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Therefore, when you divide by the mass to get the acceleration, the response of different bodies is inverse to the mass.
因此,当你拿力除以质量得到加速度时,不同物体的加速度与质量成反比
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We know now with the same spring, by this comparison, we will find all objects now can be attributed a mass.
我们现在知道利用相同的弹簧,采用这种比较的方法,就会发现,所有物体都有确定的质量
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But gravity has a remarkable property that the pull of the Earth is itself proportional to the inertia of the object.
重力有一个显著特征,即地球的引力,与物体的质量成比例
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So, a massless body cannot have a net force on it, because the acceleration of the rope cannot be infinite.
所以没有质量的物体不会受到力,因为绳子的加速度不可能是无穷大
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But the acceleration it produces on the elephant and on the mass, are in an inverse ratio of their masses.
但这个力使大象和物体产生的加速度,与它们的质量成反比
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One is inertial mass, which is how much you hate your velocity to change, how hard you resist acceleration.
一个是惯性质量,它反映了物体速度改变的难易程度,即保持加速度的难易程度
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So, massless bodies will always have, like a massless rope, equal and opposite forces on the two ends.
所以无质量的物体,比如这个绳子,两边所受的力永远都相等
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Now I can measure that, because I pull it by one centimeter and I find the acceleration it exerts on a known mass.
现在就能测量这个力了,因为把弹簧拉伸 1 厘米,我就知道它让一个质量已知的物体产生的加速度
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And know intuitively that if they move together, they will behave like an object of mass 5 and the acceleration will again be 2.
凭直觉认为既然它们一起运动,那么它们就相当于一个质量为 5 千克的物体,然后我们可以算出加速度为 2
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Mass of an object is how much it hates to accelerate in response to a force.
物体的质量,反映了物体在力的作用下加速的难易程度
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This also tells you that the mass of an object has nothing to do with gravitation.
这也表明,物体的质量与重力无关
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Other is gravitational mass, which is the measure of how much you're attracted to the Earth.
另一个是引力质量,它可以用来衡量地球对物体引力的大小
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We have not yet found a satisfactory answer to what's the mass of an object?
我们还没有一个令人满意的答案,物体的质量到底是多少
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If you look at the electrical force, the force of electricity, proton and electron or something, it's not proportional to the mass of either object.
如果你考察电作用力,即电现象产生的力,质子啊,电子啊,或者其它什么东西,这种力不和物体的质量成比例
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Imagine then from now on, we can find the mass of any object, right?
假设从现在开始,我们就能测量任何物体的质量了,对吧
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You cannot tell the mass, because what you are doing now is appealing to the notion of mass as something that's related to the pull of the Earth on the object.
你无法测出质量,因为你现在所做的是把质量,用地球对物体的引力给替代了
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We're just asking what's the mass of any object?
我们只是问物体的质量是多少
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First one says, if you knew the force acting on any body, without going into what caused the force, then you may set that force equal the mass times acceleration of the body.
第一部分是,如果你知道作用在任一物体上的力,无论这个力的来源是什么,都可以令力等于质量乘以物体的加速度
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What's the mass of this object?
这个物体的质量是多少
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We can be precise about how much bigger by saying, "If the acceleration of a body to a given force is ten times that of a one kilogram mass, then this mass is one-tenth of one kilogram."
我们能精确地知道质量能大多少,只需要说,"如果物体在给定力作用下的加速度,是一个 1 千克物体的加速度的 10 倍,那这个物体的质量就是 1 千克的十分之一"
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If you knew this was one kilogram, then the acceleration of the elephant, which will be some tiny number, maybe 100th of what this guy did; the mass of the elephant is then 100 kilograms.
如果已知这个物体的质量为 1 千克,那大象的加速度,会是一个比较小的数,可能是物体加速度的 1 / 100,大象的质量就是 100 千克
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In fact, there's a property of gravitational fields anywhere, even in outer space, but there is some residual field between all the planets and all the stars in the universe, that the force on a body is proportional to the mass of the body.
实际上,这是任何地方的引力场都具备的属性,甚至是在外太空,在所有的行星和恒星之间,存在着某种剩余场,在这个场里作用在物体上的力,和物体的质量之间存在比例关系
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We know there is no thing called a massless rope, but most ropes have a mass, but maybe negligible compared to the two blocks you are pulling, so we'll take the idealized limit where the mass of the rope is 0.
我们都知道无质量的绳子是不存在的,是绳子就有质量,但是相比于这两个物体就可以忽略不计了,所以我们有了这个理想的条件,即绳子的质量都是 0
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Newton says F = ma, so to make it a useful result of this problem, we know the mass of this guy.
牛顿指出 F = ma,这对于解决这个问题很有用,我们知道这个物体的质量
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