Physics 3.1 Measurements and their errors PPQs

- PPQ C+ - Why is the ratchet used rather than the thimble to close a micrometer screw gauge around a wire?

The thimble could apply excessive force, causing the wire to deform/change diameter and give an incorrect reading.

- PPQ C+ - A measured diameter has a percentage uncertainty of 1.2%. The density is calculated from an equation in which ρ ∝ μ/d², and μ has a percentage uncertainty of 2.0%. Calculate the percentage uncertainty in ρ.

For powers, multiply the percentage uncertainty by the power: 2(1.2%) + 2.0% = 4.4%.

- PPQ C+ - Why can the absolute uncertainty in a calibrated measurement increase as the measured quantity increases?

The scale markings become closer together as the quantity increases, so the same uncertainty in reading the scale corresponds to a larger absolute uncertainty in the measured quantity.

- PPQ C+ - Why does increasing the distance measured with a stopwatch reduce percentage uncertainty in the measured time?

The absolute uncertainty in the time remains approximately the same, while the measured time increases, so the percentage uncertainty decreases.

- PPQ C+ - A distance is determined from two position readings, each with an uncertainty of ±1 mm. What is the absolute uncertainty in the distance?

Add the absolute uncertainties: ±1 mm + ±1 mm = ±2 mm.

- PPQ C+ - Four measurements of a time are taken. How is the mean time determined?

Add all readings and divide by the number of readings: mean = sum of readings ÷ number of readings.

- PPQ C+ - How can repeated measurements be used to reduce the effect of random uncertainty?

Take several readings and calculate the mean; random variations tend to cancel out.

- PPQ C+ - A graph is used to determine the value of a quantity at a minimum. How should the minimum be determined?

Draw a best-fit curve and read the value of the independent variable where the curve reaches its minimum.

- PPQ C+ - What further measurements should be taken to reduce the uncertainty in the value of a minimum found from a graph?

Take more readings around the minimum.

- PPQ C+ - Why is a search coil unsuitable for detecting a constant magnetic flux?

A search coil requires changing magnetic flux to induce an emf; constant flux produces no induced emf. **(Uses electromagnetic induction: an emf is induced when magnetic flux linkage changes.)**

- PPQ C+ - A coil is rotated through 25° and the magnetic flux density changes from B to B cos 25°. Calculate the percentage change.

Percentage change = (1 − cos 25°) × 100 ≈ 9.4% decrease. **(Uses the magnetic-field relationship for the component of magnetic flux density: B_component = B cos θ.)**

- PPQ C+ - An angle is determined from two protractor readings, each with an uncertainty of ±0.5°. What is the absolute uncertainty in the angle?

The angle is the difference between two readings, so absolute uncertainty = 0.5° + 0.5° = ±1°.

- PPQ C+ - A liquid has a curved meniscus. Where should the volume be read?

Read the bottom/lowest point of the meniscus.

- PPQ C+ - What is the percentage uncertainty in a quantity calculated by multiplying or dividing measured quantities?

Add the percentage uncertainties of the quantities involved.

- PPQ C+ - What is the percentage uncertainty in a quantity calculated by adding or subtracting measured quantities?

Add the absolute uncertainties, then convert the resulting absolute uncertainty to a percentage of the calculated value.

- PPQ C+ - A quantity is proportional to x². How does the percentage uncertainty in x affect the percentage uncertainty in the quantity?

The percentage uncertainty is multiplied by 2.

- PPQ C+ - A quantity is proportional to s/t². The percentage uncertainty in s is known and the percentage uncertainty in t is known. How is the percentage uncertainty in the quantity determined?

Add the percentage uncertainty in s to twice the percentage uncertainty in t. **(The relationship s/t² comes from the mechanics equation being used for the measured quantity; the uncertainty rule itself is from 3.1.)**

- PPQ C+ - A measured charge is (8.0 ± 1.0) × 10⁻¹⁹ C. How can the uncertainty be used to assess whether charge quantisation is supported?

Compare the possible range of charge values with integer multiples of 1.60 × 10⁻¹⁹ C. If the range overlaps several integer multiples, the measurement cannot confirm charge quantisation. **(Uses the particle-physics value of the elementary charge and the idea that charge occurs in integer multiples of e.)**

- PPQ C+ - A measurement has several percentage uncertainties and the quantity depends on one measured quantity cubed. How is its percentage uncertainty determined?

Multiply the percentage uncertainty of the cubed quantity by 3, then add the percentage uncertainties of the other multiplicative/divisive quantities.

- PPQ C+ - Convert 1.30 MeV into joules.

1 MeV = 10⁶ eV and 1 eV = 1.60 × 10⁻¹⁹ J, so 1.30 MeV = 2.08 × 10⁻¹³ J. **(Uses the electronvolt energy unit from particle physics; the conversion itself is part of SI units and prefixes.)**