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Even in the case of this spring, when you pull it, if you pull it to the right by some force.
甚至是在这样的弹簧问题中,当你拉它的时候,如果你用力向右拉
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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
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Newton is not going to come and tell you what force the spring will exert when it's pulled by some amount.
牛顿不会过来告诉你,弹簧被拉伸一定量时会产生多大的力
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If you connect the body to a spring, which is neither compressed nor extended, there's no force acting on it.
如果将一个弹簧连在这个物体上,弹簧既没有被压缩也没有被拉伸,也不会有力作用在它上面
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First, we got to make sure the spring exerts a fixed force every time.
首先,要保证,弹簧每次产生的力是恒定的
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If every time I get the same acceleration, I'm convinced this is a reliable spring that is somehow producing the same force under the same condition.
如果每次都能得到相同的加速度,这个弹簧的可靠性就能令人信服,即它在相同的条件下能够产生相等的力
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If you pull the spring, there is a force acting on it.
如果拉这个弹簧,就有力作用在物体上了
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This is the force exerted by the spring on the mass.
这是弹簧对物体的作用力
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We don't know what the force of the spring is.
我们不知道弹簧的力多大
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A spring will, on the other hand, exert a force.
但是一个弹簧可以提供一个力
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You cannot say to me, "Take a force, due to a spring, and see what force it applies and divide by the acceleration and get the mass, " because we haven't defined force, either.
你不能说,"给弹簧施加一个力,看看它能提供多大的力,然后除以加速度,得到质量",因为我们还没给力下一个定义
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For example, how do I know that when I pull the spring the first time for the mass, it exerted the same force when I pulled the spring the second time for the elephant?
例如 怎样才能知道,第一次连着物体拉弹簧时,产生的力和,第二次连着大象拉弹簧时产生的力是相等的呢
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This is the force of the spring.
这个是弹簧产生的力
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The force may taper off, the force may not be given by a straight line, but for modest deformations, every spring will have a linear regime in which the force is linearly proportional to the stretching.
它产生的力可能会渐渐消失,力的曲线可能不是一条直线,而有轻微的弯曲,每个弹簧都有一个线性区间,在这一区间内,力和伸长量是线性关系
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But if I'm accelerating, the force exerted by the spring and therefore, the needle the weighing machine reads is m.
但是如果我在加速运动,那么弹簧的弹力,也就是称重机上指针的读数就是 m
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Therefore, it'll compress by an unknown x, which is equal to mg divided by the force constant of the spring.
因此它的压缩量为 x,也就等于 mg 除以弹簧的弹性系数
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That m times a is the force the spring is exerting.
与 a 的乘积就等于弹簧产生的力
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It says, if you pull it to the right, so that x is positive, the spring will exert a force which is in the negative direction; that's why you have a minus sign.
就是说,如果你向右拉,x 取正值,弹簧产生的力方向为负,这就是这里用负号的原因
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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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