale division - vernier division, 0.9mm You could now say that the least count of the combination of scales is 0.1 mm, which is the difference between the two least counts.
- 45. Popularly it is written as follows:- L.C. (of the instrument) = 1 MSD – 1 VSD If on the other hand, the size of the object being measured is 0.2mm long and the auxiliary scale is butted against the object the second vernier marking will coincide with the second main scale division (object length, 0.2mm + two vernier divisions, 1.8mm = 2.0mm). Going the other way around, if we did not know the size of the object and we observed that the second vernier division coincided with the second main scale division we could say that the size of the object is 0.2mm. object length, 0.2mm = 2.0mm, the second main scale division – two x vernier divisions, 1.8mm There is a pattern here and we could try extending by using the same logic and saying that if the object was 0.4mm long then the fourth vernier division would coincide with the fourth main scale division.Further if it was 0.9mm long, then the ninth vernier division would coincide with the ninth main scale division. I could write this as: Object length, 0.9mm = 9.0mm, The ninth main scale division – nine x vernier divisions, 8.1mm 0.9mm = 9 * Main scale division – 9 * Vernier scale division
- 46. Description of vernier caliper The Vernier Caliper used in the laboratory is a modern version of the age-old one. A picture of a Vernier Caliper is shown below. The Vernier Caliper consists of :- ƒƒA thin long steel bar graduated in cm and mm (4). This is the Main scale. ƒƒFixed perpendicular to the bar at the left end of the steel bar carrying the main scale is an upper fixed jaw and a lower fixed jaw. ƒƒTo the right of the fixed jaws mounted on the steel bar is a slider with a upper movable jaw and a lower movable jaw. ƒƒThe slider can be fixed to any position using the tightening screw or friction nut. ƒƒThe Vernier scale (6) is marked on the slider and moves along with the movable jaws and the slider. ƒƒThe lower jaws (1) are used to measure the external dimensions and the upper jaws (2) are used to measure the internal dimensions of objects. ƒƒThe thin bar attached to the Vernier scale at the right side (3) is called the depth probe and is used to measure the depth of hollow objects.
- 47. Using the vernier caliper The first step in using the vernier Caliper is to find out its characteristics Least count, Range and Zero error.
- 48. 1. Lower Jaws 1a. Lower Fixed Jaw 1b. Lower Movable Jaw 2. Upper Jaws 2a. Upper Fixed Jaw 2b. Upper Movable Jaw 3. Depth Probe 4. Main Scale 5. Retainer 6. Vernier 7. Friction Nut 8.Slider 1. Least Count: 2. Zero Error 3. Positive zero error 4. Negative zero error
- 51. 5.5.5. Digital vernier caliper Digital Vernier Caliper has a digital display on the slider. The slider also houses the electronic calculator which calculates the measured value that is then displayed. The user need not manually calculate the least count, the zero error etc. or take the trouble of finding the vernier coincident manually.
- 52. 5.6. MEASURING MASS When we go to a shop to buy something, say a kg of rice, we often buy it in terms of the ‘weight’. In layman’s parlance what is called ‘weight’ is actually mass in science parlance. Many things are measured in terms of the mass in the commercial world. We buy gold which is measured in grams or milligrams, medicines in 500mg or 250mg values, load trucks in terms of tons etc.
- 53. Common (beam) balance A beam balance compares the sample mass with a standard reference mass (known masses such as 100g, 200g etc.). Least counts of 20g to 50 mg are possible.
- 54. Two pan balance This type of balance is commonly used for measuring mass in shops. This balance too compares the sample mass with a standard reference mass. The pans rest on top of the beam and can be conveniently placed on a table top. Least counts are generally in the region of 10g to 50g.
- 55. Physical balance It is used in laboratories. It is similar to the beam balance but is a lot more sensitive and can measure mass of an object correct to a milligram.
- 56. 5.7. MEASURING TIME The pendulum as a reliable measure of time was first articulated by Galileo in 1602. In those days many lamps would be mounted on a large glass arrangement suspended from the ceiling. Such an elaborate arrangement was called a “chandelier”. Watching the glass chandelier of the church move to and fro in the wind, Galileo realized that a simplified form of the pendulum could be used to keep time.
- 57. 5.7.1. The pendulum A pendulum is a heavy bob suspended by a light thread. The length [L] of the pendulum is measured from the point of suspension or pivot to the centre of gravity of the bob. When the pendulum is displaced from the centre position and released, it begins to swing to and fro. One complete to and fro motion is called an oscillation. The maximum displacement of the bob from the mean position is called the amplitude of the oscillation. The time taken for one oscillation is called the time period of the pendulum (T). The time period of the pendulum: ƒƒ * It does not depend on the amplitude and this can be verified experimentally. i s proportional to the square root of the length of the pendulum. [ Tα√L]. ƒƒi s inversely proportional to the square root of the acceleration due to gravity. [ Tα ]. Putting both together along with the constant of proportionality, 2π, we get the final form of the formula:
- 58. 5.7.2. Clocks Sundial Water clock Sand clock 5.7.3. Another characteristic of instruments -Accuracy 5.7.4. Atomic clock
- 59. THANK YOU