Pendulums. P3 3.6 Lesson guide. Resources available. Specification. Keywords. Points to note. Lesson objectives

Transcription

1 P3 3.6 Lesson guide Pendulums This lesson explains the relationship between the time period and frequency of a pendulum, and looks at the factors that affect the period of a pendulum. Resources available Student Book lesson P3 3.6 Sheet number Title Sheet type reference P3 3.6a Pendulum starter Teacher and technician sheet P3.2.1e P3 3.6b Investigating a pendulum Student practical sheet P3.2.1e P3 3.6b Investigating a pendulum Teacher and technician sheet P3.2.1e P3 3.6c Natural frequency and resonance Teacher and technician sheet P3.2.1e P3 3.6d Swinging questions Homework sheet P3.2.1d, e P3 3.6e Simple harmonic motion Homework sheet P3.2.1d, e P3.2.1d For a simple pendulum: T = 1/f P3.2.1e The time period depends on the length of the pendulum. Ideas for practical work Plan and carry out an investigation into factors that affect the period of a simple pendulum (mass, length of pendulum, amplitude of swing). How Science Works Controlled Assessment: P4.1.1 Develop hypotheses and plan practical ways to test them; P4.2.1 Assess and manage risks when carrying out practical work; P4.3.2 Demonstrate an understanding of the need to acquire high quality data; P4.4.1 show an understanding of the value of means; P4.4.2 Demonstrate an understanding of how data may be displayed; P4.5.2 Review methodology to assess fitness for purpose; P4.5.3 Identify patterns in data; P4.5.4 Draw conclusions using scientific ideas and evidence; P4.6.1 Review hypotheses in the light of outcomes. Lesson objectives Most students should be able to: use the equation relating period and frequency recall that the period of a pendulum depends on its length carry out practical investigations into pendulums explain the use of pendulums in some everyday situations. Some students should also be able to: use the formula for calculating the period of a pendulum [Ext] recall that resonance can occur at the natural frequency of an object [Ext] recall that the motion of a pendulum approximates to simple harmonic motion. [Ext] Keywords Amplitude, bob, frequency, pendulum, time period. Points to note Students may be familiar with the idea of period from Unit P2. A simple pendulum is one in which the mass is concentrated in the bob, as opposed to one such as a rigid rod with a mass at the end, in which a significant proportion of the mass is in the bar. Sheet 1 of 2 Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free. 297

2 P3 3.6 Lesson guide Use of the formula T = 2π l/g (in P3 3.6b and P3 3.6d) is extension material only and students are not expected to recall it. Note that this formula only applies for very small amplitudes, and at larger amplitudes the amplitude does affect the period. Lesson activities Starter 1 Ask students what a pendulum is and to give some examples (these are likely to include swings or other similar fairground rides). If necessary, show the photo of a pendulum clock from the Student Book and ask them to suggest the purpose of the pendulum. [AfL] 2 P3 3.6a Pendulum starter Set up two different pendulums and ask students to suggest what factors could be controlling the time it takes for one swing. You could also revise conservation of energy by asking them to explain why the pendulums will eventually stop swinging. [AfL] Main tasks 1 P3 3.6b Investigating a pendulum Students investigate the factors that affect the period of a pendulum. This activity is best done before students use the textbook. (~20 30 mins) 2 Ask students to use the Internet to find images of fairground rides involving pendulums and to produce annotated sketches (or annotate the images) to point out the similarities and differences to a simple pendulum. Rides could include Freak Out and Pirate Ship. Students could also consider playground rides such as swings. 3 P3 3.6c Natural frequency and resonance Show students demonstrations of resonance and link this to the fact that even a small child can increase the amplitude of an adult on a swing by pushing at the correct points in the movement cycle. You can also show students videos of the Tacoma Narrows suspension bridge disaster and the Millenium Bridge in London to show resonance in action. This is extension material and students will not be examined on it. Plenary 1 Show students a mechanical metronome and how its period can be adjusted by moving the weight. Ask them to suggest similarities and differences between this and a simple pendulum. [AfL] 2 Explain that each 'tick' of a pendulum clock is controlled by the swing of a pendulum. Ask students to suggest how a pendulum clock is adjusted to keep good time, and why this works. [AfL] Homework/research 1 P3 3.6d Swinging questions This worksheet provides questions on pendulums and their periods. [AfL] 2 P3 3.6e Simple harmonic motion This worksheet introduces students to the idea of simple harmonic motion. This is extension material and students will not be examined on it. Route to A* Ask students to find out about Foucault Pendulums and what they demonstrate. Sheet 2 of Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free.

