Ball racing
This time I suggest you make a simple but effective device for the physics classroom. It will be a ball race. Another advantage of the track design is that it hangs on the wall without taking up much space and is always ready to show off the racing experience. Three balls start simultaneously from points located at the same height. A specially designed launch vehicle will help us with this. The balls will run along three different paths.
The device looks like a board hanging on the wall. Three transparent tubes are glued to the board, the paths along which the balls will move. The first strip is the shortest and has the shape of a conventional inclined plane. The second is the circle segment. The third band is in the form of a fragment of a cycloid. Everyone knows what a circle is, but they don't know what it looks like and where the cycloid comes from. Let me remind you that a cycloid is a curve drawn by a fixed point along a circle, rolling along a straight line without slipping.
Let's imagine that we put a white dot on the tire of a bicycle and ask someone to push the bike or ride it very slowly in a straight line, but for now we will observe the movement of the dot. The path of the point attached to the bus will surround the cycloid. You don't need to do this experiment, because in the figure we can already see the cycloid plotted on the map and all the lanes intended for the balls to run. To be fair on the starting point, we'll build a simple lever starter that will ensure all three balls start evenly. By pulling the lever, the balls hit the road at the same time.
Usually our intuition tells us that the ball that follows the most direct path, that is, the inclined plane, will be the fastest and win. But neither physics nor life is so simple. See for yourself by assembling this experimental device. Who to work. Materials. A rectangular piece of plywood measuring 600 by 400 millimeters or corkboard of the same size or less than two meters of transparent plastic pipe with a diameter of 10 millimeters, aluminum sheet 1 millimeter thick, wire 2 millimeters in diameter. , three identical balls that must move freely inside the tubes. You can use broken bearing steel balls, lead shot, or shotgun balls, depending on the inside diameter of your pipe. We will hang our device on the wall and for this we need two holders on which to hang pictures. You can buy or make wire handles with your own hands from us.
Tools. Saw, sharp knife, hot glue gun, drill, sheet metal cutter, pliers, pencil, puncher, drill, wood file and dremel which makes the job very easy. Base. On paper, we will draw the predicted three travel routes on a scale of 1: 1 according to the drawing in our letter. The first one is straight. Segment of the second circle. The third route is cycloids. We can see it in the picture. The correct drawing of the tracks needs to be redrawn on the base board, so that we later know where to glue the pipes that will become the tracks of the balls.
Ball lanes. Plastic tubes should be transparent, you can see how our balls move in them. Plastic tubes are cheap and easy to find in the store. We will cut the required lengths of pipes, approximately 600 millimeters, and then shorten them a little, fitting and trying on your project.
Track start support. In a wooden block measuring 80x140x15 millimeters, drill three holes with a diameter of tubes. The hole into which we stick the first track, i.e. depicting evenness, must be sawn and shaped as shown in the photo. The fact is that the tube does not bend at a right angle and touches the shape of the plane as much as possible. The tube itself is also cut at the angle it forms. Glue the appropriate tubes into all these holes in the block.
loading machine. From an aluminum sheet 1 mm thick, we cut out two rectangles with dimensions, as shown in the drawing. In the first and second, we drill three holes with a diameter of 7 millimeters coaxially with the same arrangement as the holes were drilled in the wooden bar that constitutes the beginning of the tracks. These holes will be the starting nests for the balls. Drill holes in the second plate with a diameter of 12 millimeters. Glue small rectangular pieces of sheet metal to the extreme edges of the bottom plate and to them of the top plate with smaller holes. Let's take care of the alignment of these elements. The 45 x 60 mm center plate must fit between the top and bottom plates and be able to slide to cover and open the holes. Small plaques glued to the bottom and top plates will restrict the lateral movement of the center plate so that it can move left and right with the movement of the lever. We drill a hole in this plate, visible in the drawing, into which the lever will be placed.
рычаг. We will bend it from a wire with a diameter of 2 millimeters. Wire can be easily obtained by cutting a length of 150 mm from the wire hanger. Usually we get such a hanger along with clean clothes from the wash, and it becomes an excellent source of straight and thick wire for our purposes. Bend one end of the wire at a right angle at a distance of 15 millimeters. The other end can be secured by putting a wooden handle on it.
Lever Support. It is made of a block measuring 30x30x35 millimeters high. In the center of the block, we drill a blind hole with a diameter of 2 millimeters, in which the tip of the lever will work. End. Finally, we must somehow catch the balls. Each caterpillar ends with a grip. They are needed so that we do not look for balls all over the room after each stage of the game. We will make the capture from a 50 mm piece of pipe. On one side, cut the tube at an angle to create a longer wall that the ball will hit to complete the route. At the other end of the tube, cut a slot into which we will place the valve disc. The plate will not allow the ball to fall out of control somewhere. On the other hand, as soon as we pull out the plate, the ball itself will fall into our hands.
Installation of the device. In the upper right corner of the board, at the marked beginning of all tracks, glue our wooden block in which we glued the tubes to the base. Glue the tubes with hot glue to the board according to the drawn lines. The cycloidal path furthest from the surface of the slab is supported along its average length by a wooden block 35 mm high.
Glue the hole plates to the upper track support block so that they fit into the holes in the wood block without error. We insert the lever into the hole of the central plate and one into the casing of the starting machine. We insert the end of the lever into the carriage and now we can mark the place where the carriage should be glued to the board. The mechanism must work in such a way that when the lever is turned to the left, all holes open. Mark the found place with a pencil and finally glue the support with hot glue.
FUN TIME. We hang the race track and at the same time a scientific device on the wall. Balls of the same weight and diameter are placed in their starting places. Turn the trigger to the left and the balls will start moving at the same time. Did we think that the fastest ball at the finish line would be the one on the shortest 500mm track? Our intuition failed us. Here it is not so. She is third at the finish line. Surprisingly, it's true.
The fastest ball is the one that moves along a cycloidal path, although its path is 550 millimeters, and the other is the one that moves along a segment of a circle. How did it happen that at the starting point all the balls had the same speed? For all balls, the same potential energy difference was converted into kinetic energy. Science will tell us where the difference in finish times comes from.
He explains this behavior of the balls by dynamic reasons. The balls are subject to certain forces, called reaction forces, acting on the balls from the side of the tracks. The horizontal component of the reaction force is, on average, the largest for a cycloid. It also causes the largest average horizontal acceleration of that ball. It is a scientific fact that of all the curves connecting any two points of the gravitational sweat, the fall time of the cycloid is the shortest. You can discuss this interesting question at one of the physics lessons. Perhaps this will set aside one of the terrible pages.
