7.2 机器

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  机器机机

  

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  A "Rube Goldberg Machine" is a complex construction of many simple machines connected end-to-end in order to accomplish a particular activity.  By design, Rube Goldberg Machines are far more intricate than necessary, and may be quite entertaining. Although this kind of construction may be extremely inefficient, simple machines commonly make work easier, and can be found all around us. 
  ::“鲁比·戈德伯格机器 ” ( Rube Goldberg Machines)是由许多连接端端到端的简单机器组成的复杂结构,它们为了完成某项特定活动而连接到端端。 设计上,鲁比·戈德伯格机器比必要的复杂得多,而且可能相当有趣。 尽管这种结构效率极低,但简单的机器通常会让工作更加容易,并且可以在我们周围找到。

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  Machines
  ::机器机机

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  A is an object or mechanical device that receives an input amount of work and transfers the to an output amount of work. For an ideal machine , the input work and output work are always the same. Remember that work is force times ; even though the work input and output are equal, the input force does not necessarily equal the output force , nor does the input distance necessarily equal the output distance .
  ::A 是接受输入工作量并将输出工作量转移至输出工作量的物体或机械装置。 对于理想机器来说,输入工作和输出工作总是相同的。 记住, 工作是强制时间; 即使工作输入和输出是相等的, 输入力不一定等于输出力, 输入距离也不一定等于输出距离 。

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  Machines can be incredibly complex (think of robots or automobiles), or very simple, such as a can opener.  A simple machine  is a mechanical device that changes the magnitude or direction of the force. There are six simple machines that were first identified by Renaissance scientists: , , , , , and . These six simple machines can be combined together to form compound machines .
  ::机器可能非常复杂(机器人或汽车的思维),或者非常简单,比如开罐器。简单的机器是改变力的大小或方向的机械装置。有六台简单的机器是文艺复兴科学家首先发现的: , , , , , , , , , 和 。 这六台简单的机器可以合并成复合机器。

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  We use simple machines because they give us a . Mechanical advantage is a measurement of the force amplification of a machine. In ideal machines, where there is no and the input work and output work are the same, 
  ::我们使用简单的机器,因为它们给了我们一个。机械优势是测量机器的功率放大的尺度。在理想的机器中,没有机器,输入和输出工作是相同的,

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  $\begin{array}{r}(\text{Effort Force})(\text{Effort Distance})=(\text{Resistance Force})(\text{Resistance Distance})\end{array}$
  :努力力)(努力距离)=(抵抗力)(抵抗力)

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  The effort is the work that you do. It is the amount of force you use times the distance over which you use it. The  is the work done on the object you are trying to move. Often, the resistance force is the force of gravity, and the resistance distance is how far you move the object.
  ::努力是您的工作。 这是您使用的强度乘以您使用的距离。 这是您试图移动的物体上完成的工作 。 抵抗力量通常就是重力, 抵抗距离是您移动物体的距离 。

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  The ideal mechanical advantage  of a simple machine is the ratio between the distances:
  ::简单机器最理想的机械优势是距离之比:

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  $\begin{array}{r}\text{IMA}=\frac{\text{effort distance}}{\text{resistance distance}}\end{array}$
  ::IMA=最大距离保持距离

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  Again, the IMA assumes that there is no friction. In reality, the mechanical advantage is limited by friction; you must overcome the frictional forces in addition to the resistance force. Therefore, the actual mechanical advantage  is the ratio of the forces:
  ::同样,IMA假设没有摩擦,实际上,机械优势受到摩擦的限制;除了抵抗力量之外,你还必须克服摩擦力量。 因此,实际机械优势是部队的比例:

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  $\begin{array}{r}\text{AMA}=\frac{\text{resistance force}}{\text{effort force}}\end{array}$
  ::AMA=抵抗力量

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  When simple machines are combined to form compound machines, the product of each simple machine's IMA gives the compound machine's IMA. 
  ::当简单机器合并成复合机器时,每台简单机器的IMA产品都提供复合机器的IMA。

