13.6 机械优势

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  机械优势

  

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  Did you ever use a hammer to break open a piggy bank? When you use a hammer to hit something, you apply force to the end of the handle. The head of the hammer, in turn, applies force to the piggy bank or whatever object you are striking. The head of the hammer moves farther than you move the handle with your hand. For all machines—not just hammers—the user applies force (input force) to the over a certain (input distance). The machine, in turn, applies force (output force) to an object, also over a certain distance (output distance). A machine makes work easier by changing the force or the distance over which the force is applied.  
  ::你曾经用过锤子来打破小猪银行吗?当你用锤子来敲打某东西时,你将力力压在把手的尽头。锤头反过来对小猪银行或你正在打击的任何物体施压。锤头比用手移动手柄更远。对于所有机器,而不仅仅是锤子,用户对一定的(输入距离)施压(输入距离)。机器反过来对一个物体施压(输出力),也使一定距离(输出距离)施压。机器通过改变力或施压距离而使工作更容易进行。

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  What Is Mechanical Advantage?
  ::什么是机械优势?

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  How much a machine changes the input force is its mechanical advantage . Mechanical advantage is the ratio of the output force to the input force, so it can be represented by the equation:
  ::机器如何改变输入力是其机械优势。机械优势是输出力与输入力之比,因此可以用方程式来表示:

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  $\begin{array}{r}\mathrm{A}\mathrm{c}\mathrm{t}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{M}\mathrm{e}\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{n}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{A}\mathrm{d}\mathrm{v}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{g}\mathrm{e}=\frac{\mathrm{O}\mathrm{u}\mathrm{t}\mathrm{p}\mathrm{u}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{c}\mathrm{e}}{\mathrm{I}\mathrm{n}\mathrm{p}\mathrm{u}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{c}\mathrm{e}}\end{array}$
  ::实际机械优势 = 产出力 = 实际机械优势 = 产出力 = 实际机械优势 = 实际机械优势 = 产出力 =

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  Note that this equation represents the actual mechanical advantage of a machine. The actual mechanical advantage takes into account the amount of the input force that is used to overcome . The equation yields the factor by which the machine changes the input force when the machine is actually used in the real world.
  ::请注意,此方程式代表机器的实际机械优势。 实际机械优势考虑到用于克服的输入力数量。 方程式产生当机器在现实世界中实际使用时机器改变输入力的系数 。

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  Ideal Mechanical Advantage
  ::理想机械优势

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  It can be difficult to measure the input and output forces needed to calculate the actual mechanical advantage of a machine. Generally, an unknown amount of the input force is used to overcome friction. It’s usually easier to measure the input and output distances than the input and output forces. The distance measurements can then be used to calculate the ideal mechanical advantage. The ideal mechanical advantage represents the change in input force that would be achieved by the machine if there were no friction to overcome. The ideal mechanical advantage is always greater than the actual mechanical advantage because all machines have to overcome friction. Ideal mechanical advantage can be calculated with the equation:
  ::很难衡量计算机器实际机械优势所需的输入和输出力。 一般来说, 输入力的未知量被用来克服摩擦。 通常比输入和输出力更容易测量输入和输出距离。 然后, 距离测量可以用来计算理想的机械优势。 理想的机械优势是机器在没有摩擦需要克服的情况下将实现的输入力变化。 理想的机械优势总是大于实际机械优势, 因为所有机器都必须克服摩擦。 理想的机械优势可以用公式来计算:

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  $\begin{array}{r}\mathrm{I}\mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{M}\mathrm{e}\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{n}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{A}\mathrm{d}\mathrm{v}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{g}\mathrm{e}=\frac{\mathrm{I}\mathrm{n}\mathrm{p}\mathrm{u}\mathrm{t}\mathrm{D}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}}{\mathrm{O}\mathrm{u}\mathrm{t}\mathrm{p}\mathrm{u}\mathrm{t}\mathrm{D}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}}\end{array}$
  ::Ideal 机械化改进= 投入事故 产出事故

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  A Simple Example
  ::简单示例

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  Look at the ramp in the Figure  . A ramp is a type of simple machine called an . It can be used to raise an object off the ground. The input distance is the length of the sloped surface of the ramp. This is the distance over which the input force is applied. The output distance is the height of the ramp, or the vertical distance the object is raised. For this ramp, the input distance is 6 m and the output distance is 2 meters. Therefore, the ideal mechanical advantage of this ramp is:
  ::查看图中的斜坡。斜坡是一种简单的机器类型,称为“一个”。它可以用来在地面上举起一个物体。输入距离是斜坡的斜坡表面长度。这是投入力应用的距离。输出距离是斜坡的高度,或者物体的垂直距离。对于这个斜坡,输入距离为6米,输出距离为2米。因此,这个斜坡最理想的机械优势是:

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  $\begin{array}{r}\text{Ideal Mechanical Advantage}=\frac{\text{Input distance}}{\text{Output distance}}=\frac{6\text{m}}{2\text{m}}=3\end{array}$
  ::理想机械优势=投入距离 输出距离=6平方米=3

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  An ideal mechanical advantage of 3 means that the ramp ideally (in the absence of friction) multiplies the input force by a factor of 3. The trade-off is that the input force must be applied over a greater distance than the object is lifted.
  ::3个理想的机械优势意味着(在没有摩擦的情况下)最理想的坡道将输入力乘以3。 权衡是,输入力必须应用到比解除物体更远的距离上。

  

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  Q : Assume that another ramp has a sloping surface of 8 m and a vertical height of 4 m. What is the ideal mechanical advantage of this ramp?
  ::问题:假设另一个斜坡的斜坡表面为8米,垂直高度为4米。这个斜坡最理想的机械优势是什么?

