What is the analogy of this to theconservation of energy? The most remarkable aspect that must be abstracted fromthis picture is that there are no blocks. Take away the first terms in (4.1)and (4.2)and we find ourselves calculating more or less abstract things. The analogy hasthe following points. First, when we are calculating the energy, sometimes someof it leaves the system and goes away, or sometimes some comes in. In order toverify the conservation of energy, we must be careful that we have not put anyin or taken any out. Second, the energy has a large number of differentforms, and there is a formula for each one. These are: gravitationalenergy, kinetic energy, heat energy, elastic energy, electrical energy,chemical energy, radiant energy, nuclear energy, mass energy. If we total upthe formulas for each of these contributions, it will not change except forenergy going in and out.
这与能量守恒，有何可类比之处？从这幅图画中，应该抽出来的、最值得说明的一点，就是没有积木。把公式（4.1）和（4.2）中的第一项拿掉，我们发现，我们或多或少是在计算抽象的事物。这个类比有以下几点。第一，当我们计算能量时，有时候，有些能量会离开这个系统，消失掉，而有时，则会有一些能量进来。为了证实能量守恒，我们就应该注意，既不要把任何能量放进来，也不要把任何能量拿出去。第二，能量有多种不同的形式，对于每种形式，都有一个公式。这些能量就是重力能量、动能、热能、弹性能量、电子能量、化学能量、辐射能、原子能、质能。如果我们把这些能量公式都统计起来，就会发现的，除了能量的此出彼进外，没有何变化。

It is important to realize that in physicstoday, we have no knowledge of what energy is. We do not have a picturethat energy comes in little blobs of a definite amount. It is not that way.However, there are formulas for calculating some numerical quantity, and whenwe add it all together it gives “28 ”—always the same number. It is an abstract thing in that it does not tellus the mechanism or the reasons for the various formulas.
有一点很重要，那就是在今天的物理学中，我们要意识到，对于能量究竟是什么，我们并没有任何知识。我们并没有一幅图像嗯，在其中，能量是以一定量的块，一块一块地到来。事情并不是那样。然而，是有一些公式，可用来计算一些数字的量，当我们把这些量加起来时，会得到“28”--总是这个数。计算能量，是一个抽象的事情，它不能告诉我们各种不同公式的机制或原因。

4–2Gravitational potential energy 4-2重力势能
Conservation of energy can be understoodonly if we have the formula for all of its forms. I wish to discuss the formulafor gravitational energy near the surface of the Earth, and I wish to derivethis formula in a way which has nothing to do with history but is simply a lineof reasoning invented for this particular lecture to give you an illustrationof the remarkable fact that a great deal about nature can be extracted from afew facts and close reasoning. It is an illustration of the kind of worktheoretical physicists become involved in. It is patterned after a mostexcellent argument by Mr. Carnot on the efficiency of steam engines.1
能量有多种形式，每种形式都有其公式，只有当我们拥有了所有能量的公式只时，能量守恒才可被理解。我希望讨论接近地球表面的重力能量的公式，我希望这样来派生它：即与历史性，没有任何关系，而只是一种简单的推理过程，此过程是专为本讲座发明的，目的是给你们展示一个引人注目的事实，即关于自然的大量东西，可以从少数几个事实和严密的推理得出。它所展示的，就是理论物理学家正在开始从事的工作。卡诺先生，对于蒸汽机的效率，做过一个最杰出的论证，在此之后，上述工作，就变成了一种模式。

Consider weight-lifting machines—machineswhich have the property that they lift one weight by lowering another. Let usalso make a hypothesis: that there is no such thing as perpetual motionwith these weight-lifting machines. (In fact, that there is no perpetual motionat all is a general statement of the law of conservation of energy.) We must becareful to define perpetual motion. First, let us do it for weight-liftingmachines. If, when we have lifted and lowered a lot of weights and restored themachine to the original condition, we find that the net result is to have lifteda weight, then we have a perpetual motion machine because we can use thatlifted weight to run something else. That is, provided the machine whichlifted the weight is brought back to its exact original condition, andfurthermore that it is completely self-contained—that it has notreceived the energy to lift that weight from some external source—like Bruce’sblocks.
我们考虑起重机，它有这样一个特性，即可以通过降低一个重量，来举起另一个重量。我们先做一个假设：对于这些起重机来说，并没有永动机这种东西。（事实上，根本没有任何永动，是能量守恒规律的一个一般声明。）要定义永动，我们必须很仔细。首先，让我们为起重机做此事。如果，在我们举起并降下很多重量之后，把机器恢复到它的起始状态，我们发现，最终结果，就是举起了一些重量，然后，我们就有一种永动机，因为我们可以用此被举起的重量，来运行其他的事情。也就是说，假设举起重量的这个机器，被带回了起始的状态，另外，它也是完全自我包容的，--它并没有从任何外部的源泉，接收能量，以举起重量，就像布鲁斯的积木。