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  Simple Machines
  ::简易机器

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  Lever
  ::燃烧

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  A lever consists of an inflexible length of material placed over a pivot point called a fulcrum . The resistance is the object to be moved (shown here in red), and is placed to one side of the fulcrum. The resistance distance in a lever is called the resistance arm. The effort is exerted elsewhere on the lever, and the effort distance is called the effort arm or effort lever arm. The lever shown here is the most common type of lever, a Class One Lever, but there are two other types of levers.
  ::杠杆由放在一个支点上称为支架的不灵活材料长度组成。 阻力是要移动的物体( 以红色显示) , 并放在支架的一边 。 杠杆的阻力距离被称为抗力臂 。 努力在杠杆的其他地方进行, 努力距离被称为努力臂 或努力杆 。 这里显示的杠杆是最常见的杠杆类型, 一级 Lever , 但有另外两种类型的杠杆 。

  

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  The effort work is the effort force times the effort lever arm. Similarly, the resistance work is the resistance force times the resistance lever arm. If we ignore any friction that occurs where the lever pivots over the fulcrum, this is an ideal machine . Suppose the resistance force is 500. N, the resistance arm is 0.400 m, and the effort arm is 0.800m. We can calculate exactly how much effort force is required to lift the resistance in this system:
  ::工作是努力力乘以努力的杠杆臂。 同样, 抵抗工作是抵抗力量乘以抵抗的杠杆臂。 如果我们忽略在支架上拉杆支点发生的任何摩擦, 这是一个理想的机器。 假设抵抗力量为500米。 N, 抵抗力量为0. 400米, 努力力量为0. 800米。 我们精确计算出在这个系统中提高抵抗力需要多少努力力:

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  $\begin{array}{r}\text{Output Work}=\text{Input Work}\end{array}$
  ::产出工作=投入工作

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  $\begin{array}{r}(\text{Resistance Force})(\text{Resistance Arm})=(\text{Effort Force})(\text{Effort Arm})\end{array}$
  :抵抗力量)(抵抗武装)=(努力力量)(努力武装)

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  $\begin{array}{r}(500.\text{N})(0.400\text{m})=(x)(0.800\text{m})\end{array}$
  :500.N)(0.400米)=(x)(0.800米)

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  $\begin{array}{r}x=250.\text{N}\end{array}$
  ::x=250. Nx=250.

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  In this case, since the effort arm is twice as long as the resistance arm, the effort force required is only half the resistance force. This machine allows us to lift objects using only half the force required to lift the object directly against the pull of gravity. The distance the effort force is moved is twice as far as the resistance will move. Thus, the input work and the output work are equal.
  ::在此情况下,由于努力臂是抵抗臂的两倍,所需的努力力仅是抵抗力量的一半。这台机器只允许我们用一半的力量来提升物体,直接在引力的拉动下将物体抬起来。努力力移动的距离是抵抗力移动的两倍。因此,输入力和输出力是相等的。

   

   

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  Example 1  
  ::例1

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  (a) How much force is required to lift a 500. kg stone using an ideal lever whose resistance arm is 10.0 cm and whose effort arm is 2.00 m?
  :a) 使用一种理想的杠杆,其抗力臂为10厘米,其努力力臂为2米,需要多少武力才能举起500公斤的石块?

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  (b) What is the IMA?
  :b) 什么是IMA?

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  (c) If the actual effort force required to lift the stone was 305 N, what was the AMA?
  :c) 如果提石所需的实际工作部队是305 N,那么什么是AMA?

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  (a) $\begin{array}{r}(\text{resistance force})(\text{resistance arm})=(\text{effort force})(\text{effort arm})\end{array}$
  :a) (抵抗力量)(抵抗武装)=(努力力量)(努力武装)

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  $\begin{array}{r}\text{effort force}=\frac{(\text{resistance force})(\text{resistance arm})}{(\text{effort arm})}=\frac{(4900\text{N})(0.100\text{m})}{(2.00\text{m})}=245\text{N}\end{array}$
  ::功率=(抵抗力)(抵抗力)(抗力臂)(努力臂)=(4900 N)(0.100 m)(2.00 m)=245 N

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  (b) $\begin{array}{r}\text{IMA}=\frac{\text{effort arm}}{\text{resistance arm}}=\frac{2.00\text{m}}{0.100\text{m}}=20\end{array}$
  :b) IMA=最大手臂阻力臂=2.00 m.00 m.100 m=20

