Can you explain the concept of energy conservation?

Law of Conservation of Energy.Can anyone explain this example from the Feynman Lectures on Physics?

• Explain the following extract from the Feynman lectures so that a 10th grader can understand.Note that I do not want you to explain what conservation of energy is,I just want understand the following extract clearly.Try to be as simple as possible. "The principle of the conservation of energy is very useful for deducing what will happen in a number of circumstances. In high school we learned a lot of laws about pulleys and levers used in different ways. We can now see that these "laws" are all the same thing, and that we did not have to memorize 75 rules to figure it out. A simple example is a smooth inclined plane which is, happily, a three-four-five triangle (Fig. 4-3). We hang a one-pound weight on the inclined plan.e with a pulley, and on the other side of the pulley, a weight W. We want to know how heavy W must be to balance the one pound on the plane. How can we figure that out? If we say it is just balanced, it is reversible and so can move up and down, and we can consider the following situation. In the initial circumstance, (a), the one pound weight is at the bottom and weight W is at the top. When W has slipped down in a reversible way, we have a one-pound weight at the top and the weight W the slant distance, (b), or five feet, from the plane in which it was before. We lifted the one-pound weight only three feet and we lowered W pounds by five feet. Therefore W = 3/5 of a pound. Note that we deduced this from the conservation of energy, and not from force components. Cleverness, however, is relative. It can be deduced in a way which is even more brilliant, discovered by Stevinus and inscribed on his tombstone. Figure 4-4 explains that it has to be 3/5 of a pound, because the chain does not go around. It is evident that the lower part of the chain is balanced by itself, so that the pull of the five weights on one side must balance the pull of three weights on the other, or whatever the ratio of the legs. You see, by looking at this diagram, that W must be 3/5 of a pound. (If you get an epitaph like that on your gravestone, you are doing fine.)" Links:Figure 4-3:http://i769.photobucket.com/albums/xx332/RedjacketYA/4-3.gif Figure 4-4:http://i769.photobucket.com/albums/xx332/RedjacketYA/4-4.gif

• Answer:

  Stevinus is a more logic rather than mathmatics. You get the same result as I got below without all the math crap. Look at the picture. Note that the weight of the balls below the triangle pull the chain toward the center. It must be in equlibrium otherwise, the balls would rotate endlessly (Perpetual Motion). Cannot be that! There must be at least 5 balls on the 5 side or the balls will not hang over both edges and it cannot be more than 5 because the side is only 5 long. Thus it must be 5. There must be 3 balls on the 3 side because that is the length of the side. Thus, the number of balls below the triangle is not important. All this hangs on Conservation of Energy ===> Perpetual Motion is impossible. The balls must be in equlibrium as shown. ===> 3 balls vertical balance 5 balls on the slope. Conservation of Energy says that energy conversions are "Path independent." This means that if you ignore things like friction, it does NOT matter how you do something. It ALWAYS takes the exact same amount of energy. In Feynman's example: The mass over the edge moves vertically ====> if it moves 1 meter vertically then the mass on the slope must also move vertically 1 meter. ====> How far must it move along the slope in order for it to move vertically 1 meter? Put another way: The 2 masses are a "system." and the slope is frictionless. PE1 is the potential energy of the hanging mass = MGH1 where H1 is the vertical elevation of Mass1 PE2 is the potential energy of the mass on the slope = MGH2 where H2 is the vertical elevation of Mass2 Conservation of Energy: PE1 + PE2 = constant Note any positive change in PE1 (mass is raised higher) results in an equal decrease in PE2. Note what changes H1 and H2. This puts us back to the trig. Sine angle of ramp = Motion Mass1 / Motion Mass2 sine = opposite/hyporenuse = 3/5 ====> Motion Mass1 = 3/5 * Mass2 Where: Motion Mass1 is vertical Motion Mass2 is along the slope (That is how far Mass2 must slide to move the same distance vertically) This same argument applies to the ratio of the 2 masses. Their PE must be equal if the slope is frictionless. Otherwise, the masses would move under gravity. The mass with the larger PE will fall pulling the mass with the smaller PE up until both have the same PE. Lets move M1 (the hanging mass 1 meter) how far will M2 move? 1 = 3/5 Call mass1 = 1 mass unit what must the mass2 be? PE1 = PE2 M1*G * 1m = M2 * G * 3/5 m (G cancels) M1 = 3/5 M2 Only with this ratio of mass will the 2 masses be in equlibrium at the same vertical elevation.