Measurement

Predictions, Ch. 1, Activity 2

Measurements

• What form of measurement existed 2,000 years ago?– Parts of the body were originally used:

• Palms

• Hands (in use today)

• Digits

• Feet (in use today)

• Cubit (still referenced today)

Measurements

• Circumference of the Earth was determined by Erathosthenes (276 – 195 B.C.) by comparing the noontime shadows in two different cities and determining the differing angle of the sun at each location– He assumed a spherical Earth

SI System

– Sytems International• Regulated by the International Bureau of Weights

and Measures in France.

• NIST (National Institute of Science and Technology in Maryland).

– SI maintains the standards for:• Length (meter)

• Time (second)

• Mass (kilogram)

Standard Units of Measurement

• Meter (m):– Circa 1790 - Originally defined as the

1/10,000,000 of the distance between the North Pole and the Equator.

– Circa 1890 - defined as the distance between two lines on a platinum-iridium bar.

– In 1983 it was defined as the distance that light travels in a vacuum in 1/299792458 s.

Measurement Error

• Random error:– Error that occurs due to the inherent

uncertainty in any measurement tool.– Error that is the result of the natural variability

in any measurement.

• Systematic error:– Error that occurs due to improperly reading or

recording a measurement.

Precision

• Precision is a measure of the repeatability of a measurement. The smaller the variation in experimental results, the better the repeatability.

• Precision can be improved by instruments that have high resolution or finer measurements.– e.g. A ruler with millimeter (mm) divisions has

higher resolution than one with only centimeter (cm) divisions.

Which group of data has better precision?

TrialMeasurements

Group 1 Group 2

1 10 10

2 15 11

3 5 14

4 13 13

5 17 12

Average 12 12

Accuracy

• How close are your measurements to a given standard?– Accuracy is a measure of the closeness of a

body of experimental data to a given known value.

– In the previous table, the data would be considered inaccurate if the true value was 15, whereas it would be considered accurate if the standard value was 12.

Estimation

• When a precise measurement is not necessary use an estimate.– An estimate relies on past experiences and

good judgment.• A college football player has a mass of 100 kg.

– Since 100 kg is about 220 lbs, this appears to be a good estimate.

• A high school basketball player is 4 m tall.– 4 m is about 14 feet! Not a good estimate.

Estimation

• Your teacher works 1440 minutes every day.– That is every minute in 24 hours!

• A poodle has a mass of 60kg– Not a toy poodle. Maybe a standard poodle.

• Your classroom has a volume of 150m^3.– Not too far off

• The distance across the school grounds is 1km.– Again, close.

Precise Measurements

• How would you record this measurement using a centimeter ruler? – 5.15 centimeters.– Measure to the smallest division + 0.5.

Precision: What do you think?

• An Olympic swimming pool is 50 m long. How precise do you think that is?

• An oil tanker holds 5x10^6 barrels of oil. How precise is this?

• A 2” x 4” piece of lumber is a standard size. How precise do you think this measurement is?

Measurement tools

• When would you use each of these?– Meterstick– Ruler– Measuring tape– Vernier caliper– Micrometer caliper

Measurement

• What does it mean to calibrate?