chapter 1 physical quantities, units, measurements and estimation in the quest to understand nature,...

Chapter 1

Chapter 1

Physical Quantities, Units, Measurements and Estimation

Physical Quantities, Units, Measurements and Estimation

In the quest to understand nature, scientists use physical quantities to

describe the world around us.

In the quest to understand nature, scientists use physical quantities to

describe the world around us.

A real life story… Gimli GliderA real life story… Gimli Glider

Nasa’s “Mars Climate Orbiter”Nasa’s “Mars Climate Orbiter”

Two Teams, Two Measures Equaled One Lost Spacecraft (New York Times, October 1, 1999)Simple confusion over whether measurements were metric or not led to the loss of a $125 million spacecraft last week as it approached Mars, the National Aeronautics and Space Administration said on Thursday.

An internal review team at NASA's Jet Propulsion Laboratory said in a preliminary conclusion that engineers at Lockheed Martin Corporation, which had built the spacecraft, specified certain

measurements about the spacecraft's thrust in pounds, an English unit, but that NASA scientists thought the information was in the metric measurement of newtons.

The resulting miscalculation, undetected for months as the craft was designed, built and launched, meant the craft, the Mars Climate Orbiter, was off course by about 60 miles as it approached Mars.

AccuracyAccuracy

• refers to the degree to which an experimental result agrees with the expected value.

PrecisionPrecision

• different measuring instruments have different precisions.

-Ruler = 0.1 cm

-Vernier calipers = 0.01 cm

-Micrometer screw gauge = 0.001 cm

• Actual Height of Ms Tan = 1.59 m

• Precise but not accurate answer = 1.57 m

• Accurate and not precise answer = 1.6 m

Accuracy & PrecisionAccuracy & Precision

Significant FiguresSignificant Figures

Example 1:7.12 1.23 x 12 = leave to lowest sf

Example 2: 98.23 - 0.744 = leave to lowest d.p

Example 3:(5.65 + 0.0547) (0.11 x 5.4) = finally to 2 sf

For multiplication and division

For additional and subtraction

Leave to 2 d.p Leave to 2 sf

Using prefixesUsing prefixes

Speed of light = 300 000 000 m/s

Size of atom = 0.000000000010 m

Secret world.

Prefixes

Vernier caliperVernier caliper

http://www.members.shaw.ca/ron.blond/Vern.APPLET/index.html

Micrometer Screw GaugeMicrometer Screw Gauge

http://www.members.shaw.ca/ron.blond/Micrometer.APPLET/index.html

vernier calipers vernier calipers

Zero ErrorZero Error

When the two jaws of the vernier calipers touch each other, both zero marks on the main scale and on the vernier scale should coincide.

If not, there is a zero error in the vernier calipers.

When the two jaws of the vernier calipers touch each other, both zero marks on the main scale and on the vernier scale should coincide.

If not, there is a zero error in the vernier calipers.

supposing observed reading is 3.24 cm, then corrected reading = observed reading – zero error = 3.24 – (+0.01)

= 3.23 cm

0 105

zero error = +0.01 cm

main scale (fixed)

vernier scale (movable)

0 1

If the two jaws touch each other, but the zero marks of the main scale and vernier scale do not coincide as shown below, the zero error is positive.

If the two jaws touch each other, but the zero marks of the main scale and vernier scale do not coincide as shown below, the zero error is positive.



supposing observed reading is 4.03 cm, then corrected reading = observed reading – zero

error = 4.03 – (-0.02)

= 4.05 cm

0 10

zero error = -0.02 cm

main scale (fixed)

vernier scale (movable)

0 1

If the two jaws touch each other, but the zero marks of the main scale and vernier scale do not coincide as shown below, the zero error is negative.

5



micrometer screw gaugemicrometer screw gauge

accuracy = 0.01 mm / 0.001 cm

anvil spindle sleeve thimble ratchet

frame

Micrometers measure small diameters or thicknesses.Micrometers measure small diameters or thicknesses.



reading on sleeve = 4.5 mmreading on thimble = 0.12 mmactual reading of object = 4.5 + 0.12

= 4.62 mm

thimblesleeve



When the anvil and spindle of the micrometer touch each other, the scales should read zero.

If not, there is a zero error in the micrometer.

When the anvil and spindle of the micrometer touch each other, the scales should read zero.

If not, there is a zero error in the micrometer.



If the anvil and spindle touch each other, but the scales do not read zero as shown below, the zero error is positive.If the anvil and spindle touch each other, but the scales do not read zero as shown below, the zero error is positive.

supposing observed reading is 2.37 mm, then corrected reading = observed reading – zero error = 2.37 – (+0.02)

= 2.35 mm

supposing observed reading is 2.37 mm, then corrected reading = observed reading – zero error = 2.37 – (+0.02)

= 2.35 mm

} 2 divisions



If the anvil and spindle touch each other, but the scales do not read zero as shown below, the zero error is negative.If the anvil and spindle touch each other, but the scales do not read zero as shown below, the zero error is negative.

supposing observed reading is 2.87 mm, then corrected reading = observed reading – zero error = 2.87 – (-0.03)

= 2.90 mm

supposing observed reading is 2.87 mm, then corrected reading = observed reading – zero error = 2.87 – (-0.03)

= 2.90 mm

} 3 divisions


chapter 1 physical quantities, units, measurements and estimation in the quest to understand nature,...

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