01 Measurements, Physical Quantities, Units

What are the SI base units?

• A basic set from which all other SI units can be derived

Dervived units

• defined in terms of the seven base quantities via a system of equations

• SI derived units for these derived quantities can be obtained from these equations and the seven SI base units

Derived physical quantities

Prefixes

Reading

• only one judgement is needed

• precision is half the smallest division

Measurement

• 2 judgements are needed

• precision is the smallest division of the scale

Precision

• a measurement is precise if it is close to other values obtained by repeating the determination using the same procedure

• also refers to the smallest measurement that can be read using an instrument

Resolution

• smallest division that can be read off the scale of an instrument

• instrument with a better resolution is more precise

Accuracy

• a measurement is accurate if it is close to the true value

Error

• anything that causes a measurement to differ

• parallex error: incorrect positioning of the eyes while taking a reading on a measuring scale

• random error: influences from environment, fluctuations in instrument etc. Does not cause the same error every time

• zero error: occur when measuring instruments are not properly calibrated (i.e. not at 0)

Rules for significant digits

1. All non-zero digits are significant

2. Zeros between two significant digits are always significant

3. Trailing zeros (on the right) in a number containing a decimal point are significant

4. Leading zeroes (on the left) in a number containing a decimal point are not significant

5. The significance of trailing zeroes in a number not containing a decimal point can be ambiguous (see what question wants)

6. In scientific notation, all digits before the multiplicaiton sign are significant

Digital calipers (precisions + parts)

• precision 0.1 mm or 0.01 cm (record one less than digital display, to account for significant source of error)

• Outside jaws

• Inside jaws

• Tail

Digital calipers: use of parts

• Outside jaws

  • To measure external diameter or width of an object

• Inside jaws

  • to measure internal diamter of object

• Tail

  • to measure depth of an object

Digital micrometer screw gauge (precision + parts)

• precision: 0.01 mm or 0.001 cm (record 1 less dp than digital display, to account for other significant source of error, eg overtightening)

• anvil

• spindle

• lock

• scale

• ratchet

• thimble

How to use digital micrometer screw guage

1. Before measurement, wipe down the anvil and spindle surfaces with a clean cloth. This removes dirt and dust from the surfaces, which enables accurate measurements.

2. Switch on the micrometer.

3. Turn the ratchet until the anvil just meets the spindle (clicking sound).

4. Press the zero button to reset the displayed length to zero.

5. Ensure the unit chosen is mm.

6. Place the object between the anvil and the spindle and rotate the thimble till the two surfaces are close to (but not touching) the object.(prevents damage to instrument and inaccurate reading

7. Then turn the rachet until the object is just gripped between the anvil and spindle (you hear a clicking sound). This prevents over-tightening and ensures that there is identical pressure applied on the object.

8. Record the reading displayed.

Simple pendulum

• One complete oscillation is from B to A to C and back to B

• T, Period: time taken for the pendulum to complete one oscillation

• frequency refers to the number of complete oscillations the pendulum makes in one second

  • f = 1/T where T is in seconds

  • SI unit for frequency is Hertz (Hz)

• period T is only dependent on length of the simple pendulum

• errors increase when the pendulum is swinging

  • with large angular amplitude

  • not swining in a vertical plane

Density

• defined as the mass per unit of volume of a body

• ρ = m/v

• measures how compact the particles are packed in a unit volume

• for a mixture of substances, averge desnity = total mass/total volume

• density of water = 1.0 g cm^-3

• = 100 kg m^-3