Limitation of Physical Measurements (AQA A Level Physics)

The measurement of a physical quantity may be subject to random errors and systematic errors.

Which statement is correct?

In an experiment, a radio-controlled car takes 2.50 ± 0.05 s to travel 40.0 ± 0.1 m.

What is the car’s average speed and the uncertainty in this value?

Four students each made a series of measurements of the acceleration of free fall g. The table shows the results obtained.

Which set of results could be described as precise but not accurate?

The Young modulus of the material of a wire is to be found. The Young modulus E is given by the equation below.

E =

The wire is extended by a known force and the following measurements are made.

Which measurement has the largest effect on the uncertainty in the calculated value of the Young modulus?

The strain energy W of a spring is determined from its spring constant k and extension x. The spring obeys Hooke’s law and the value of W is calculated using the equation shown.

The spring constant k is 100 ± 2 N m^–1 and the extension x is 0.050 ± 0.002 m.

What is the percentage uncertainty in the calculated value of W?

Four different students use a ruler to measure the length of a 15.0 cm pencil. Their measurements are recorded on four different charts.

Which chart shows measurements that are precise but not accurate?

Some students carry out an experiment to determine the resistivity of a metal wire.

They determine the resistance from measurements of potential difference between the ends of the wire and the corresponding current.

They measure the length of the wire with a ruler and the diameter of the wire using a micrometer. Each measurement is made with an uncertainty of 1 %.

Which measurement gives the largest uncertainty in the calculated value of the resistivity?

When comparing systematic and random errors, the following properties of errors were recorded:

Which properties apply to random errors?

A steel wire is stretched in an experiment to determine the Young modulus for steel.

The uncertainties in the measurements are given below.

What is the percentage uncertainty in the Young modulus?

A researcher plots a graph to investigate the variation of current and potential difference of a resistor, as shown in the diagram.

After realising they have read the manufacturers label of their electrical equipment incorrectly, they determine the size of the error bars shown should decrease.

Which row correctly describes how this will affect the value of the maximum gradient G_max, the minimum gradient G_min, and the resistance of the resistor R?

In an experiment investigating the electrolysis of copper, a student sets out to find the electrochemical equivalent, Z.

The electrochemical equivalent of a substance is the amount of substance deposited on a cathode per Coulomb of charge.

This can be determined using the equation:

Z = 

Where:

• Mass of cathode before passing current, m₁ = (56.32 ± 0.01) × 10^–3 kg

• Mass of cathode after passing current, m₂= (51.28 ± 0.01) × 10^–3 kg

• Current,  = (3.00 ± 0.05) A

• Time, = (4800 ± 1) s

What is the largest possible value of Z from these readings?

A student uses a digital ammeter to measure a current. The reading of the ammeter is found to fluctuate between 1.98 A and 2.02 A.

The manufacturer of the ammeter states that any reading has a systematic uncertainty of ±1%.

Which value of current should be quoted by the student?

The uncertainty in the value of the momentum of a trolley passing between two points X and Y varies with the choice of measuring devices.

Measurements for the same trolley made by different instruments were recorded as follows:

Which measurements, one for each quantity measured, leads to the least uncertainty in the value of the momentum of the trolley?

In an experiment to determine the acceleration of free fall g, a ball bearing is held by an electromagnet.

When the current to the electromagnet is switched off, a clock starts, and the ball bearing falls. After falling a distance h, the ball bearing strikes a switch to stop the clock which measures the time t of the fall.

Systematic errors may cause t and h to be measured incorrectly.

Which of the following must cause g to appear greater than 9.81 m s^–2?

The diagram shows an experiment to measure the speed of a small ball falling at constant speed through a clear liquid in a glass tube.

There are two marks on the tube. The top mark is positioned at 115 ± 1 mm on the adjacent rule and the lower mark at 385 ± 1 mm. The ball passes the top mark at 1.50 ± 0.02 s and passes the lower mark at 3.50 ± 0.02 s.

The constant speed of the ball is calculated to be 135 mm s^–1

Which expression calculates the fractional uncertainty in the value of this speed?

A student finds the density of a liquid by measuring its mass and volume. The following is a summary of his measurements.

mass of empty beaker = (20 ± 1) g

mass of beaker + liquid = (70 ± 1) g

volume of liquid = (10.0 ± 0.5) cm³

He correctly calculates the density of the liquid as 5.0 g cm^–3.

What is the uncertainty in this value?

Max Planck was one of the pioneers of quantum theory. He proposed a system in which the base units are based on the speed of light, c, the gravitational constant, G, and the reduced Planck constant,  , which is equal to Planck’s constant, , divided by 2π:

In the Planck system, length is replaced by the Planck length, , which is theorised to be the smallest distance there is.  is defined by

= 

The percentage uncertainties in the accepted values of G and are ±7 × 10^–2 % and ±6 × 10^–4 % respectively.

What is the corresponding percentage uncertainty in the conversion factor between the Planck length and metres?

A mass is dropped from rest and falls through a distance of 2.0 m in a vacuum. An observer records the time taken for the mass to fall through this distance using a manually operated stopwatch and repeats the measurements a further two times.

The average result of these measured times, displayed in the table below, was used to determine a value for the acceleration of free fall. This was calculated to be 9.8 m s^–2.

Which statement best describes the quality of the measurements taken for this experiment?

A student collects values of the time period, T, of a pendulum at different lengths of string, L. They want to investigate the relationship:

T = 2π

They plot the values on a graph along with the error bars associated with each point, as shown in the diagram.

What is the percentage uncertainty in the experimental value of g?

Which of the following experimental techniques would not reduce the random error of the quantity being investigated?