When you spin a tank of water on a lazy Susan, the surface of the water forms a curve called a parabola.
Note: This Snack may be difficult to build properly or may not clearly show the desired results. This may be due to the effects being very subtle and/or hard to observe. The construction technique may require exceptionally fine tuning and tinkering, or it may just be inherently difficult to execute properly. That being said, if you're up for a challenge, go for it!
- Clear, thin, rectangular plastic box with a lid, about 12 × 12 × 1 inches (30 × 30 × 2.5 centimeters)—you can buy a ready-made one or glue together pieces of plastic (available at a plastics store)
- Silicone seal adhesive to make the box waterproof
- Strong glue
- Two wood or plastic blocks, each about 2 × 6 × 1/2 inches (5 × 15 × 1.25 cm)
- Lazy Susan or other appropriate turntable
- The seams of the box need to be watertight, so use the silicone seal adhesive to plug any leaks.
- Cut a hole in the top of the box, or leave the top of the box open.
- Glue the blocks to the Lazy Susan along each side of the box so that the box is held firmly in place.
Fill the box half-way with water and rotate the Lazy Susan. Notice the shape of the surface of the water.
When the waves settle down, the surface of the water forms a curve called a parabola. As the box spins, the water tends to continue moving in a straight line tangent to the circle. However, the box restrains the water and forces it to keep moving in a circle. The water near the edge of the box goes around in one large circle in the same time that the water near the center goes around in a small circle. That means the water near the edge travels faster than the water near the center. The faster an object moves in a circle, the larger the force necessary to hold it in the circle. This force is called the centripetal force.
The surface of a body of water in equilibrium is always perpendicular to the net forces on the water. The diagram below (click to enlarge) shows the forces on the water in relation to the tilt or slope of the water surface.
The diagram shows that the tilt or slope of the water surface indicates the size of the force holding the water in its circular path. The flat bottom of the parabola shows that little force is needed to hold the water there in its circular path, while the steep outer regions show that a large force is required in those areas.
The horizontal component of the buoyancy provides the centripetal force.
You can prove to yourself that the water forms a parabola. A parabola has the equation:
$$y = x^2$$
Draw a parabola close to the size of the one in your Snack on a piece of graph paper and tape the paper to one side of your rectangular box so that you can look through the box and see the paper. Then rotate the box until you find the speed at which the bottom of the parabola you drew matches up with the lowest part of the water surface. (Note that the X and Y axes of this graph must have the same scale.) The water surface should exactly match the curve of the parabola drawing at every other point.
Make a raft small enough to float inside your rotating box—a small, flat piece of wood with a toothpick mast works well. Place the raft on the water surface near the edge of the box and then spin the box. The raft will stay in place even when it is on the slope of a hill of water. Its mast will always be perpendicular to the water. (Click the diagram below to enlarge.)