Last revised 16/04/2021

2.1 Pendulum system and measurement

Curriculum links

ACSSU190 Energy conservation in a system can be explained by describing energy transfers and transformations. KEY IDEAS • Energy transfers and transformations accompany observable events and processes. • Kinetic energy is energy associated with the movement of objects or the random motion of particles, such as atoms and molecules. • Potential energy is associated with fields – electrical, magnetic or gravitational.

ACSHE191 Scientific understanding, including models and theories, is contestable and is refined over time through a process of review by the scientific community.

ACSHE192 Advances in scientific understanding often rely on technological advances and are often linked to scientific discoveries.

ACSIS198 Formulate questions or hypotheses that can be investigated scientifically.

ACSIS199 Plan, select and use appropriate investigation types, including field work and laboratory experimentation, to collect reliable data; assess risk and address ethical issues associated with these methods.

ACSIS200 Select and use appropriate equipment, including digital technologies, to collect and record data systematically and accurately.

ACSIS203 Analyse patterns and trends in data, including describing relationships between variables and identifying inconsistencies.

ACSIS204 Use knowledge of scientific concepts to draw conclusions that are consistent with evidence.

Lesson outcomes At the end of this activity students will be able to: • explain that a simple pendulum is a system involving the pendulum and the Earth • determine through experimentation which variables affect the motion of a simple pendulum • explain the relationship between the simple pendulum and the international unit of measurement of distance: the metre.

Motion and Energy Transfer 1 Last revised 16/04/2021

Key vocabulary: Pendulum, system, period, metre, kinetic energy, gravitational potential energy. Equipment list: Each GROUP will require: • heavy retort stand • heavy cotton or light string • masses (50 g to 1 kg) • metre ruler • stopwatch. Each STUDENT will require: • Science by Doing Notebook. Things to consider This is an inquiry activity, with minimal guidance for students. In Step 1, they are given the basic equipment and the instruction to build a seconds pendulum (a pendulum that takes one second to swing from one side to the other, or two seconds to swing forwards and back to its original position). They should have sufficient time to determine possible variables and to test them. Teacher content information: Mass - Students will discover that varying the mass of the pendulum has no effect on its motion. Amplitude - Adjusting the amplitude of the swing has a minimal effect, within a range of about plus or minus five per cent, but not sufficient to solve the problem. Length - The only significant variable is the length of the pendulum which is measured from the point of suspension to the centre of mass of its bob. The equation describing this relationship is

푙 푇 = 2휋√ 푔

T is the period of the pendulum in seconds (time for one complete swing forward and back), l is the pendulum length in metres, g is the acceleration due to gravity in m/s2. The only variable (other than T) in the equation is l, which is the only variable that affects the period of a pendulum. The other key aspect of this activity is accurate measurement. Students must determine the time taken for one half period of a pendulum of one second. Simply timing one swing of the pendulum would involve a measurement error of about ten per cent (+/- 0.1 s). The most obvious way to improve this situation is to take multiple measurements. If 10 swings are measured, the measurement error is reduced to one per cent (+/- 0.01 s). Similarly, by recording all the individual pendulum lengths for the whole class and calculating the average, a more accurate estimate of this variable can be obtained. This gives students a sense of why scientists often carry out multiple replicates to achieve more accurate results.

Motion and Energy Transfer 2 Last revised 16/04/2021

You should find this second pendulum has a length very close to one metre. This seems coincidental; that a pendulum that takes exactly one second to swing from one side to the other should have a length of exactly one metre. In fact, there is a historical significance to these values, dating back to when the French Système international (basically our metric system) was being established in France. (Incidentally, this was also the time of the French revolution). The seconds pendulum was a contender for a standardized unit of length (the metre). In the end, it was not accepted as the standardized unit due to variations with latitude and altitude and different geographic positions on the Earth’s surface, but the approximate length was retained as a convenient one to work with. It was standardized against the length of the longitude between the North Pole and the equator passing through Paris. A system can be "closed" or "open". A closed system has no matter entering or leaving it. The pendulum system is a closed system. A system can be "isolated" or "non-isolated". An isolated system has no energy flowing in or out. If we can accept that the loss of energy of the pendulum through air resistance is negligible, then the pendulum system is an isolated system. Lesson plan Step 1: Students construct a pendulum with a period of exactly two seconds. This pendulum takes one second to swing from one side to the other and has historically been called a seconds pendulum. This pendulum must be what is described as a simple pendulum. This means the string is as light as possible, the mass is as small as possible, and the string is firmly attached to its support so there is no movement at the fulcrum. Step 2: Students should consider the most accurate way to measure if their pendulum takes exactly one second to swing from one side to the other. Step 3: When they think they have a pendulum with a total period of exactly two seconds, they should let you know. Step 4: Once you have checked a student’s pendulum, they should measure its length from the centre of the swinging mass to the fulcrum. Students write this result on the class board. Step 5: Invite a class discussion of each of the discussion questions. Follow-up: Show students the video ‘How we measure time’ (1:30 minutes) by Australia’s Chief Metrologist, Dr Bruce Warrington from the National Measurement Institute. https://www.youtube.com/watch?v=oPLirFEFflY

Motion and Energy Transfer 3