Measuring Scales. Measuring Scales

Transcription

1 Measurig Scales To measure a legth, a metre scale is geerally used, which is graduated to cetimeter ad millimeter, ad is oe metre i legth. For the measuremet of a legth with a metre scale we adopt the followig procedure. Note the value of oe smallest divisio of the scale. Hold the scale o its side such that markig of the scale are very close to the poits betwee which the distace is to be measured. (c) Take readig by keepig the eye perpedicular to the scale above the poits for which measuremet is made. (d) Avid usig zero of the scale as it may be damaged. Measure the distace as a differece of two scale readig. For situatios where direct placig of the scale is icoveiet, use a divider. I this case the divider is set to the legth to be measured ad the trasferred to the scale for actual measuremet of the legth. The verier or verier scale is a additioal scale. The verier scale was iveted i its moder form i 1631 by the Frech mathematicia Pierre Verier ( ). I some laguages, this device is called a oius. It was also commoly called a oius i Eglish util the ed of the 18 th cetury. Noius is the Lati ame of the Portuguese astroomer ad mathematicia Pedro Nues ( ) who i 1542 iveted a related but differet system for takig fie measuremets o the astrolabe that was a precursor to the verier. A verier scale slides across a fixed mai scale. By usig it a uiformly graduated mai scale ca be accurately read to a fractioal part of a divisio. I priciple, ot oly for measurig legths, it ca be used o ay measurig device with a graduated scale. Veriers are commo o sextats used i avigatio, scietific istrumets used to coduct experimets, machiists' measurig tools (all sorts, but especially calipers ad micrometers) used to work materials to fie toleraces ad o theodolites used i surveyig. Types of Verier Direct Verier or Forward Verier: Refer to Fig. 1. I case of direct verier both scales, amely verier ad mai, move i the same directio ad verier divisios are marked i the same directio as that of the mai scale. As i Fig. 1 i direct verier scale, verier divisios are compressed ito the space of ( 1) mai scale divisios, ad we say the verier-scale ratio is [( ):( 1)]. Let d = value of smallest divisio o the mai scale v= value of smallest divisio o the verier scale The, v d The smallest distace measured usig a verier scale is kow as the least cout (LC) -1 d = d v d - d The verier costat (v.c.) is give by 1

2 Verier costat (v.c.) = LC value of 1 mai scale divisio. Sice the verier scale show i Fig 1. is costructed to have te divisios i the space of ie o the mai scale, ay sigle divisio o the verier scale is 0.1 divisios less tha a divisio o the mai scale. Naturally, this 0.1 differece ca add up over may divisios. Figure 1 Direct Verier measurig the legth of the rectagle usig a direct verier scale So, the divisios o the verier scale are ot of a stadard legth, but the divisios o the mai scale are always of some stadard legth e.g. millimeters. A verier scale eables a uambiguous iterpolatio betwee the smallest divisios o the mai scale. Measuremet usig a verier For takig readig usig a verier scale ote the divisio o the verier scale that coicides with some divisio of the mai scale. Multiply this umber of verier divisio with the verier costat. This is the verier scale readig. Record the observed readig by addig the verier scale readig to the mai scale readig. (Note: The mai scale readig is the readig o the mai scale which appears o or before the zero of the verier scale.) Fig. 2 Measuremet of diameter of circles of differet radii usig slide calipers, a istrumet i which a verier is attached. 2

3 Retrograde Verier or Backward Verier: I case of retrograde verier, verier ad mai scales move i the opposite directio ad verier divisios are marked i the opposite directio as that of the mai scale. Figure 3. Retrograde Verier measurig the legth usig a retrograde verier scale (ote the arrow) I retrograde verier scale, verier divisios are expaded ito the space of ( + 1) mai scale divisios, we say the verier-scale ratio is [( ): ( + 1)]. Thus, i case of retrograde verier, the divisios of the verier scale will be larger tha those o the mai scale ad will facilitate i easy readig. Let d = value of smallest divisio o the mai scale v = value of smallest divisio o the verier scale The, v d d Least cout (LC) = v d d - d It is to be oted that the LC of direct ad retrograde veriers are same. Fig. 3 illustrates a retrograde verier i which 11 parts of the mai scale divisios coicide with 10 divisios of the verier. The value of oe smallest divisio o the mai scale is 0.1 ad the umber of divisio o the verier are 10. Therefore the least 0.1 cout is The readig o the verier i Fig. 3 is Exteded Verier: This type of verier is similar to the direct verier scale except that every secod divisio is omitted. Therefore, i case of exteded verier scale, (2-1) divisios of the mai scale are take ad they are divided ito equal parts. Let d = value of smallest divisio o the mai scale v= value of smallest divisio o the verier scale Figure 4. Exteded Verier measurig the legth usig a exteded verier scale (ote the arrow) 3