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  (c) $\begin{array}{r}\text{AMA}=\frac{\text{resistance force}}{\text{effort force}}=\frac{4900\text{N}}{305\text{N}}=16\end{array}$
  :c) AMA=抗力功力=4900 N305 N=16

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  Pulley
  ::普利

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  A  pulley  is a wheel on an axle that is designed to rotate with movement of a cable along a groove at its circumference. Pulleys are used in a variety of ways to lift loads, apply forces, and to transmit power, but the simplest of pulleys serves only to reverse the direction of the effort force. It consists of a single pulley attached directly to a non-moving surface with a rope or cable through it. As a downward force is applied to one side of the pulley, the other side of the pulley, with the attached resistance force, is pulled upward. This type of pulley is called a  fixed pulley , and is labeled  A  in the image below.
  ::滑轮是一个轴轮轮,其设计是用电缆在环绕的角上旋转而旋转。 滑轮以各种方式用来举载、施用力和传输电力,但最简单的滑轮只能倒转力力方向。 滑轮由用绳索或电缆直接连接未移动的表面的单滑轮组成。 当滑轮的一边向下施压时, 滑轮的另一侧与附着的抵抗力量被拉向上。 这种滑轮被称为固定的滑轮, 在下面的图像中标有A的标签 。

  

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  Another type of pulley is shown above as  B . This type of pulley is called a  movable pulley.  A set of pulleys assembled so they rotate independently on the same axle form a block. It is shown below in a system called a  block and tackle . A block and tackle consists of two blocks, in which one block is fixed and the other is movable; the movable block is attached to the load.  Play around with the simulation below to further explore the block and tackle:
  ::另一类滑轮在上文以B表示。这种滑轮称为可动滑轮。组装的一组滑轮在同一个轴形的区块上独立旋转。在下面称为区块和钩的系统中显示。一个区块和钩子由两个区块组成,其中一个区块固定,另一个区块是可移动的;动产区块附在负载上。在下面的模拟中玩耍,以进一步探索区块和钩子:

   

   

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  The IMA of a pulley system can be determined by counting the number of supporting strands of rope in the system. Be careful though, because in some systems the rope to which the effort force is applied will be a supporting strand, but in others it is not. For example, in the image above with the five pulley systems, the rope to which the effort force is applied (the one with the arrowhead) in  A  is not a supporting strand because it does not hold up any of the of the load. The IMA of  A  is 1. In  B , however, the effort rope is supporting half of the weight of the load and is therefore a supporting strand.  B  has 2 supporting strands and an IMA of 2.
  ::滑轮系统的IMA 可以通过计数系统中支撑绳条数来确定。 注意, 因为在某些系统中, 使用努力力的绳子是支持绳子, 但在其他系统中则不是。 例如, 在以上图像中, 5个拖车系统, A 中使用努力力的绳子( 有箭头的绳子) 并不是支持绳子, 因为它不能支撑任何负荷。 A 的 IMA 是 1 。 但是, 在 B 中, 努力绳子支撑着一半的重量, 因此是支持绳子。 B 有2个支撑绳子和2个IMA 。

   

   

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  Example 2  
  ::例2

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  Determine the IMA for  C, D,  and  E  in the image above.
  ::在上述图像中确定 C、 D 和 E 的 IMA 。

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  C = 2 supporting strands; IMA = 2
  ::C=2个支撑线;IMA=2

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  D = 3 supporting strands; IMA = 3
  ::D=3个支撑线;IMA=3

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  E = 3 supporting strands; IMA = 3
  ::E=3个支撑线;IMA=3

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  If the direction of the effort force is in the same direction and the movement of the load, the effort strand will be a supporting strand. If the direction of the effort force is in the same direction as the resistance force, the effort strand is not a supporting strand. Look again at the five pulley systems to ensure this is true. 
  ::如果部队部队的方向与载荷的移动方向相同,则工作线将是辅助线。如果部队的方向与抵抗部队的方向相同,则工作线不是辅助线。再看看五个拖轮系统,以确保这是正确的。

  

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  Example 3    
  ::例3

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  Consider the pulley system sketched above.  Given that the resistance force is 8500. N, find
  ::想想上面所描绘的滑轮系统。 鉴于抵抗力量是8500。

