Simple Nature - Light and Matter

m / Discussion question C.n / A hydraulic jack.The seesaw example demonstrates the principle of the lever,which is one of the basic mechanical building blocks known as simplemachines. As discussed in more detail in chapters 3 and 4, theprinciple applies even when the interactions involved aren’t gravitational.Note that although a lever makes it easier to lift a heavy weight,it also decreases the distance traveled by the load. By reversing thelever, we can make the load travel a greater distance, at the expenseof increasing the amount of force required. The human muscularskeletalsystem uses reversed levers of this kind, which allows us tomove more rapidly, and also makes our bodies more compact, at theexpense of brute strength. A piano uses reversed levers so that asmall amount of motion of the key produces a longer swing of thehammer. Another interesting example is the hydraulic jack shownin figure n. The analysis in terms of gravitational energy is exactlythe same as for the seesaw, except that the relationship between ∆y 1and ∆y 2 is now determined not by geometry but by conservationof mass: since water is highly incompressible, conservation of massis approximately the same as a requirement of constant volume,which can only be satisfied if the distance traveled by each piston isin inverse proportion to its cross-sectional area.Discussion QuestionsA Hydroelectric power (water flowing over a dam to spin turbines)appears to be completely free. Does this violate conservation of energy?If not, then what is the ultimate source of the electrical energy producedby a hydroelectric plant?B You throw a steel ball up in the air. How can you prove based onconservation of energy that it has the same speed when it falls back intoyour hand? What if you threw a feather up? Is energy not conserved inthis case?C Figure m shows a pendulum that is released at A and caught by apeg as it passes through the vertical, B. To what height will the bob riseon the right?D What is wrong with the following definitions of g?(a) “g is gravity.”(b) “g is the speed of a falling object.”(c) “g is how hard gravity pulls on things.”2.1.6 Equilibrium and stabilityo / The surfaces are frictionless.The black blocks are inequilibrium.The seesaw in figure k is in equilibrium, meaning that if it startsout being at rest, it will stay put. This is known as a neutral equilibrium,since the seesaw has no preferred position to which it willreturn if we disturb it. If we move it to a different position andrelease it, it will stay at rest there as well. If we put it in motion, itwill simply continue in motion until one person’s feet hit the ground.Most objects around you are in stable equilibria, like the black86 Chapter 2 Conservation of Energy