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Dylan Collins
Dylan Collins

Pendulum Immersion 2010 DOH [UPD]

Home Insulation - is thicker better? Ceiling insulation is one way of improving the energy efficiency of a home. Insulation materials such as polyester, fibreglass or wool "batts", metal foil and shredded newspaper are just some of the ways it can be done. In 2010 the Australian Government subsidized the installation of batts and foil in 550000 homes at a cost of $2.45 billion. Many were installed improperly and in some case fires and death occurred. The research question that could be useful for a Senior Physics EEI is what factors affect the thermal insulation property of a material?

Pendulum Immersion 2010 DOH

The EEI suggested here involves rolling steel ball-bearings of different diameters across the concave surface of a watch glass, lens or mirror. The ball behaves like a pendulum speeding up as it rolls towards the centre and then slowing as it rises up the other side. Have a look at my video at (see below).

You could consider a comparison of velocity by ballistic pendulum and by the range formula. A bow and arrow is not considered a "weapon" under the Queensland Weapons Act (even though it could be lethal - but so could a baseball bat or kitchen knife). It only becomes a "weapon" when used for a "behavioural offence" such as attacking a person. You should see the "weapons" note above. Some good advice on archery safety procedures is given in the Archery Australia Policy Number 1018 "Safety Guidelines" (2011) on their Policy and ProceduresWebsite.

Magnetic Field in a SlinkyThe availability of inexpensive Hall Effect magnetic field probes enables an interesting EEI to be done into the magnetic field strength inside a slinky. You can insert the probe beteen adjacent turns (see photo below) and measure the field as a function of the distance between turns (or turns/metre). For a second variable you could try changing the current or placing the probe at different distances from the centre. However, if you don't have a Hall Effect probe (eg from Vernier Software) and want to make your own there is a good article (for download) in Physics Education V45(5), September 2010, page 529.

Bifilar pendulumA bifilar suspension pendulum is one in which two (bi) filaments (filar) support a rod. A schematic of this arrangement is shown in the figure below. Bifilar pendulums have been used to record the irregular rotation of the earth as well as to detect earthquakes. If a magnet is used instead of the rod, the rate of oscillating can be used to measure magnetic filed strength. If a plain metal bar is suspended symmetrically in the horizontal plane by two strings of equal length and set to swing about a vertical axis through its centre, the period of the swing (T) may depend upon some, or all of the following quantities that define the system: the length of the supporting strings L; the distance apart of the strings, s; the mass of the suspended bar, m; and the length of the suspended bar, l.

Torsion pendulumA torsion pendulum consists of a weight suspended by a wire or some other fibre. The pendulum oscillates by repeatedly twisting and untwisting about the axis through the centre of the wire. Though it is not strictly a pendulum since it does not oscillate because of the force of gravity, the mathematical formulas that describe the motion of a torsion pendulum are similar to the equations that describe the simple harmonic motion of a simple pendulum. It is commonly used in those ornate clocks in glass cases (see below).

Newton's Cradle and non-elastic collisionsNewton's cradle, named after Sir Isaac Newton, is a device that demonstrates conservation of momentum and energy. It has no real-world application other than as a toy. A typical Newton's cradle has a series of identically sized metal balls suspended in a metal frame so that they are just touching each other at rest. Each ball is attached to the frame by two wires of equal length angled away from each other. This restricts the pendulums' movements to the same plane. There are plenty of videos and demos on the internet if you have not seen one live. They work well for steel balls; but what about brass, what about lead. Is there a relationship between starting height and final height when less elastic metals are used. It's no good just finding out there is a difference without having some hypothesis to test. Is it a density thing, or interatomic force thing? There must be some quantitative difference between the metals that gives rise to observed differences in the balls' behaviour. This will be hard.

The Physics of the Bungee JumpNational Geographic magazine first reported this sort of jump by Pentacost Island natives in 1955. It was later popularised by A. J. Hackett in NZ. The conversion from GPE to EPE is an interesting one but the relationship is far from simple. You could model a bungee using rubber bands and brass weights, or do something more dramatic. You may even find out why they say bungee jumping is glue sniffing for Yuppies. One of the problems is that as the jumper falls the mass of rope hanging below is getting less so acceleration is actually greater than g. That sounds wrong but it appears to be true. Have a look at: Understanding the Physics of Bungee Jumping from Physics Education V45(1) 63-72 (January 2010) and you'll see what I mean.

Flight of a Golf Ball This was first investigated by Prof. Peter Tait of Edinburgh University in 1900. His son was Scottish National Golf Champion who could hit a ball further than the mechanics formulas of the time predicted because they didn't know about spin. It still makes a great EEI as there are so many things to investigate. Try: angle vs. number of dimples; try sanding off one-quarter of them and putting gloss paint to make it smooth again; then try half (see below), and three-quarters. Design a device for giving it a constant velocity, eg falling pendulum, or something spring-loaded. Vary angle, try at different speeds. How to get top spin?

Coupled pendulaIf you have a rigid horizontal support such as a rod between two retort stands and hang two pendulums (pendula) of different lengths off the rod you get a strange effect when you start one oscillating. The "rigid" rod is not quite as rigid as you may think. It's not quite as simple as some books make out and in fact makes a great EEI (particularly if you like a bit of maths). Using a non-rigid support (called a Barton's pendulum) is much easier to get the oscillations going.

Coupled pendula with springsAnother type of coupled pendula is shown below. They are solid rods or strings attached to a rigid support much the same as the figure above left (the broom). However, they have a lightweight spring attached between them. There is a great article in Physics Education, Volume 45 No. 4, July 2010 about coupled pendula that provides background reading. Click the link to download it. I have only provided some of it to avoid copyright problems.

Magnetic braking IV - supermagnet pendulumAnother suggestion is to investigate a supermagnet pendulum. If a pendulum is allowed to oscillate between two pieces of aluminium (or other non-ferrous metal) the eddy currents should slow it down. But you'll need to find out if the period of oscillation changes. Some people also measure the 'decay time' - that is the time taken for the amplitude to decay to 1/e of the original amplitude. You could pose the question: does the period and/or decay time vary with the amount of aluminium, or perhaps with the distance between magnet and aluminium. You could compare a freely swinging magnet (as a control) with the same one swinging as in the photo - between two aluminium slabs (I used two hotplates on their sides but I could detect some attraction to some hidden iron). One difficulty is coping with terrestrial magnetism which loves to interfere. Some variables: length of string (related to period and hence speed), distance between plates. I had a good time with this until the bell went for the end of lunch.

Magnetic braking V - supermagnet pendulumA variation on the experiment above is to lay a sheet of aluminium flat on the bench. Then let the magnet swing over the aluminium and watch it come to rest quickly. Probably best to use a long length of string so that the distance between magnet and aluminium is fairly constant as it swings.What will your independent and dependent variables be. There are a lot to choose from. Will the manipulated variable be thickness, width, separation distance, type of metal (compare aluminium and copper and see if any variation is related to resistivity), release angle, length of string and so on. For thickness, you could try aluminium foil (1 sheet, 2 sheets and so on) but you will probably need some thicker pieces. What will be your dependent variable: period, amplitude/time graph, decay time (see above)? If they do affect any of these, is there a linear relationship or exponential, or something else? Perhaps you could use a data logger to measure displacement (amplitude) so that you get a heap of data points for analysis.

The earliest known scientific discussion of synchronization dates back to 1657 when Christian Huygens built the first working pendulum clock. Huygens studied systems of two pendulum clocks mounted on a common base. He observed that the clocks would swing at the same frequency and 180 degrees out of phase. This motion was robust, after a disturbance the synchronized motion came back in about half an hour. Huygens spent some time exploring this curious phenomena. You could investigate what starting conditions are necessary for phase locking. Maybe start with presstisimo (208 Hz) which is the fastest setting and make them 180Â out of phase. No more hints but you should see the amazing demo on You Tube: =W1TMZASCR-I

Doppler Effect of source moving on a pendulum bob Similar to the one above but with the buzzer attached to a 9V battery - making a good pendulum bob. You can calculate the speed mathematically at any point on it's journey by relating the change in GPE to KE (mgh = Âmv2) and calculating h by simple trigonometry. A long string may be better as the period is longer. Of course, the bigger the amplitude (q) the higher the speed. Some students have found that the frequency shift is too small to measure, but by a careful use of a sound sampling program (I find the free-to-students "Soundcard Scope" digital oscilloscope works pretty well). 350c69d7ab


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