4 2 The, v d Least cout (LC) = 2-1 d 2d v 2d- d The exteded verier is, therefore, equivalet to a simple direct verier i which every secod graduatio is egraved. The exteded verier is regularly employed i the astroomical sextat. Fig. 4 shows a exteded verier. It has 6 spaces o the verier equal to 11 spaces of the mai scale each of 1 mm. The least cout is therefore 1 mm. The readig o the verier illustrated i Fig. 4 is 2.67 mm. 6 Double Folded Verier: Figure 5. Measurig the legth usig a double folded verier scale (ote the arrow) The double verier is employed where the legth of the correspodig direct verier would be so great as to make it impracticable. This type of verier is sometimes used i compasses havig the zero i the middle of the scale. The full legth of verier is employed for readig agles i either directio. The verier is read from the idex towards either of the extreme divisios ad the from the other extreme divisio i the same directio to the ceter. Whe the mai scale is ruig both the directios with commo zero, it becomes easier to employ a sigle verier scale with a commo zero. Extreme care should be exercised to properly read the verier scale, ie. The directios of readig of mai ad verier scales should be the same. Fig. 5 shows double folded verier i which 20 verier divisios=19 mai scale divisios. The least cout of the verier is equal to d 1 3 (with d=1 o ). For 20 motio to the right, the verier is read from 0 to 30 at the right extremity ad the from 30 at the left extremity to 60 (or zero) at the ceter. Similarly, for motio to the left, the verier is read from 0 to 30 at the left extremity ad the from 30 at right extremity to the 60 (or zero) at the ceter. The readig of the verier illustrated i Fig. 4 is 112 o 18 (x) to the right ad 247 o 42 (360 o -x) to the left. Verier to Circular Scales: Figure 6. Verier to circular scale 4

5 The above examples of veriers were for the liear scales. Veriers are also extesively used to circular scales i variety of scietific istrumets. Fig. 6 shows typical arragemet of double direct veriers. I Fig. 6 the scale is graduated to 1 o ad value of =10 o the verier. 10 verier divisios=9 mai scale divisios. Hece the least cout is =d/=1 o /10=6. The readig is 19 o 48 Fig. 7 Typical verier to circular scale of a spectrometer A typical verier to circular scale of a spectrometer, which you fid i the lab is show i Fig. 7. A Liear Scale ad a Circular Scale Fig. 7 Liear scale ad a circular scale It has a liear scale called the mai scale, ad aother scale called the circular scale. The circular scale ca be rotated by a head screw. O turig the screw, the circular scale advaces liearly o the mai scale. The distace moved by the tip of screw whe it is give oe complete rotatio, is called the pitch of the screw. Dividig the pitch of screw by the total umber of divisio o the circular scale, we get the distace which the screw advaces o rotatig the screw by 1 divisio o its circular scale. This distace is called the least cout (LC) of the istrumet. Thus LC Total umber of Pitch divisio ( ) o the circular scale Geerally, the screw advaces by 1 or ½ divisio o mai scale whe the screw is give oe rotatio. If there are total 100 divisio o its circular scale ad the value of 1 divisio o mai scale is 0.1 cm, the least cout = cm. Net readig = liear scale readig + least cout circular scale readig. I Fig. 7 the measuremet correspodig to the give positio will be 5.66 mm Refereces: Surveyig Vol. 1 B.C Pumia, Asok Kumar Jai Aru Kumar Jai Egieerig Drawig, Agrawal ad Agrawal Egieerig Graphics, Bhattacharya ad Bera ad web. 5