Fig. 4–1.Simple weight-lifting machine. 简单的起重机
A very simple weight-lifting machine is shownin Fig. 4–1.This machine lifts weights three units “strong.” We place three units on onebalance pan, and one unit on the other. However, in order to get it actually towork, we must lift a little weight off the left pan. On the other hand, wecould lift a one-unit weight by lowering the three-unit weight, if we cheat alittle by lifting a little weight off the other pan. Of course, we realize thatwith any actual lifting machine, we must add a little extra to get it torun. This we disregard, temporarily. Ideal machines, although they donot exist, do not require anything extra. A machine that we actually use canbe, in a sense, almost reversible: that is, if it will lift the weightof three by lowering a weight of one, then it will also lift nearly the weightof one the same amount by lowering the weight of three.
图4-1所示，是一种简单的起重机。这台机器可以举起三个单位“强”的重量。然而，为了让它真正地能够工作，我们必须从左边的盘子中，抬起一点重量。另一方面，我们可以通过降低三个单位的重量，来抬起一个单位的重量，如果我们小小地欺骗一下，即把另一端的盘子，往上抬一点。当然，我们也意识到，对于任何实际的起重机来说，我们应该增加一点额外的{重量}，以让它能够运行。这点我们暂时先不管。理想的起重机，虽然不存在，但它们并不要求任何额外的{重量}。我们实际上使用的起重机，在某种意义上，几乎是可以反转的，也就是说，如果它可以通过降低一个单位的重量，来抬起三个单位的重量，那么同样，它也可以通过降低三个单位的重量，来抬起一个单位的重量。

We imagine that there are two classes ofmachines, those that are not reversible, which includes all realmachines, and those that are reversible, which of course are actuallynot attainable no matter how careful we may be in our design of bearings,levers, etc. We suppose, however, that there is such a thing—a reversible machine—whichlowers one unit of weight (a pound or any other unit) by one unit of distance,and at the same time lifts a three-unit weight. Call this reversible machine,Machine A . Suppose this particular reversible machine lifts the three-unit weighta distance X . Then suppose we have another machine, Machine B , which is not necessarily reversible, which also lowers a unit weighta unit distance, but which lifts three units a distance Y . We can now prove that Y is not higher than X ; that is, it is impossible to build a machine that will lift a weightany higher than it will be lifted by a reversible machine. Let us seewhy. Let us suppose that Y were higher than X . We take a one-unit weight and lower it one unit height withMachine B , and that lifts the three-unit weight up a distance Y . Then we could lower the weight from Y to X , obtaining free power, and use the reversible Machine A, running backwards, to lower the three-unit weight a distance Xand lift the one-unit weight by one unit height. This will put theone-unit weight back where it was before, and leave both machines ready to beused again! We would therefore have perpetual motion if Y were higher than X , which we assumed was impossible. With those assumptions, we thus deducethat Y is not higher than X , so that of all machines that can be designed, the reversible machineis the best.
我们可以想象，我们有两类机器，一类是不可反转的，包括所有真正的机器，另一类是可反转的，但实际上，不论当我们用轴承、杠杆来设计时，是如何地仔细，这种机器，都是得不到的。然而，我们可以假设，存在这样的东西，即一个可反转的机器，它通过降低一个单位的重量（一磅或任何其它单位）一个单位的距离，来抬起三个单位的重量。这个可反转的机器，被称为机器A。假设这个可反转的机器，可以把三个单位的重量，提高一个X距离。然后，假设我们还有另外一台机器B，它并不必然是可反转的，同样，它也可以把一个单位的重量，降低一个单位的距离，但是，却可以把三个单位的重量，提高一个Y的距离。我们现在可以证明，Y并不比X高；也就是说，把一定重量举高，新建的机器所能做到的，与可反转机器所能做到的相比，并不更高。现在看为什么。先假设Y比X高。我们用机器B，把一个单位的重量，降低一个单位的高度，这样，就可以把三个单位的重量，提高Y的高度。然后，我们把重量从Y降到X，就能获得力量，然后，再使用可反转的机器A，反向运转，把三个单位的重量，降低X距离，并且，把一个单位的重量，提高一个单位的距离。这样，就把一个单位的重量，放回了其原处，从而让两台机器，都可被重新使用！如果Y比X高的话，我们就可以有一台永动机了，而这我们假设是不可能的。根据这些假设，我们就可以推出，Y不可能比X高，所以，在我们所能设计的所有机器中，可反转的机器，是最好的。

