I draw a graph here of the amount by which I pull the spring versus the force it exerts.

我在这里画个图,纵轴是弹簧的拉伸量,横轴是力的大小

耶鲁公开课 - 基础物理课程节选

you're looking for that equal and opposite forces acting at two ends of the rope.

你就得求出作用在绳子两端的,大小相等方向相反的力

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Therefore, what we have done now is, we can take all kinds of springs and we can calibrate the force they will exert under various conditions.

因此,我们现在能做到的就是,我们能处理各种各样的弹簧,我们能测出它们在不同的情况下,产生的力的大小

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Newtons acting on 2 kg, gives you an acceleration of 2.

牛的力作用在 2 千克的物体上,那么其加速度大小就是 2

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That is the force which I do not know in magnitude.

我并不知道这个力的大小

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The force is not known, but it's the same force.

力的大小未知,但与前一个力大小相等

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We didn't have to know its magnitude.

我们无需知道这个力的大小

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Then the acceleration of the planet is the force of gravity between the planet and the Sun, which Newton will tell you is directed towards the Sun and it depends on how far you are.

行星的加速度源自,行星和太阳之间的作用力,牛顿认为这个力指向太阳,它的大小取决于行星离太阳有多远

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That's how by either balancing the unknown force with a known force or by simply measuring the acceleration as I fall towards this podium and multiplying by mass, you can find the force that exerts on me.

我们既可以让未知力与已知力平衡,也可以只测量我冲向讲台时加速度的大小,再与我的质量相乘,都能求出作用在我身上的力的大小

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Then I know that kx is equal to the force that is exerting at this separation.

然后我就能知道 kx 等于,这个位置上讲台产生的力的大小

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We did the comparison with the elephant or something; a is the second derivative of x and for this problem, when F is due to a spring, we know the force is that by studying the spring.

我们也已经把它与大象或其它东西作过比较,a 是 x 的二阶导数,在这个问题中,F 是由弹簧产生的,我们在讨论弹簧问题时已经知道了力的大小

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