4.1 引力和灌木板

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  引力和灌木板

  

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  This photograph was taken by Apollo 8 crew member Bill Anders on December 24, 1968, showing the Earth rising above the lunar surface. Gravitational forces keep the moon orbiting the Earth.
  ::这张照片是1968年12月24日由阿波罗8号机组成员比尔·安德斯拍摄的,显示地球升至月球表面上空,引力使月亮绕地球运行。

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  Gravitational Force and Inclined Planes
  ::引力和灌木板

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  Every object has a center of gravity . The center of gravity is the point at which the entire of a body may be considered to be concentrated; if supported at this point, the body would remain in equilibrium in any position. For example, if we were discussing a 12-inch ruler, the center of gravity for the ruler would be at the center of the 6-inch line. You could put your finger directly under the 6-inch line to hold the ruler and it would not fall either left or right. If you placed your finger underneath any other place on the ruler, it would fall off to one side or the other.
  ::每个对象都有一个重力中心。 重力中心是整个身体可以被视为集中的点; 如果在这一点上支持, 身体将保持任何位置的平衡。 例如, 如果我们讨论一个12英寸尺尺, 标尺的重力中心将位于6英寸线的中心。 您可以直接将手指放在6英寸线下, 以保持标尺, 它不会落在左或右。 如果您将手指放在标尺上任何其他地方的下方, 它会掉落到一边或另一边 。

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  The force of gravity acting on an object is directed through this center of gravity and toward the center of the Earth. The object’s weight, $\begin{array}{r}W\end{array}$ , can be represented by a vector directed down (along the line the object would fall if it were dropped). When this object is resting on a level surface, its weight acts perpendicularly to the surface and will be equal to the normal force , which is the force keeping the object from falling through the table. The normal force is always perpendicular to the surface; when the surface is not level, the normal force will be equal to some subset of the weight. This is seen in the image below, which shows a box on an .
  ::物体的重力作用力通过这个重力中心向着地球的中心。物体的重量,W,可以用向下方向的矢量表示(如果投下,该物体会落在直线上)。当物体处于一个水平表面时,其重量与表面垂直,与正常的强度相等,即保持物体从表面掉下的力量。正常的强度总是与表面垂直的;当表面不处于水平时,正常的强度将等于重量的某个子集。在下方显示一个框的图像中可以看到这一点。

  

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  The weight of the box acts through the center of gravity and directly towards the center of the Earth. The weight vector in the sketch is red and labeled W. The normal force acts perpendicular to the surface of the inclined plane to keep the box from falling through the plane. The force of the box on the plane is equal to the normal force (as specified in Newton’s Third Law), and is indicated by the green vector labeled W _{perpendicular} . The normal force, $\begin{array}{r}{F}_N\end{array}$ , is purple in the image above. In addition, there is a force acting on the box parallel to the surface of the plane and pushing the box down the plane. This force is drawn in blue and is called the parallel force . The weight vector (W), is the sum of the normal force vector (F _N ) and the parallel force vector (F _parallel ).
  ::框的重量通过重力中心, 并直接朝向地球的中心。 草图中的重量矢量是红色的, 标记为 W。 正常力在倾角平面表面的垂直作用, 以防盒子从平面上掉下。 平面上的框力等于正常力( 如牛顿第三法则所指定 ) , 并用绿色矢量标签显示。 普通力 FN 在上面的图像中是紫色的。 此外, 正常力与平面的表面平行, 并将盒子推下飞机。 这种力是蓝色的, 被称为平行力 。 重量矢量( W) 是正常力矢量和平行力矢量( Fparallel) 的总和 。

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  The triangle of the black inclined plane and the yellow triangle are similar triangles; the corresponding sides are mutually perpendicular. Therefore, the angle at the top of the yellow triangle is also 30°. For a right triangle, if we know one other angle (the 30° angle) and one side (the weight), we can calculate the other two sides. Therefore, we can calculate the parallel force pushing the box down the incline and we could also calculate the of the box.
  ::黑色倾角平面和黄色三角形的三角形是相似的三角形; 对应的两边是相互垂直的。 因此, 黄色三角形顶端的角也是 30 ° 。 对于右三角形, 如果我们知道另一个角( 30 °角) 和 一边( 重量) , 我们就可以计算另外两边。 因此, 我们可以计算平行力将盒子推下内线, 我们也可以计算框的大小 。

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  Examples
  ::实例

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  A 500. N box is resting on a plane inclined at 30° with the horizontal. 
  ::A500. N盒在倾角为30°与水平倾角的平面上休息。

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  Example 1 
  ::例1

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  Find the normal force and the parallel force acting on this box. 
  ::找到正常的力量和平行的力量 在这个盒子上行动

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  (a)  $\begin{array}{r}{F}_N=W\cos {30}^{\circ }=(500.\text{N})(0.866)=433\text{N}\end{array}$
  :a) FN=Wcos30(500.N)(0.866)=433 N

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  $\begin{array}{r}{F}_{\text{parallel}}=W\sin {30}^{\circ }=(500.\text{N})(0.500)=250.\text{N}\end{array}$
  ::Fparallel=Wsin30(500.N)(0.500=250.N)

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  Example 2
  ::例2

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  Find the acceleration of the box.
  ::找到盒子的加速度。

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    $\begin{array}{r}\text{mass of the box}=\frac{500.\text{N}}{9.81{\text{m/s}}^2}=51.0\text{kg}\end{array}$
  ::N9.81 m/s2=51.0千克

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  $\begin{array}{r}a=\frac{F_{\text{parallel}}}{\text{mass}}=\frac{250.\text{N}}{51.0\text{kg}}=4.90{\text{m/s}}^2(\text{The direction is down the plane}.)\end{array}$
  ::a=Fparallmass=250. N51.0kg=4.90m/s2(方向在飞机下方。 )

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  Have you ever been in a car as it is driving around a banked turn? A banked turn is simply a corner of a road that is tilted at an angle and acts as an inclined plane. As a car drives around one of these corners, it experiences the force of , gravity and normal force acting on it. Use the PLIX Interactive below to explore how each of these forces affect what the car does in the turn:
  ::你曾经坐过车吗? 银行转弯只是一个方向倾斜并起倾斜作用的公路的角落。 当汽车绕着一个角行驶时,它经历着车面上的力、重力和正常力。 使用下面的PLIX互动来探究这些力量如何影响汽车的运行:

   

   

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  Summary
  ::摘要

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  • Each object has a center of gravity, which is the point at which the weight can be considered to be concentrated when balancing the object.
    ::每个对象都有一个重心,这就是在平衡对象时可以认为重量集中的点。
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  • The weight of an object is a vector that is directed toward the center of the Earth.
    ::物体的重量指向地球中心的矢量。
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  • When an object is placed on an inclined plane, its weight vector can be resolved into the normal force, which is equal to the force of the object perpendicular to the plane, and a parallel force, which pushes the object down the inclined plane.
    ::当一个物体放在倾斜平面上时,其重量矢量可以溶解成正常力,相当于与该平面垂直的物体的威力,以及将该物体推下倾斜平面的平行力。

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  Review
  ::回顾

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  1. A car weighing 12,000 N is parked on a 36° slope. 
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     1. Find the force tending to cause the car to roll down the hill.
        ::找到导致车从山上滚下来的力量
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     2. Find the acceleration of the car rolling down the hill.
        ::找到从山上滚下来的汽车加速度
     
     ::一辆重12,000牛顿的汽车停在36度斜坡上,发现力力促使汽车滑下山坡,发现汽车加速滑下山坡。