We can also see that all reversiblemachines must lift to exactly the same height. Suppose that B were really reversible also. The argument that Y is not higher than X is, of course, just as good as it was before, but we can also make ourargument the other way around, using the machines in the opposite order, andprove that X is not higher than Y . This, then, is a very remarkable observation because it permits us toanalyze the height to which different machines are going to lift something withoutlooking at the interior mechanism. We know at once that if somebody makesan enormously elaborate series of levers that lift three units a certaindistance by lowering one unit by one unit distance, and we compare it with asimple lever which does the same thing and is fundamentally reversible, hismachine will lift it no higher, but perhaps less high. If his machine isreversible, we also know exactly how high it will lift. To summarize:every reversible machine, no matter how it operates, which drops one pound onefoot and lifts a three-pound weight always lifts it the same distance, X. This is clearly a universal law of great utility. The next questionis, of course, what is X ?
我们还可以看到，所有可反转的机器，都应该举到同样的高度。假设B也确实是可反转的。关于Y并不比X高的论证就是，以相反的顺序使用起重机，从而证明X并不比Y高；当然，这种论证，正如以前一样好，但是，我们也可以用另外的方式，给出我们的论证。因此，这一观察，引人注目，因为，不同的起重机，都会把某物提升到一个高度，而此观察，允许我们去分析这些高度，且不用去查看内部的机制。所以，如果某人制造了巨大的复杂的杠杆系列，可以通过把一个单位的重量降低一个单位的距离，来把三个单位的重量提高一定的距离，假设还有另外一种简单的杠杆，也可以做同样的事情，且是可反转的，那么，我们比较这两种机械，马上就会知道，前一机器，并不会举的更高，或许还更低。如果他的机器是可反转的，那么我们也会准确地知道，它能举多高。总结：每种可反转的机器，如果它是通过把一磅的重量降低一英尺，来抬高三磅的重量，那么，不论它是怎么运行的，总是抬高同样的距离：X。很清楚，这是普遍的伟大实用的规律，下一个问题当然就是：X是什么？

