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英语煎蛋小学堂视频百科97:物死早系列之能量守恒定律的简单证明(MP3+中英双语)

cocotang 于2015-04-27发布 l 已有人浏览
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英语视频:煎蛋小学堂97:物死早系列之能量守恒定律的简单证明,以幽默诙谐的方式为你解答那些那些你意想不到的科学小知识,含有中英双语字幕视频,mp3下载。
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One of the fundamental principles in modern physics is that there's no absolute time.And I'm not not even talking about relativity making time go at different rates.if you're going near light sead,I just mean that any time is as good as any other to set your clock to zero,The predictions of physics work all the same,and it's not like there's some "absolute starting time". I mean,if there were,time zones wouldn't work,In addition to allowing time zones,the fact that there's no absolute time,also implies the law of conservation of energy.

“绝对时间不存在”是现代物理基本定理之一,我说的不是接近光速时 相对论使得,时间流逝速率不同,我是说 在任意时间将时钟归零都一样,物理所做的预测完全相同,“绝对开始时间”这种东西并不存在,如果有的话 那么时区就无效了,除时区之外“绝对时间不存在”也暗示着能量守恒定律.

Here's simple proof to show that if a force doesn't depend explicitly on time,then that force conserbes energy! First conserving energy just means that there's a certain number,called the energy,which doesn't change as time passes.If you compare the energy at two different times,you'll see no difference.And the total energy of a system isthe sum of its energy of motion,or kinetic energy,and its energy due to position-the potential energy,So all we need os to find the change in kinetic and potential energiesover time.and add them up!

这里简单证明下 若外力不显式地依赖于时间,那么该力储存能量,首先 储存能量仅意味着有一个可称为“能量”的解切数字,不随时间变化,如果你在两个不同时间比较它们也不会看到区别,系统的总能量为其运动的能量 或动能,加上由位置决定的热能之总和,我们要找的就是动能和势能随时间的改变量,把它们相加.

Ok,we know the kinetic energy of an object is half of its mass times its velocity squared,So the change in kinetic energy over time is just,one half m times the differenceof the squares of the velocities,Some clever algebra can rearrange this expression to become,the average velocity times m times the CHANGE in velocity,But a change of velocity over time is just an acceleration,and mass times acceleration is equal to the force on the object,So the change in kinetic energy of an object over time is just velocity times force.

好了 我们知道物体的动能为1/2物体质量乘经速度平方,那么 动能随时间的变化就是,1/2.m(物体质量).速度改变量平方,机智的代数变化可将此表达式变为,平均速度.m(质量).速度改变量,不过 速度随着时间的改变量就是加速度,质量乘以加速度等于施加在物体上的力,那么 物体动能随时间的改变量就是速度乘以力.

On the other hand,the change in the potential energy of an object ,is negative the amount of work it takes to get the object to its  current position form its previous position independent of the path taken,that is,potential energy is the negative of the foece applied times the change in position,This is where the "there's no absolute time"part comes into play,You can't have potential energy for a force that changes over time,And just to be clear, "no changing over time" doesn't mean that,an object can't experience a changing force along the course of journey,the foece might be different at different places,but at any particular place.the force must remain the same.

另一方面 物体势能的改变量,为将物体从原先位置带到现在为止所需的功的负值,与所选取路径无关,即 势能等于物体所受力乘以位置变化量之积取负值,现在“绝对时间不存在”可要掺合进来啦? 随时间变化的力不可用势能衡量,这里要说清楚“不随时间改变”,不是说,物体在运动过程中不可能受到变力作用,不同地点力的大小也许不同.但在某一处,力一定是相同的(包括大小和方向).

Anyway,this is all just to say that the change in potential energy is negative F times the change in position.The negative comes from the fact that if you let the force push you along,your potential energy decreases,while if you fight in opposition to the force your potential energy increases.So the change in potential energy  over time is the negative of the force times the change in position over time,but change in position over time is velocity!

无论如何  这只说明势能改变量为,负的F(力的大小)乘以位置变化量,有负号是因为 如果你让这个力一直推着你,你的势能就会降低,而当你反抗该力而行 你的势能会增加,因此 势能随时间的改变量,就是负的力的大小乘以一段时间内位置变化量,但一段时间内位置变化量就是速度.

Which means change in potential energy of an object over time is negative velocity times force.And thus the change in the total energy over time,which is the sum of the changes in the kinetic and potential energies over time,is v*F plus negative v*F,which equals zero!And zero change in energy over time is precisely conservation of energy!All for the same reason that time zones work.

也就是说 一段时间内的势能改变量就是负的速度乘以力,因此 一段时间内总能量的改变量,即动能和势能随时间的改变量之和,就是V*F(-(V*F))等于0,能量随时间改变量为零正是能量守恒,同样理由也适用于时区.

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