3 P3 3.6a Teacher and technician sheet Pendulum starter To show students pendulums with different periods and elicit ideas about the factors controlling the period. P3.2.1e For demonstration: clamp and stand G-clamp string optional: stepladder large and small masses Safety Ensure the stand is securely clamped to the bench. If using ceiling hooks, use a stepladder to fasten the string. Ensure weights cannot fall on students if a string breaks. 1 Set up a pendulum with a very long string, using a hook in the ceiling if possible. This one should have a fairly small mass. Set up a much smaller pendulum with a larger mass using a clamp and stand fastened to the bench. 2 Set the pendulums swinging with different amplitudes and ask the students to identify the differences between them (they should note length, masses, amplitude and period). Ask them to suggest which factor/s might affect the time it takes the pendulum to complete one swing (introduce the term period if students do not recall it from work on alternating current in P2). 3 You could extend the activity by asking students to explain why the pendulum will eventually stop swinging in terms of energy transfers. Follow this up by asking what they would see if the period depended on amplitude. (In fact, there is a dependence on amplitude for larger swings, but the difference is about 1% for swings of 23 from the vertical, so students are unlikely to notice this in their investigations and are not required to recall it). Students suggest factors which may affect the period of a simple pendulum. Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free. 299

4 P3 3.6b Teacher and technician sheet Investigating a pendulum To determine that the period of a simple pendulum depends on its length and not on its amplitude or the mass of the bob. P3.2.1e; CA: P4.1.1a, b, c; P4.2.1a, b; P4.3.2a, c, d, e, f; P4.4.1a, b, P4.4.2a, b, c; P4.5.2a, b, c, d; P4.5.3a; P4.5.4a, d; P4.6.1a, b. For each student or group: clamp and stand G-clamp metre rule stacking masses stop clock string optional: light gate and datalogger Other resources Student practical sheet P3 3.6b Safety notes Ensure the stand is securely clamped to the bench. Ensure weights cannot fall on students if a string breaks. 1 The worksheet provides hints to help the students to plan their own investigations. 2 Question 2 on the worksheet is designed to make students think about the inherent inaccuracies in timing the pendulum by eye. The following methods could be suggested to improve the quality of the measured periods if students do not think them up for themselves. You could suggest each method and ask students to explain why each one should help to provide better quality data. Measuring the time taken for (say) 10 swings and dividing by 10 (any errors resulting from human reaction time or misjudging the point at which a swing is completed are divided by 10) Using the point at which the pendulum swings through the vertical (line up with the stand, or put a marker on the bench below), as this point is often easier to judge than the endpoints of the swing. 3 Students investigating the effect of mass or length should keep the amplitude to a maximum of 10 either side of the vertical. Students determine that the longer the pendulum the greater the period, but that the relationship is not linear (see Figure 3 in the Student Book). 300 Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free.

5 P3 3.6c Teacher and technician sheet Natural frequency and resonance To introduce the idea of resonance and demonstrate some of its effects. P3.2.1e For demonstration: Barton's pendulums (pendulums of various lengths with very light bobs suspended from a length of string, plus a pendulum with a much heavier bob of the same length as one of the others, suspended from the same string) access to Internet videos (or downloaded videos see below) wine glass (test that you can make it 'sing' before the lesson) Safety Ensure stand is securely clamped to bench. Ensure weights cannot fall on students if a string breaks. 1 Show students the Barton's pendulum arrangement and ask them to describe how the periods of the pendulums would differ. Ask them to predict what will happen when the pendulum with the heavy bob (the 'driver') is swung and then show them what happens. Explain that the pendulum with the same period (the same 'natural frequency') as the one with the heavy bob will swing with the greatest amplitude. This phenomenon is called resonance. 2 Explain that many objects will vibrate at a certain frequency. Demonstrate a 'singing' wine glass and explain that vibrations from your finger, repeatedly sticking slightly as you rub it around the rim, can make the wineglass vibrate at its natural frequency, at which point the continued vibrations increase the amplitude so that you can hear the sound it makes. 3 Show students that a wineglass can be made to oscillate at a big enough amplitude to break it. It is possible for this to be done by the human voice, but this is extremely difficult without amplification. 4 Explain that many things, including wind, can make structures vibrate and show a video of the collapse of the Tacoma Narrows Bridge to show what can happen if structures are not designed with possible resonance in mind. This is newsreel footage from the time, with suitably dramatic commentary. 5 If time permits, show a video about the resonance problem with the Millennium Bridge in London. This explains resonance in bridges and why the problem occurred with the Millennium Bridge. Students appreciate that objects have a natural frequency which needs to be taken into account in engineering design. Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free. 301