As we promised, this puzzle is solved without mathematics, but we used principles and methods that are at the foundation of mathematics. Stanton de Riel informs me of one. The puzzle could still be solved by devious methods. This drawing shows his military tank, powered, as shown at the left, by gears and cranks. Yet published papers argue about the details of these processes. Does this affect the outcomes? Is it possible that with this method for some dimensions of the "L" the two lines would never cross? In Euclidean geometry propositions are solved using only a compass and an unmarked straightedge. Return to the main puzzle page. If the gravitational attraction of the ball were much larger than Resolve this apparent contradiction. The zero-force situation defines a frame of reference, convenient for analysis, but that doesn't say that that frame has any "reality" outside of the problem at hand. Now imagine the two spheres being consolidated, the slices of one fitting between the slices of the other. This same system was used in medical endoscopes, long flexible tubes that could be snaked into bodily orifices to view your inner self. Press, 1997). Consider the system shown. The water shifts to the left side, as Archimedes says, "seeking its own level". A straightforward calculus solution is also included. Textbook end-of-chapter problems are usually of this sort. So how can the string do any work on the ball to sustain its motion? Is circuit theory and classical electromagnetic theory wrong? The balls have equal mass. Historical manuscript illustrations aren't either. Textbook illustrations of the Ptolemaic system are never to uniform scale. Find their centers, and the line joining them. Roll them down an inclined plane. It is an oblate spheroid, bulging at the equator. This is an old problem designed to expose student misapplication of Newton's laws. Questions about physical phenomena, dependent on real world data. 922-928. A block and tackle does that, lifting a heavy weight upward as you pull downward on the rope. In some engineering texts this is called "rolling friction". Not only will this device give an endless stream of fresh water but can be used to run a small generator. Write the equations for kinetic energy and momentum. Refrigerator magnets have thir magnetized surface on only one side, and being so closely spaced, the pole stripes have short effective range. The force due to friction of the floor must act forward, in the direction you are walking. His system still needed epicycles, but, he claimed, fewer of them. We didn't ask for the system's weight. represents a decrease in the potential energy, and because Δm ∝ ε, this decrease Some can also be solved by tedious formal mathematical analysis, but only as a last resort. An answer is given in the April. The blue vector has no horizontal component, so it doesn't cause rolling of the ball. Parallel light rays have zero convergence. Answer: It is possible to strengthen the qualitative reasoning given above with a Physics Puzzles helps exercising the brain and develop it to think logical and solve real world problems differenlty. The requirement that the cylindrical hole be 6 inches in length, whatever its diameter, forces the sphere to be a different diameter for each hole size considered. The acceleration due to gravity, g You'd think there's not enough information given. Working backwards from the far end, this would lead us to the conclusion that the current in each successive link is also zero, and the input current also zero. The given answers to the first part are correct. Return to Donald Simanek's front page with the full menu, 15 1 2 12 Google prism recombine white light and view the images. So what is the initial acceleration of the top coil after release? 2 6 10 14 The force on its upper end is not the same size. Now remove every other disk without changing the overall volume. Every rotating body eventually comes to a stop, so its angular momentum is then returned to the earth, and the net effect on the body of the earth is zero. Shouldn't this initial motion bias the pendulum to retain that motion for the rest of the day, so its plane of motion wouldn't change at all with respect to the building? They should be banned from all textbooks, in my opinion. At each In fact, in a well-designed lens, all rays from a point object, passing through the lens take the same time to travel from object to image, and are in phase at the image point. The gearing is the common "lantern gear" of the time. There's an easier way, if you consider the angular speed of moon and sun across the sky. Not to scale. The two lines cross somewhere (fourth figure) and that must be the true center of mass of the L-shaped figure. Or just imagine removing every other atom in the volume. You will need to use L'Hospital's rule. is "Which came first, the action force or the reaction force?". Definite solution of the two (many) capacitors paradox byVladan Pankovic, A problem of missing energy when charging a second capacitor, A Short Foucault Pendulum Free of Ellipsoidal Precession. The bottom end is stationary as the rest of the spring compresses. Answer: To sustain the circular motion you must move your hand in a small circle. Textbooks and professors avoid this by seldom raising such questions. Not surprising. The only other force that could exert a torque would be a tangential force at the wall. This is why camera lenses have anti-reflection coatings to minimize such ghost images. The energy stored in an Alnico-5 magnet bar of that size is 1.2 Joules. The round sand particles wedge against each other and the sides of the straw. It considers a mountain below the ocean surface, and asks whether the water surface above the mountain is affected. At 918 meters, it is the longest navigable aqueduct in the world. And suppose that the bottle design was such that after separation, the cream exactly fills the upper cylinder and the milk the lower one. Can you find its center of mass, using only an unmarked straightedge?
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