Fig. 4–2.A reversible machine. 一个可逆的机器
Suppose we have a reversible machine[A1] which is going to lift this distance X , three for one. We set up three balls in a rack which does not move,as shown in Fig. 4–2. Oneball is held on a stage at a distance one foot above the ground. The machinecan lift three balls, lowering one by a distance 1 . Now, we have arranged that the platform which holds three balls hasa floor and two shelves, exactly spaced at distance X , and further, that the rack which holds the balls is spaced atdistance X , (a). First we roll the balls horizontally from the rack to theshelves, (b), and we suppose that this takes no energy because we do notchange the height. The reversible machine then operates: it lowers the singleball to the floor, and it lifts the rack a distance X , (c). Now we have ingeniously arranged the rack so that theseballs are again even with the platforms. Thus we unload the balls onto therack, (d); having unloaded the balls, we can restore the machine to itsoriginal condition. Now we have three balls on the upper three shelves and oneat the bottom. But the strange thing is that, in a certain way of speaking, wehave not lifted two of them at all because, after all, there were ballson shelves 2 and 3 before. The resulting effect has been to lift one ball adistance 3X . Now, if 3X exceeds one foot, then we can lower the ball to return themachine to the initial condition, (f), and we can run the apparatus again.Therefore 3X cannot exceed one foot, for if 3X exceeds one foot we can make perpetual motion. Likewise, we can provethat one foot cannot exceed 3X , by making the whole machine run the opposite way, since it is areversible machine. Therefore 3X is neither greater nor less than a foot, and we discover then,by argument alone, the law that X=13 foot. The generalization is clear: one pound falls a certaindistance in operating a reversible machine; then the machine can lift p pounds this distance divided by p . Another way of putting the result is that three pounds times theheight lifted, which in our problem was X , is equal to one pound times the distance lowered, which is one footin this case. If we take all the weights and multiply them by the heights atwhich they are now, above the floor, let the machine operate, and then multiplyall the weights by all the heights again, there will be no change. (Wehave to generalize the example where we moved only one weight to the case wherewhen we lower one we lift several different ones—but that is easy.)
假设我们有一个可反转的机器，它可以通过降低三个X的距离，来抬高一个X的距离。我们在一个固定的支架上，放三个球，如图4-2。另一个球，在一定距离之外被托着，比地面高一英尺。此机器，可以通过把一个球降低1英尺，来抬高三个球。现在，有个装三个球的平台，它有三层，每层高都是X，我们把它放在距支架X处，（a）。首先，我们把球，滚到平台的各层上，（b），我们假定这不消耗能量，因为我们并未改变高度。然后，可反转机器开始运行：它把那个单个的球，降到地板，从而把平台抬高一个X的距离，（c）。现在，我们巧妙地安排平台，已让这些球，与架子相平。这样，我们就把这些球，卸载到了架子上，（d）;卸载了这些球之后，我们就可以把机器，恢复到起原始状态。现在三个球在架子的上三层，一个在底层。但是，以某种方式来说，奇怪的事情就是，我们根本没有抬高其中的两个球，因为，毕竟这两个球，以前就是在第二层和第三层。实际结果就是，把一个球，抬高了3X的距离。现在，如果3X超过了1英尺，那么，我们就可以把球降低，然后让机器回到它的初始状态，（f），这样，我们就可以重新运行这个装置了。因此，3X不能超过1英尺，因为如果那样，等于我们造出了一个永久运动。同样，因为这个机器，是可反转的，所以，通过让这个机器反向运行，我们也可以证明，1英尺不能超过3X。所以，3X既不比1英尺大，也不比它小。所以，通过这个论证，我们就发现了规律，即X=1/3英尺。可以清晰地概括如下：运行一台可反转的机器，让一磅重量降下一定距离，那么，这个机器，就可以把p磅的重物，抬高此一定距离的1/p。表示这一结果的另一方法就是，三磅乘以抬高的高度，在我们这个问题中就是X，等于一磅乘以降下的距离，这里就是1英尺。如果我们让所有的重量，乘以它们现在的在地板之上的高度，然后，让机器运行，再然后，让所有的重量，再乘以所有的高度，将没有任何变化。（在我们的例子中，我们是把一个重量降低，抬高了几个重量，对此例子，我们应该归纳一下，即我们实际只移动了一个重量，然而，这种归纳，并不容易。）
[A1]

We call the sum of the weights times the heights gravitational potential energy—the energy which an object has because of its relationship in space, relative to the earth. The formula for gravitational energy, then, so long as we are not too far from the earth (the force weakens as we go higher) is
gravitationalpotential energy for one object=(weight)×(height).(4.3)
我们把重量乘以高度的总和，称为重力势能，一个对象，拥有这种能量，乃是因为，它在空间中相对于地球的关系。因此，只要我们离地球不是很远（高度越高，力量越弱），那么，重力势能的公式就是：
一个对象的重力势能=重量*高度。 （4.3）

It is a very beautiful line of reasoning. The only problem is thatperhaps it is not true. (After all, nature does not have to go alongwith our reasoning.) For example, perhaps perpetual motion is, in fact,possible. Some of the assumptions may be wrong, or we may have made a mistakein reasoning, so it is always necessary to check. It turns outexperimentally, in fact, to be true.
这条推理思路，非常漂亮。唯一的问题就是，或许它不是真的。（毕竟自然没有必要按我们的思路走。）例如，永动机事实上或许是可能的。有些假定可能是错的，或者，我们在推理时犯了错，所以，检查总是必要的。事实上，从实验的角度看，是真的。

