H2 Physics - Measurement

State what is meant by a homogenous equation

It is when every term on both sides of the equal sign of the equation has the same units

State 2 facts about homogenous equations

• An equation which is not homogenous is wrong.

• A homogenous equation does not imply the equation is correct.

State the quantity assigned to the 8 main prefixes.

• Pico- (10^-12) (p)

• Nano- (10^-9) (n)

• Micro- (10^-6) (μ)

• Milli- (10^-3) (m)

• Kilo- (10³) (k)

• Mega- (10⁶) (M)

• Giga- (10⁹) (G)

• Tera- (10¹²) (T)

State 3 reasons why there are uncertainties in measurements.

• Limitations of the instrument (e.g. its resolution)

• Limitations of the object/material (e.g. a liquid with an uneven meniscus, measuring the length of a soft compressible material - it may deform when measuring)

• Limitations of the method/procedure of the measurement (e.g. human reaction time, parallex error)

Define the resolution of an instrument.

It is the smallest graduation on the scale.

State the 2 kinds of errors.

• Systematic error

• Random error

Define systematic error.

Systematic errors are errors which result in measurement/readings always either above or below the true value by a fixed amount.

Give 2 examples of systematic error.

• Not accounting for zero-error in measurement.

• Not accounting for background radiation when measuring activity of a radioactive source.

Define random error.

Random errors are errors which result in measurements/readings scattered around a mean value, with an equal probability of being positive or negative.

State 2 ways that random errors can be reduced.

• Repeating the measurements and finding the average value.

• Plotting a graph and drawing a line of best fit for the plotted points.

Give 2 examples of random error.

• Variation in the diameter of a piece of wire.

• Fluctuation in the count-rate of a radioactive decay.

Define accuracy.

It is the degree of closeness of the mean value of the measurements to the true value.

Define precision.

It is the degree of agreement between repeated measurements of the same quantity.

Which error is accuracy affected by?

Systematic errors

Which error is precision affected by?

Random errors

Define responsiveness of an instrument.

It is the ability of an instrument to detect rapid variations in the quantity being measured.

Define sensitivity of an instrument.

It is the ability of an instrument to detect small changes in the quantity being measured.

Define reliability of an instrument.

It is a measure of the confidence that can be placed in a set of measurements. A reliable set of measurements are both accurate and precise.

Define reproducibility.

It is the agreement between repeated measurements of the same physical quantity.

State the rounding of sf for absolute uncertainty.

1 sf

State the rounding of sf for fractional uncertainty.

2 sf

State the rounding of sf for percentage uncertainty.

2 sf

State the 3 main uncertainty formulae.

• ΔQ = |a|ΔX + |b|ΔY (if Q = aX ± bY)

• ΔQ/Q = |m|ΔX/X + |n|ΔY/Y (if Q = Xᵐ [* or /] Yⁿ)

• ΔQ = (Qₘₐₓ - Qₘᵢₙ)/2