Chapter 1 Physical Quantities, Units, Measurements and Estimation In the quest to understand nature, scientists use physical quantities to describe the world around us.

A real life story… Gimli Glider

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.

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

Precision different measuring instruments have different precisions. -Ruler = 0.1 cm -Vernier calipers = 0.01 cm -Micrometer screw gauge = 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 & Precision

Significant Figures Example 1: 7.12  1.23 x 12 = leave to lowest sf Example 2: = leave to lowest d.p Example 3: ( )  (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 prefixes Speed of light = m/s Size of atom = m Secret world.

Prefixes

Vernier caliper

Micrometer Screw Gauge

vernier calipers Zero 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 zero error = cm main scale (fixed) vernier scale (movable) 01 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. vernier calipers Zero Error

supposing observed reading is 4.03 cm, then corrected reading = observed reading – zero error = 4.03 – (-0.02) = 4.05 cm 010 zero error = cm main scale (fixed) vernier scale (movable) 01 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 vernier calipers Zero Error

micrometer screw gauge accuracy = 0.01 mm / cm anvilspindlesleevethimbleratchet frame Micrometers measure small diameters or thicknesses. Zero Error

micrometer screw gauge reading on sleeve = 4.5 mm reading on thimble = 0.12 mm actual reading of object = = 4.62 mm thimble sleeve Zero Error

micrometer screw gauge 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. Zero Error

micrometer screw gauge 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 Zero Error

micrometer screw gauge 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 Zero Error