The general name of energy which has to dowith location relative to something else is called potential energy. Inthis particular case, of course, we call it gravitational potential energy.If it is a question of electrical forces against which we are working, insteadof gravitational forces, if we are “lifting” charges away from other chargeswith a lot of levers, then the energy content is called electrical potentialenergy. The general principle is that the change in the energy is the forcetimes the distance that the force is pushed, and that this is a change inenergy in general:
(change inenergy)=(force)×(distanceforceacts through).(4.4)
有些能量，与相对于其它某物的位置有关，这种能量，我们称之为势能。当然，在这种特殊情况下，我们称之为重力势能。如果我们所谈的问题，是与电力有关，而不是与重力有关，如果我们是用很多杠杆，把电荷从其它电荷中“提升”，那么，这个能量的内容，我们称之为电势能。一般的原理就是，能量的变化，是力乘以力所作用的距离，这就是一般能量的变化：
能量中的变化=(力)×(力所作用的距离).(4.4)

Fig. 4–3.Inclined plane. 倾斜的平面
The principle of the conservation of energyis very useful for deducing what will happen in a number of circumstances. Inhigh school we learned a lot of laws about pulleys and levers used in differentways. We can now see that these “laws” are all the same thing, and thatwe did not have to memorize 75 rules to figure it out. A simple example is a smooth inclined planewhich is, happily, a three-four-five triangle (Fig. 4–3). Wehang a one-pound weight on the inclined plane with a pulley, and on the otherside 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 thatout? If we say it is just balanced, it is reversible and so can move up anddown, 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, (b), we have a one-pound weightat the top and the weight W the slant distance, or five feet, from the plane in which it wasbefore. We lifted the one-pound weight only three feet and we loweredW pounds by five feet. Therefore W=3/5 of a pound. Note that we deduced this from the conservation ofenergy, and not from force components. Cleverness, however, is relative. Itcan be deduced in a way which is even more brilliant, discovered by Stevinusand inscribed on his tombstone. Figure 4–4explains that it has to be 35 of a pound, because the chain does not go around. It is evidentthat the lower part of the chain is balanced by itself, so that the pull of thefive 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 Wmust be 3/5 of a pound. (If you get an epitaph like that on your gravestone, youare doing fine.)

Fig. 4–4.The epitaph of Stevinus. 斯蒂维纽司的墓志铭
很多情况下，究竟会发生什么，都可以用能量守恒原理来解释。在高中，我们学了滑轮和杠杆在不同方式下使用的规律。现在我们可以看到，这些规律，都是同一个事情，这样，我们就没必要去记75条规则，以把它搞清楚了。一个简单的例子，就是一个光滑的斜面，它恰好是3、4、5三角形，见图4-3。我们在斜面上，用一个滑轮，吊着一磅重，在滑轮的另一面，是重量W。我们想知道，W应该有多重，才能平衡斜面上的那一磅。我们如何才能搞清楚呢？如果我们说，它刚好已经平衡了，那么，它就是可反转的，于是就可以来回移动，这样我们就可以考虑下面的情况。在初始情况下，（a），一磅重，在底部，重量W，在顶部。当W以一种可反转的方式，滑动到下面时，（b），一磅重，在顶部，而重量W，距其先前所在位置的距离，就是斜面的长度，或五英尺。我们把一磅重抬高了三英尺，把W降低了五英尺。因此W是1磅的3/5。注意，我们是从能量守恒，推出这点的，而不是从力的构成。然而，聪明是相对的。还有一种更加才华横溢的方法，可以推出它。该方法由斯蒂维纽司发现，且刻在他的墓碑上。图4-4解释了，确实应该是一磅的3/5，因为链子并不是转着圈走。很明显，下部的链子，是自平衡的，于是，在一侧拉这五个重量的，与另一侧拉三个重量的，应该平衡，且不论这个绳子的比例是多少。你看，通过看这个图，W应该是一磅的3/5。（如果你的墓碑上，有这么一个墓志铭，说明你很棒。）

Let us now illustrate the energy principle with a more complicated problem, the screw jack shown in Fig. 4–5. A handle 20 inches long is used to turn the screw, which has 10 threads to the inch. We would like to know how much force would be needed at the handle to lift one ton (2000 pounds). If we want to lift the ton one inch, say, then we must turn the handle around ten times. When it goes around once it goes approximately 126 inches. The handle must thus travel 1260 inches, and if we used various pulleys, etc., we would be lifting our one ton with an unknown smaller weight W applied to the end of the handle. So we find out that W is about 1.6 pounds. This is a result of the conservation of energy.

