Hands-on: Vernier calipers

Parts of a vernier caliper

 

 

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Scale

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Here I’m trying to measure the width of my eraser, which is 2.41 cm.

Other measurements:

– Pen width: 0.96 cm

– Water bottle width: 7.86 cm

– iPhone 4 width: 5.99 cm

* The picture is a little slanted, so there might be some parallax error if you look at the reading from here.

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Using measuring instruments

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Vernier calipers

Precision: 0.1 mm, for things between 1 and 10 cm long

Typed instructions: How to use and read

Animation:

Using_the_caliper_new_en

Zero error: (measured when the jaws are closed)

  1. None – when the 0 mark of both scales are in line with each other
  2. Positive – when the 0 mark of the vernier scale is to the right of the fixed scale’s 0 mark.

How to remove: Count it from the left of the vernier scale (0 mm->). For example, if the 0.6 mm marking on the vernier scale coincides with a marking on the main scale, the zero error is +0.6 mm. Therefore, subtract 0.6 mm from the final reading.

3. Negative – when the 0 mark of the vernier scale is to the left of the fixed scale’s 0 mark.

How to remove: Count it from the right of the vernier scale (<-1.0 mm). For example, if the 0.6 mm marking on the vernier scale coincides with a marking on the main scale, the zero error is -0.4 mm instead because it is counted from the right. Therefore, add 0.4 mm to the final reading.

Micrometer screw gauge (aka MSG 🙂

Precision: 0.01 mm, for things less than 1 cm long

Parts:

vfig10a

Steps:

  1. Turn the thimble until the spindle and anvil are nearly touching the object. Do not squash it!
  2. To fine-tune the measurement, turn the ratchet until it starts to click. This is when the spindle and anvil are touching the object
  3. Lock the micrometer screw gauge.

Animation:

Micrometer_no_zero_error

Zero error:

  1. None – The 0 mark on both the datum line and the thimble are in a straight line.
  2. Positive – The 0 mark on the thimble is below the datum line.

How to remove: Take the reading on the thimble and subtract it from the final reading.

3. Negative – The 0 mark on the thimble is above the datum line.

How to remove: Count the number of divisions between the 0 marks of the datum line and thimble. Add this reading to the final reading.

* Pendulum

An oscillation is one complete to-and-fro movement of the bob.

A period is the time taken to complete an oscillation.

– Only the length of the pendulum affects the period of an oscillation!

What is it used for?

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Significant Figures and calculations

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What are significant figures anyway?

(According to Google search: What are significant figures)

Each of the digits of a number that are used to express it to the required degree of accuracy, starting from the first nonzero digit.

How do you know if a digit is a significant figure?

  1. It is a non-zero number. (e.g. 122 – 3 sf)
  2. It is a zero between non-zero numbers. (e.g. 102 – 3 sf)
  3. It is a final zero after a decimal point (e.g. 2.0 cm – 2 sf)
  4. In a number < 1, it is a zero after a non-zero number (e.g. 0.20 cm – 2 sf)

Not a significant figure:

  1. Leading zeros in a number < 1 (e.g. 0.002 cm – 1 sf)
  2. In a non-decimal number, final zeros may/may not be significant

e.g. 102000 cm – may be 3/4/5/6 sf depending on the original number it is derived from

Important!

102000.00 has 8 significant figures! (Refer to rule 3)

Exam format: How to use significant figures and decimal places in calculations?

The general rule is to round the answer to the least precise measurement used in
the calculation.

Addition/ Subtraction (+/-): Follow the term with the least number of decimal places

E.g. 3.55 cm + 0.1 cm = 3.7 cm NOT 3.65 cm

Multiplication/ Division (×/ ÷): Follow the term with the least number of significant figures

E.g. 4.0 m / 2 s = 2 m/s NOT 2.0 m/s

Combined measurements:

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Ignore counting numbers:

e.g. 1000 cm / 24 –> The answer will be in 4 sf (following 1000 cm)

How to use significant figures in unit conversion?

Ensure that the converted figure has the same number of significant figures as the original figure.

e.g. 0.3 m = 30 cm (as 0.3 m only has 1 sf, the converted figure 30 cm only has 1 sf too)

0.30 m = 30 cm (since 0.30 m now has 2 sf, 30 cm has 2 sf as well)

Note: Assume that all digits are sf when the original figure has final zeros.

e.g. 50 mm = 0.050 m (2 sf)

 

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