1.2 Uncertainties & Errors

The length l of a simple pendulum is increased by 6%.

The time period T of a pendulum is also related to the amplitude of oscillations θ. Measurements are taken and a graph is obtained showing the variation of with angular amplitude θ, where T₀ is the period for small amplitude oscillations:

Typically, using a simple pendulum to determine the acceleration of free fall g involves measuring the periodic time T and the pendulum length l. 

An experiment is designed to explore the relationship between the temperature of a ball T and the maximum height to which it bounces h. 

The ball is submerged in a beaker of water until thermal equilibrium is reached. The ball is then dropped from a constant height and the height of the first bounce is measured. This is repeated for different temperatures. The results are shown in the graph, which shows the variation of the mean maximum height h_mean with temperature T:

The experimenter hypothesises, from their results, that h_mean is proportional to T². 

It is known that the energy per unit time P radiated by an object with surface area A at absolute temperature T is given by:

P = eσAT⁴

where e is the emissivity of the object and σ is the Stefan-Boltzmann constant.

In an experiment to determine the emissivity e of a circular surface of diameter d, the following measurements are taken: 

• P = (3.0 ± 0.2) W
• d = (6.0 ± 0.1) cm
• T = (500 ± 1) K

The power dissipated in a resistor can be investigated using a simple electrical circuit. The current in a fixed resistor, marked as 47 kΩ ± 5%, is measured to be (2.3 ± 0.1) A. 

A student investigates the relationship between two variables T and B. Their results are plotted in the graph shown: 

The student suggests that the relationship between T and B is of the form:

where a and c are constants. To test this suggested relationship, the following graph is drawn: