In some of the experiments a constant head apparatus is mentioned. This is simply a device for maintaining a constant head of water at an outlet.

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1 GRAVITY General theory for this section: When an object falls from rest and accelerates under the effect of the Earth's gravity the distance it falls (h) in a time t is given by the equation: h = ½ (gt 2 ). The gravitational field strength at the surface of the Earth is approximately 9.81 Nkg 1 and this will give a mass of one kg an acceleration of 9.81 ms 2. That means that if an object is dropped near the Earth's surface its speed increases by about 10 ms 1 every second if the effects of air resistance are ignored. When a projectile is thrown it has a constant vertical acceleration (g) towards the ground but a constant horizontal velocity if we ignore air resistance. The horizontal and vertical motions are independent. In some of the experiments a constant head apparatus is mentioned. This is simply a device for maintaining a constant head of water at an outlet. 1. Mooing carton 2. Pearls in air 3. g with a water jet 4. Diluted gravity 5. Diluted gravity projectile paths 6. g Gramophone turntable 7. Vertical acceleration 8. Two joined falling balls 9. Falling can and water what happens? 10. The contracting stream 11. Diluted gravity again 12. Falling helical spring 13. Falling bar method for g 14. Monkey and hunter 15. Dropping books and paper 16. Galileo inclined planes 17. Guinea and feather tube 18. Falling can with hole at one side 19. Floating block in a falling jar 20. Two tennis balls 21. Smiley pop ups 1. Mooing milk carton The mooing milk carton can be used as a fun problem to show the constancy of vertical acceleration in free fall and also to demonstrate g forces. Turn it upside down and drop it in "mid moo". Observe the change in the sound as it goes down. The mooing stops in free fall and starts again when the high deceleration forces occur as it is caught. Age range: depending on treatment Apparatus required: Mooing milk carton 2. Pearls in air (a) This is a classic demonstration designed to show the parabolic path of projectiles in a gravitational field. A water jet is formed by using the glass part of a dropping pipette fixed to a thin walled rubber tube and connected to the water tap. The rubber tube is passed through an old style ticker timer or over a vibration generator so that the tube is alternately squeezed and released when the device is switched on V DC 1

2 The water jet falls in a parabola from an initial horizontal direction but is also interrupted by the pulsing so that droplets of water are formed instead of a continuous stream. If the arrangement is illuminated with a stroboscope, pearl like droplets of water can be made to stand still or move slowly through the air. The constant horizontal velocity and the increasing vertical velocity can be seen by observing the positions of successive drops. To get a permanent record you could mark the position of the shadows of the water drops on a screen behind the jet or even photograph it. A truly beautiful demonstration. (b) An extension of the basic version is what I call the Double Pearls in Air. In this experiment two jets are used from different water taps but with tubes running under the same ticker timer bar. One is adjusted to give a parabola while water simply dribbles out from the other, falling vertically. The vertical acceleration of the drops can then be compared. Of course you can make two parabolas and compare these. (c) I have heard of a version using a single parabola of water but TWO strobe lights, one with a red filter and one with a blue filter. Apparently, changing the flashing speed of the strobes can result in red drops moving in one direction and blue drops seemingly travelling back the other way. I have not had a chance to try this myself, but it apparently amazes people. Warnings about the use of stroboscopes or flashing lights should be given for all sections of this experiment. Any pupil suffering from photo sensitive migraine should be allowed to leave if they request it. Since h = 1/2gt 2 and s = vt the equation for the parabolic path for the water is h = gs 2 /2v 2 horizontal distance travelled, h the vertical distance and v the horizontal velocity of the jet where s is the Apparatus required: Ticker timer Two water jets Constant head apparatus Bucket Stroboscope 3. g with a water jet The value of the acceleration due to gravity (g) can be found in a rather novel way by using a jet of water projected horizontally from a dropper attached to a constant head to give a parabolic path. The shape of the path is found by measuring pairs of values of the height fallen (h) and the distance horizontally from the orifice (s) and if the rate of flow of the water is also found the value of g can be calculated. Measure the diameter of the jet to calculate its cross sectional area (A). The horizontal velocity (v) is obtained from the equation V = Av where V is the volume of water leaving the dropper per second (measure this by directing the jet into a measuring cylinder) and A is the cross sectional area of the jet. Using a TV camera to give an image on the screen, or shining light from a projector to make a shadow of the path on a board, are both helpful ways of making the measurements easier to take. s = vt h = 1/2gt 2 v = V/ r 2 Apparatus required: Water jet Constant head apparatus Rulers Base clamp Measuring cylinder Stop clock Travelling microscope or vernier or TV camera Bucket Mop! 2