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  A : The ramp has an ideal mechanical advantage of:
  ::A:坡道具有理想的机械优势:

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  $\begin{array}{r}\text{Ideal Mechanical Advantage}=\frac{8\text{m}}{4\text{m}}=2\end{array}$
  ::理想机械优势=8 m4 m=2

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  Mechanical Advantage of Different Types of Machines
  ::不同类型机器的机械优势

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  Many machines—including inclined planes such as ramps—increase the strength of the force put into the machine but decrease the distance over which the force is applied. Other machines increase the distance over which the force is applied but decrease the strength of the force. Still other machines change the direction of the force, with or without also increasing its strength or distance. Which way a machine works determines its mechanical advantage, as shown in the Table  .
  ::许多机器——包括斜坡等倾斜式飞机——增加了投入机器的力量,但缩小了使用武力的距离;其他机器增加了使用武力的距离,但降低了力量的强度;还有一些机器改变了力量的方向,无论是否增加了力量或距离;如表所示,机器的运转方式决定了机械的优势。

  Strength of Force	Distance Over which Force is Applied	Mechanical Advantage	Example
  increases	increases	> 1	ramp
  decreases	increases	< 1	hammer
  stays the same (changes direction only)	stays the same	= 1	flagpole

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  Summary
  ::摘要

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  • The actual mechanical advantage of a machine reflects the increase or decrease in force achieved by the machine. It takes into account the force needed to overcome friction.
    ::机器的实际机械优势反映了机器所实现的增减,考虑到了克服摩擦所需的力量。
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  • The actual mechanical advantage can be calculated with the equation: $\begin{array}{r}\mathrm{A}\mathrm{c}\mathrm{t}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{M}\mathrm{e}\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{n}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{A}\mathrm{d}\mathrm{v}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{g}\mathrm{e}=\frac{\mathrm{O}\mathrm{u}\mathrm{t}\mathrm{p}\mathrm{u}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{c}\mathrm{e}}{\mathrm{I}\mathrm{n}\mathrm{p}\mathrm{u}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{c}\mathrm{e}}\end{array}$
    ::实际的机械优势可以用以下等式计算:实际机械优势=外力
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  • The ideal mechanical advantage of a machine reflects the increase or decrease in force there would be without friction. It is always greater than the actual mechanical advantage because all machines must overcome friction.
    ::机器最理想的机械优势反映了没有摩擦力的增减。 它总是大于实际的机械优势,因为所有机器都必须克服摩擦。
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  • The ideal mechanical advantage can be calculated with the equation: $\begin{array}{r}\mathrm{I}\mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{M}\mathrm{e}\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{n}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{A}\mathrm{d}\mathrm{v}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{g}\mathrm{e}=\frac{\mathrm{I}\mathrm{n}\mathrm{p}\mathrm{u}\mathrm{t}\mathrm{D}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}}{\mathrm{O}\mathrm{u}\mathrm{t}\mathrm{p}\mathrm{u}\mathrm{t}\mathrm{D}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}}\end{array}$
    ::理想的机械优势可以通过等式来计算:
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  • The mechanical advantage of a machine may be greater than, less than, or equal to 1, depending on the type of machine.
    ::机器的机械优势可能大于、小于或等于1,视机器类型而定。

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  Review
  ::回顾

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  1. What is the mechanical advantage of a machine?
     ::机器的机械优势是什么?
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  2. How is the actual mechanical advantage of a machine calculated?
     ::机器的实际机械优势是如何计算的?
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  3. How does ideal mechanical advantage differ from actual mechanical advantage? Why is the ideal mechanical advantage of a machine always greater than the actual mechanical advantage of the machine?
     ::理想的机械优势与实际的机械优势有何不同? 为什么机器的理想机械优势总是大于机器的实际机械优势?
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  4. A ramp has an input distance of 9 cm and an output distance of 3 cm. What is its ideal mechanical advantage?
     ::坡道的输入距离为9厘米,输出距离为3厘米。 其理想的机械优势是什么?

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  Explore More
  ::探索更多

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  Watch the video about mechanical advantage, and then solve the problems below.
  ::观看关于机械优势的视频, 然后解决下面的问题。

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  1. Juan uses a lever to lift a rock. He places the rock on the short arm of the lever and pushes down on the other arm of the lever. He applies 30 N of force over a distance of 1 m. The other end of the lever moves in the opposite direction and raises the rock a distance of 0.2 m. What is the weight (force) of the rock?
     ::Juan用杠杆抬起岩石。 他将岩石放在杠杆的短臂上, 并推倒杠杆的另一臂。 他在1米的距离内施用30牛顿力。 杠杆的另一端向相反的方向移动, 将岩石抬高0.2米。 岩石的重量(力)是多少?
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  2. What is the mechanical advantage of the lever in question 1?
     ::问题1中杠杆的机械优势是什么?