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Info
For this experiment, it is not necessary to use your own laptop (other than to take notes).

1.      Context of the Experiment

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  • Knowing: uncertainty, complete measurement, errors, steps in handling calipers
  • Abilities: calculate uncertainties and absolute/relative errors, handling calipers, choosing the correct measurement instrument
  • Understand: measurement accuracy and being able to assess it, review of measurement method

3.      Literature

Necessary further reading: how to use a caliper!, error propagation, rounding to significant figures!:

[1] DIN 1319-4. Grundlagen der Meßtechnik. Teil 3: Auswertung von Messungen - Meßunsicherheit (9.2). Ausgabe 2, Februar 1999.

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[5] Lectures: MT-Motivation, Measurement TheoryNecessary further reading: how to use a caliper!, error propagation, rounding to significant figures!


4.      Basics/Fundamentals

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Mathinline
body--uriencoded--Average: x ̅\bar%7Bx%7D=\cfrac%7B1%7D%7BN%7D \sum \limits_%7Bi=1%7D%5e%7BN%7Dx_i=\cfrac%7Bx_1+x_2+x_3+⋯+x_N%7D%7BN%7D
(1)

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Mathinline
body--uriencoded--Uncertainty propagation: u_y=\sqrt%7B\sum \limits_%7Bi%7Bj=1%7D%5e%7BN%7D \left(\cfrac%7B∂f(x_ij)%7D%7B∂x_i )%7D uj%7D a_%7Bx_i%7Dj%7D\right)%5e2 %7D
(3)

A complete measurement result for a statistically determined quantity x is therefore

Mathinline
body--uriencoded--x=M_x \pm u_x = \bar%7Bx%7D \pm \sigma_x
with the measurand Mx and the uncertainty ux.

4.3 vernier caliper gauge

There are four three types of measurements that can be made with a vernier caliper gauge: Inside measurements, outside measurements , and depth and steps.
When the vernier caliper is closed, the scale should read exactly 0. To take a measurement of an inside dimension, the jaws of the caliper are now opened until they exactly cover the area to be measured. To measure an outside dimension, the caliper jaws are opened and then closed again until they touch the object. For measuring depths (e.g. drilled holes), the depth gauge at the end of the caliper can be used - the main element of the caliper is pressed against the higher surface and the depth gauge is positioned at the deepest point of the hole.

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Examples:  3.123*4.54=14.18     2     3.123*0.1=0.3     3.123*0.0012=0.0037

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1.1.1 Measure the inner diameter of the o-ring using the caliper and the ruler. Note both values.

1.1.2 Which value is more exactcloser to the real value?

1.2 Find out, which of the two flat objects is thicker, has a higher thickness t, object A or B.

Drawio
bordertrue
viewerToolbartrue
fitWindowfalse
diagramNamethickness
simpleViewerfalse
width
diagramWidth358
revision2

Fig. 1: object A (left) and object B (right)

1.3 Cylinder measurement:

   1.3.1 Pick one of the cylinders cylinder and measure its length and diameter.

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   1.3.3 Now ask your neighbor to measure your wooden part cylinder with their caliper!

  • Did 1.3.1, 1.3.2 and 1.3.3 yield the same result? Which of the steps was for testing reproducibility (A) and which for repeatability (B)?

1.4 Measure Take the measurements of the cylinder again to find the volume of the cylinder again by carrying out the following steps:

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1.4.2 Calculate the propagated uncertainty (using the accuracy as uvariable uncertainty ax) and supply a complete measurement of the volume (rounded to significant figures and including the uncertainty)! Use the equation given in the explanation 4.2.

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For this, first calculate the standard deviation for each measured variable (d, l and w) and then use this as the uncertainty of the variable axj for the calculation of the propagated uncertainty.

1.5.3 Calculate the amount of beans that fit into the container (47 x 39 x 55 mm) you took them from.  Assume that there is no air in between the beans. Just consider the absolute volume of the container and the beans.

1.6 (creative) Find a way to measure the volume of a very irregular shape (e.g. your hand) and describe your steps.

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The following values should be entered to vips in Stud.ip:. Please note that only 30 minutes are available for entering values in vips, after which the vips entry is automatically terminated. The test is only to hand in the final values, so be prepared and have all values ready and at hand!

  1. Matriculation number
  2. reproducibility
  3. repeatability
  4. instrument accuracy (1.4.1)
  5. complete measurement of the volume of the cylinder 1.4.2
  6. table from 1.5.1
  7. complete measurement result for 1.5.2 volume
  8. number of beans in the container 1.5.3
  9. (free text) explain your measurement steps and the final result of 1.6