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  (a) the IMA.
  :a) IMA。

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  (b) the ideal effort force required to list this weight.
  :b) 列出这一权重所需的理想努力力量。

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  (c) the distance the weight will rise if the effort force moves 1.0 m.
  :c) 如果工作力移动1.0米,重量将增加距离。

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  (d) the AMA if the actual effort force is 2000. N.
  :d) 如果实际战斗力为2000年,则AMA。

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  (a) Since the effort strand moves in the opposite direction of the resistance, it is not a supporting strand.  Therefore, there are 5 supporting strands and that makes the IMA = 5.
  :a) 由于努力线向抵抗运动的相反方向移动,它不是一个支持线,因此,有5个支持线,使IMA=5。

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  (b) $\begin{array}{r}\text{Effort force}=\frac{\text{resistance force}}{\text{IMA}}=\frac{8500\text{N}}{5}=1700\text{N}\end{array}$
  :b) 努力力=抵抗力IMA=8500 N5=1700 N

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  (c) Since the IMA is 5, the resistance distance will be 1/5 of the effort distance: the resistance distance is 1.0m/5 = 0.20 m
  :c) 由于IMA为5,抗力距离为工作距离的1/5:抗力距离为1.0m/5=0.20米。

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  (d) $\begin{array}{r}\text{AMA}=\frac{\text{resistance force}}{\text{effort force}}=\frac{8500\text{N}}{2000\text{N}}=4.25\end{array}$
  :d) AMA=抗力功力=8500 N2000 N=4.25

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  Wheel and Axle
  ::轮轴和轮轴

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  Just like it sounds, a  wheel and axle  is composed of two connected cylinders of different diameters. Since the wheel has a larger radius (distance) than the axle, the axle will always have a larger force than the wheel. The ideal mechanical advantage of a wheel and axle is dependent on the ratio between the radii:
  ::就像声音一样,方向盘和轴由两个不同直径的相联圆筒组成。由于方向盘的半径(距离)大于轴,轴的强度总是大于方向盘。方向盘和轴的理想机械优势取决于弧度之间的比例:

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  $\begin{array}{r}\text{IMA}=\frac{{\text{Radius}}_{\text{wheel}}}{{\text{Radius}}_{\text{axle}}}\end{array}$
  ::IMA=拉迪乌斯轮式拉迪乌萨克斯

   

   

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  Inclined Plane
  ::浸入式平板机

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  An inclined plane is also a simple machine. The resistance is the weight of the box resting on the inclined plane. In order to lift this box straight up, the effort force would need to be equal to its weight. However, assuming no friction, less effort (a smaller effort force) is required to slide the box up the incline. We know this intuitively; when moving boxes into a truck or onto a platform, we use angled platforms instead of lifting it straight up.
  ::倾斜式飞机也是一个简单的机器。 阻力是停留在倾斜式飞机上的盒子的重量。 为了直直提升这个盒子, 努力力需要与它的重量相等。 但是, 假设没有摩擦, 只需少一点努力( 较小的努力力) 才能将盒子滑到斜线上。 我们直观地知道这一点; 当将箱子移入卡车或平台时, 我们使用角度平台, 而不是直升平台 。

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  The red triangle that hangs below the yellow box is a similar triangle to the inclined plane. The vector perpendicular to the inclined surface is the normal force and this normal force is equal to the portion of the weight of the box that is supported by the surface of the plane. The parallel force is the portion of the weight pushing the box down the plane and is, therefore, the effort force necessary to push the box up the plane.
  ::挂在黄盒下的红色三角形与倾斜面的三角形相似。 垂直于倾斜面的矢量是正常力, 而这种正常力相当于由平面表面支持的框重量部分。 平行力是将盒子推下平面的重量部分, 因此是将盒子推上平面所需的努力力 。

  

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  The effort distance, in the case of an inclined plane, is the length of the incline and the resistance distance is the vertical height the box would rise when it is pushed completely up the incline. The mechanical advantages for an inclined plane are
  ::对于倾斜平面来说,努力距离是斜平面的长度,阻力距离是垂直高度,当它被完全推上斜平面时,该框会上升。 对于倾斜平面而言,机械优势是

