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That is, you minimize potential energy and you see things falling under the force of gravity and so forthgoing to potential energy minima in conformance with this result.
换句话说，你使得势能最小化,然后发现我们关注的东西,在重力或者其他力的作用下下落,直到势能最小的地方,这和我们刚才的结果是一致的。
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By the way, when I say there's 10 Newtons acting this way, you might say, "What about gravity? What about the table?"
顺便提一下我说有 10 牛的作用力,你也许会问,"那重力呢,桌子对它的力呢"
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If all you know is the particle is falling under the affect of gravity, that's not enough to say where the particle is, right?
如果你只知道,质点受重力作用下落,那并不足以表明物体的位移,对吧
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For example, let's take the case where the particle is falling under gravity.
比如说,举个例子,一个质点正在重力的作用下下落
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The reason it comes down is gravity is pulling it.
物体向下运动是因为重力作用
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You feel heavy and it reads more because the poor spring not only has to support you from falling through the floor, but also accelerate you counter to what gravity wants to do.
你感到自己变重以及读数增加,因为现在弹簧不仅要支撑你,不让你掉下来,还要抵消重力的作用让你加速
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It knows that this particle happened to have a height of 15, at the time of 0, and a velocity of 10, and it is falling under gravity with an acceleration of -10.
这个质点恰好处在高度为15的地方,零时刻,初速为10,并在重力作用下以-10的加速度下坠
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So，the point is,every object falling under gravity is given by the same formula, but there are many, many objects that can have many histories, all falling under gravity, and what's different from one object and the other object is, when was it dropped, from what height, and with what initial speed.
关键是,每一个受重力作用下落的物体,都有同样的表达式,但是各个受重力作用下落的物体,都有不同的初始条件,所以它们的区别在于,下落时刻,下落高度和初始速度
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You are pushing down with the weight mg, and the floor has got to be pushing up with the mg, because the spring is not going anywhere.
你向下的作用力是重力 mg,然后地面向上的支持力也是 mg,因为弹簧现在根本没动
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For example, suppose you use vertical motion and you use y instead of x; and a would be g or -g; that's a particle falling down under the affect of gravity.
例如,假设在竖直运动中,你用 y 来代替 x,那么 a 就是 g 或者 -g,这就是一个受重力作用下落的质点
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For most of us, gravity acts this way, defines a vertical direction very naturally and the blackboard is oriented this way, so very natural to call that x and call that y and line up our axes.
对我们多数人来说,重力作用下,很自然地确定了竖直方向,而我们的黑板又是这个指向的,所以很自然地定出 x 轴和 y 轴,并标出我们的坐标系
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Conversely, if you get an answer and it doesn't seem to make sense, then you've got to go back and ask, am I violating some of the assumptions, and here you will find the assumption that the particle had that acceleration a is true as long it's freely falling under gravity but not when you hit the ground.
反过来说,如果你得到一个结果,发现似乎是错的,那么你就应该回过头来问问自己,我是不是违反某些前提了,这个模型中,你就发现,只要质点在重力作用下自由下落,质点具有加速度a的前提是正确的,但是落地后就不成立了
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