3 4. Diluted gravity (a) Realising the problem of making accurate measurements of the acceleration due to gravity, Galileo diluted gravity by rolling balls down slopes. His original apparatus is in the History of Science Museum, Florence. We can recreate his experiment by rolling a marble down an inclined plastic ramp or tube and measuring the time it takes to travel a measured distance. The gravitational acceleration (g) has been "diluted to g sina where A is the angle that the tube makes with the horizontal. Carrying out the experiment by using a rider on a tilted linear air track (I used one 2m long) can give extremely accurate values for g. A piece of plastic electrical trunking supported by a strip of wood makes an excellent ramp down which to roll the marbles. (b) An alternative version of the diluted gravity experiment of Galileo can be performed on a large scale with an aerial ropeway type arrangement fixed across the lab. A wire should be fixed tightly from a high point on one side of the lab to a low point on the other. A small cup either fixed to a pulley wheel or simply tied to a loop of wire can then travel down the wire. Time, distance and angle can easily be measured. Acceleration down the plank or wire = g sina s = 1/2 gsina t 2 It is worth pointing out that it is much more accurate to measure the small angles by trigonometry than by fiddling around with a protractor! Age range: Apparatus required: Wooden ramp and track or plastic tube Marble Stop Ruler Wire Cup and pulley wheel 5. Diluted gravity projectile paths An extension of the diluted gravity experiment (see experiment 4) is to investigate a diluted projectile path. Get a drawing board and fix a large sheet of paper to it. On top of this fix a piece of carbon paper face downwards. Tilt the board and then roll a heavy ball bearing across the top of the paper in a horizontal direction. The path of the ball bearing will be produced on the paper. Different angles of tilt and different path directions can be used. This would be suitable for an introduction to projectiles or, at a more advanced level, where a calculation of the parameters of the paths can be made. Apparatus required: Drawing board Large ball bearing Carbon paper White paper 3

4 6. g Gramophone turntable A rather quaint experiment is the use of an old gramophone turntable to measure the acceleration due to gravity (g). The problem with all such measurements is to find a way of determining the time of fall that will always be pretty small over the distances possible in a laboratory. In this method this small time is found by using a gramophone turntable. First, fix a piece of tape along a radius. Hold a ball bearing a height h above the rotating turntable and release it at just the moment when the tape passes beneath it. The angle through which the turntable has rotated before the ball bearing hits it is found by either covering the surface with plasticine or a piece of carbon paper over a white sheet of paper. The period of rotation of the turntable is determined using a stopwatch and may be used to calculate the time of fall (t). The acceleration due to gravity is then worked out using the formula g = 2h/t 2. Admittedly it's a very inaccurate method, but it does give you a means of getting g and then commenting on why it would be an unreliable answer. Apparatus required: Gramophone turntable or an electric drill and plywood disc Large ball bearing Carbon paper and white paper or plasticine Ruler 7. Vertical acceleration The "feel" of the value of the acceleration due to gravity can be gained by putting a small object such as a ball bearing on your hand and then moving your hand downwards. If you move it with an acceleration of less than g the ball bearing stays in contact with your hand but if your hand accelerates with a greater acceleration than g the ball bearing leaves the surface. It is rather more difficult to do this with your hand on top of the object. You can compare this with the loop the loop in a roller coaster or with people in a car going over a bumpy road. You will leave your seat in a car if it travels over the bumps too rapidly. 8. Two balls falling joined by stretched elastic An interesting problem involving gravity is to take two balls that are joined together by a piece of stretched elastic and hold one of them so that the other hangs below it, the elastic between them being stretched. Now release them so that they fall. What happens to their separation as they fall? It is worth doing the experiment, first with two balls of the same mass and then with two of different masses. With the two different masses try it with the greater mass at either the top or bottom. The upper ball falls with a greater acceleration than the other the two are pulled together by the elastic and so the acceleration varies until the elastic becomes slack, when they both fall with an acceleration of g. a' a'' Apparatus required: Two power balls Piece of elastic 4

5 9. Falling can and water what happens? Take a tin can and drill a hole in the bottom. The size isn't critical but two or three millimetres in diameter will be fine. Put your finger over the hole and fill the can with water. Now drop the can the water stays inside. This is much as you would expect, since all objects accelerate downwards at the same rate if air resistance is ignored. Now repeat the experiment but drop the can after you have allowed some of the water to start streaming out. What happens to the water? It looks as if the can is continuing to empty itself, but this would mean that the water is falling with a greater acceleration than g. This is impossible of course! The can and the water both accelerate at the same rate, g, and the can has the same amount of water in it when it reaches the ground as it had at the start of the drop. Apparatus required: Bowl or bucket Tin can with hole 10. The contracting stream The speed of a jet of water falling vertically from a tap into a sink increases the further from the tap it gets. This would seem to suggest that more water reaches the sink every second than is being emitted from the tap. Clearly impossible! This can only be explained if the stream of water gets thinner with increasing depth below the tap. This can be verified by turning the tap on slightly and observing the stream. Apparatus required: Water tap Please note The other experiments listed in this section will be found in: 'The New Resourceful Physics Teacher This 272 page illustrated book is available through the website. 5