Fig. 4–5.A screw jack. 图4-5 一个螺丝千斤顶
现在，我们用一个更复杂的问题，即一个螺丝千斤顶，如图4-5，来说明这个能量原理。一个20英寸长的手柄，被用来转这个螺丝，这个螺丝有10条螺线/英寸。我们希望知道，把一吨（2000磅）举高，在手柄上要加多少力。如果我们想把这一吨，抬高一英寸，那么，我们应该把手柄转十次。手柄转一圈，约走126英寸。这样，手柄就应该走了1260英寸，如果我们使用各种不同的滑轮等等，作用于手柄末端，我们就是高用一个较小的重量W，来举此一吨。所以我们发现，W约为1.6磅。这是一个能量守恒的结果。

Fig. 4–6.Weighted rod supported on one end.图4-6 一端有支持的重锤杆
Take now the somewhat more complicated exampleshown in Fig. 4–6. A rodor bar, 8 feet long, is supported at one end. In the middle of the bar isa weight of 60 pounds, and at a distance of two feet from the support there isa weight of 100 pounds. How hard do we have to lift the end of the bar in orderto keep it balanced, disregarding the weight of the bar? Suppose we put apulley at one end and hang a weight on the pulley. How big would theweight W have to be in order for it to balance? We imagine that the weightfalls any arbitrary distance—to make it easy for ourselves suppose it goes down4 inches—how high would the two load weights rise? The centerrises 2 inches, and the point a quarter of the way from the fixed endlifts 1 inch. Therefore, the principle that the sum of the heights timesthe weights does not change tells us that the weight W times 4 inches down, plus 60 pounds times 2 inches up, plus 100 pounds times 1 inch has to add up to nothing:
−4W+(2)(60)+(1)(100)=0,W=55 lb.(4.5)
Thus we must have a 55 -pound weight to balance the bar. In this way we can work out the lawsof “balance”—the statics of complicated bridge arrangements, and so on. Thisapproach is called the principle of virtual work, because in order toapply this argument we had to imagine that the structure moves alittle—even though it is not really moving or even movable. Weuse the very small imagined motion to apply the principle of conservation ofenergy.
现在我们看一个更复杂的例子，见图4-6。杆长八英尺，一端有支点。杆的中间，有60磅的重量，距支点两英尺处，有100磅的重量。为了在杆的另一端举起它，以保持平衡，我们要用多大的力呢？杆重忽略不计。假设我们在另一端放一个滑轮，把重量吊在滑轮上。那么，要保持平衡，W应有多重？我们假设这个重量，可以下降任意的距离，为了方便，我们假设是四英寸，那么？杆上的这两个重量，能被抬多高呢？中间的抬高两英寸，与固定支点相距1/4杆长的那个，抬高一英寸。因此，高度乘以重量之和不变这条原理，告诉我们，重量W乘以4英寸向下，加上60磅乘以两英寸向上，再加上100磅乘以1英寸，应为零。
−4W+(2)(60)+(1)(100)=0，W=55 lb。 (4.5)
这样，要让杆平衡，我们就要有55磅的重量。以这种方式，我们就得出了“平衡”的规律，即复杂的桥的安排的静态{力学}，等等。这一解决方案，被称为虚拟的工作原理，因为，为了应用这种论证，我们必须想象这个结构，移动了一点，虽然，它可能并未真正地移动，或者根本不能移动。我们利用很小的想象出来的运动，来应用能量守恒的原理。

4–3Kinetic energy 4-3 动能
To illustrate another type of energy weconsider a pendulum (Fig. 4–7). If wepull the mass aside and release it, it swings back and forth. In its motion, itloses height in going from either end to the center. Where does the potentialenergy go? Gravitational energy disappears when it is down at the bottom;nevertheless, it will climb up again. The gravitational energy must have goneinto another form. Evidently it is by virtue of its motion that it is ableto climb up again, so we have the conversion of gravitational energy into someother form when it reaches the bottom.

Fig. 4–7.Pendulum. 图4-7 单摆
为了示例另外一种能量，我们考虑单摆（图4-7）。如果我们把那个圆块，拉到一边，然后放开它，那么，它就会来回摆动。在其运动中，无论从哪边到中间，它都会失去高度。潜在的能量去了哪里呢？当它在底部时，重力势能消失，尽管如此，它还是会再升起来。重力势能应该是变成了另外一种形式。最终，正是由于运动，它才能重新升起，所以，我们就得到，当它到达底部的时候，重力势能转换成了某种其他形式的能量。