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  $\begin{array}{r}\text{IMA}=\frac{\text{effort distance}}{\text{resistance distance}}=\frac{\text{length}}{\text{vertical height}}=\frac{1}{\sin \theta }\end{array}$
  ::IMA = 最大距离距离距离= 长垂直高度= 1sin

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  $\begin{array}{r}\text{IMA}=\frac{\text{resistance force}}{\text{effort force}}=\frac{\text{weight}}{\text{applied force}}\end{array}$
  ::IMA=抗抗力功力=重量力

   

   

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  Example 4  
  ::例4

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  Suppose, in the sketch above, the weight of the box is 400. N, the angle of the incline is 35°, and the surface is frictionless. Find the normal force (by finding the portion of the weight acting perpendicular to the plane), the parallel force, and the IMA for the box on this incline.
  ::假设在上文的草图中,盒子的重量是400。 N, 斜角是35°, 表面是无摩擦的。 找到正常的力量( 找到与平面垂直的重量部分 ) , 平行的力量 , 以及这个直线上的框的IMA 。

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  $\begin{array}{r}\text{Normal force}=(400.\text{N})(\cos {35}^{\circ })=(400.\text{N})(0.82)=330\text{N}\end{array}$
  ::正常力=(400.00.N)(cos35)=(400.00.N)(0.82)=330 N

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  $\begin{array}{r}\text{Parallel force}=(400.\text{N})(\sin {35}^{\circ })=(400.\text{N})(0.57)=230\text{N}\end{array}$
  ::平行力=(400.N)(sin35)=(400.N)(0.57=230 N)

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  $\begin{array}{r}\text{IMA}=\frac{1}{\sin \theta }=\frac{1}{\sin {35}^{\circ }}=\frac{1}{0.57}=1.74\end{array}$
  ::IMA=1sin=1sin=1sin=1sin=1sin=35}10.57=1.74

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  Wedge
  ::边缘

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  A wedge is essentially two inclined planes back to back. Like an inclined plane, the IMA of a wedge is the ratio between the length of the wedge and the width of the wedge. Unlike an inclined plane, a wedge does not have a right angle; the IMA of a wedge cannot be found with sines.
  ::偏差基本上是指两架飞机背对背的倾角。 和倾角平面一样, 斜面的IMA是介面长度和宽度的比。 与斜面不同的是, 斜面没有正确的角度; 无法用正弦找到介面的IMA 。

   

   

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  Screw
  ::去他妈的

  

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  A screw  is an inclined plane wrapped around a cylinder. When on a screw, inclined planes are called threads, which can be seen in the image above. The mechanical advantage of a screw increases with the density of the threads. The calculations to determine the IMA for a screw involve the circumference of the head of the screw and the thread width.  When the screw is turned completely around one time, the screw penetrates by one thread width.  So, if the circumference of the head of a screw is 3.0 cm and the thread width is 0.60 cm, then the IMA would be calculated by
  ::螺旋是一个环环环圆圆圆柱体的倾斜平面。在螺旋上,倾斜平面被称作线线,可以在上面的图像中看到。螺旋的机械优势随着线密度的密度增加而增加。确定螺纹IMA的机械优势是螺旋的机械优势。确定IMA的机械优势的计算涉及螺旋头环绕和线宽度。当螺旋完全旋转一次时,螺旋穿透一个线宽。因此,如果螺旋头的环环为3.0厘米,线宽为0.60厘米,那么IMA的计算方法是:

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  $\begin{array}{r}\text{IMA}=\frac{\text{effort distance}}{\text{resistance distance}}=\frac{3.0\text{cm}}{0.60\text{cm}}=5.\end{array}$
  ::IMA=最大距离距离距离=3.0厘米0.60厘米=5厘米。

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  When simple machines are joined together to make compound machines , the ideal mechanical advantage of the is found by multiplying the IMA’s of the simple machines.
  ::当简单机器合在一起制造复合机器时,最理想的机械优势在于将简易机器的IMA乘以IMA。

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  Further Reading
  ::继续阅读

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  Summary
  ::摘要

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  • A machine is an object or mechanical device that receives an input amount of work and transfers the energy to an output amount of work. 
    ::机器是一种物体或机械装置,接收输入量的工作,并将能量转移到输出量的工作。
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  • For an ideal machine, the input work and output work are always the same.
    ::对于理想的机器来说,输入工作和产出工作总是一样。
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  • The six common simple machines are the lever, wheel and axle, pulley, inclined plane, wedge, and screw.
    ::六台普通的简单机器是杠杆、轮子和轴、滑轮、倾斜平面、网形和螺丝。
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  • For all simple machines, the ideal mechanical advantage is  $\begin{array}{r}\frac{\text{effort distance}}{\text{resistance distance}}\end{array}$ .
    ::对于所有简单的机器来说,最理想的机械优势是努力距离距离。
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  • For all simple machines, the actual mechanical advantage is  $\begin{array}{r}\frac{\text{resistance force}}{\text{effort force}}\end{array}$ .
    ::对于所有简单的机器来说,实际的机械优势是抵抗力。
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  • When simple machines are joined together to make compound machines, the ideal mechanical advantage of the compound machine is found by multiplying the IMA’s of the simple machines.
    ::当简单机器合在一起制造复合机器时,复合机器最理想的机械优势在于将简易机器的IMA乘以IMA。

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  Review 
  ::回顾

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  1. Is it possible to get more work out of a machine than you put in?
     ::能不能从机器里得到比你多的工作?
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  2. A worker uses a pulley system to raise a 225 N carton 16.5 m.  A force of 129 N is exerted and the rope is pulled 33.0 m.
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     1. What is the IMA of the system?
        ::该系统的IMA是什么?
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     2. What is the AMA of the system?
        ::系统AMA是什么?
     
     ::工人用滑轮系统提升225牛顿16.5米。 施加了129牛顿的力量,绳子拉了33.0米。 该系统的IMA是什么?系统AMA是什么?
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  3. A boy exerts a force of 225 N on a lever to raise a 1250 N rock a distance of 0.13 m.  If the lever is frictionless, how far did the boy have to move his end of the lever?
     ::一个男孩用225牛顿的力量在杆子上拉高1 250牛顿岩石0.13米的距离。 如果杆子没有摩擦,那男孩要把杆子的尽头移到多远?
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  4. How can you increase the ideal mechanical advantage of an inclined plane?
     ::怎样才能增加倾斜式飞机 最理想的机械优势呢?
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  5. Diana raises a 1000. N piano a distance of 5.00 m using a set of pulleys.  She pulls in 20.0 m of rope.
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     1. How much effort force did Diana apply if this was an ideal machine?
        ::如果戴安娜是个理想的机器 戴安娜用了多少力气?
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     2. What force was used to overcome friction if the actual effort force was 300. N?
        ::如果实际战斗力为300 N,用什么力量来克服摩擦?
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     3. What was the work output?
        ::工作产出是什么?
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     4. What was the ideal mechanical advantage?
        ::理想的机械优势是什么?
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     5. What was the actual mechanical advantage, if the input force was 300N?
        ::如果输入力是300N,实际的机械优势是什么?
     
     ::戴安娜用一套滑轮拉起一台1000米的N型钢琴。 她用20米的绳子拉了起来。 如果这是一台理想的机器,戴安娜用了多少力力? 如果实际的力力力是300,那么用什么力来克服摩擦? 工作产出是什么? 理想的机械优势是什么? 如果输入力是300N, 实际的机械优势是什么?
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  6. A mover’s dolly is used to pull a 115 kg refrigerator up a ramp into a house.  The ramp is 2.10 m long and rises 0.850 m.  The mover exerts a force of 496 N up the ramp.
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     1. How much work does the mover do?
        ::搬运工做了多少工作?
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     2. How much work is spent overcoming friction?
        ::克服摩擦花费了多少工作?
     
     ::移动器的圆圈用来把115公斤的冰箱拉到一个斜坡上的房子里。斜坡长2.10米,上升0.850米。移动器在斜坡上方施压496牛顿。移动器做了多少工作?克服摩擦花费了多少工作?
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  7. What is the ideal mechanical advantage of a screw whose head has a diameter of 0.812 cm and whose thread width is 0.318 cm?
     ::螺丝的直径为0.812厘米,而其线宽为0.318厘米,这种螺丝的螺丝在机械上有什么理想的优势?