7.3 电源

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  电力

  

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  Typical Pressurized Water Reactors (PWR), a type of nuclear power reactor originally built in the 1970s, produce 1100 to 1500 megawatts, or about 1,500,000,000 Joules/second. By comparison, a windmill farm with hundreds of individual windmills produces about 5 megawatts (5,000,000 Joules/second).
  ::典型的加压水反应堆(PWR)(PWR)是原建于1970年代的一种核电反应堆,生产1100至1500兆瓦,约1500亿焦耳/秒。 相比之下,一个有数百个风车的风车农场生产了大约5兆瓦(5 000万焦耳/秒 ) 。

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  Power
  ::电力

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  Power is defined as the rate at which work is done, or the rate at which is transformed.
  ::权力的定义是完成工作的速度或转变的速度。

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  $$\begin{array}{r}Power=\frac{Work}{Time}\end{array}$$

  
  ::Power=工作时间

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  In SI units, power is measured in Joules per second, which is given a special name: the watt , $\begin{array}{r}W\end{array}$ .
  ::在SI单元中,电量以每秒约勒斯测量,给它一个特殊的名称:瓦特,W。

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  1.00 watt = 1.00 J/s
  
  ::1.00瓦=1.00焦耳/秒

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  Another unit for power that is fairly common is horsepower.
  ::另一种相当常见的权力单位是马力。

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  1.00 horsepower = 746 watts
  ::1.00马力=746瓦

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  Example 1  
  ::例1

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  A 70.0 kg man runs up a long flight of stairs in 4.0 s. The vertical height of the stairs is 4.5 m. Calculate the power output of the man in watts and horsepower.  
  ::一个70.0公斤的男子在4.0秒内长长的楼梯飞行。 楼梯的垂直高度是4.5米。 计算男子以瓦特和马力的功率输出。

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  The force exerted must be equal to the of the man: $\begin{array}{r}mg=(70.0\text{kg})(9.80{\text{m/s}}^2)=686\text{N}\end{array}$
  ::施加的力必须等于男子的力:mg=(70.0公斤)(9.80米/秒)=686奈。

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  $\begin{array}{r}W=Fd=(686\text{N})(4.5\text{m})=3090\text{N m}=3090\text{J}\end{array}$
  ::W=Fd=(686 N(4.5米)=3090 Nm=3090 J)

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  $\begin{array}{r}P=\frac{W}{t}=\frac{3090\text{J}}{4.0\text{s}}=770\text{J/s}=770\text{W}\end{array}$
  ::P=Wt=3090 J4.0 s=770 J/s=770 W

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  $\begin{array}{r}P=770\text{W}=1.03\text{hp}\end{array}$
  ::P=770 W=1.03 hp

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  Since  $\begin{array}{r}P=\frac{W}{t}\end{array}$ and $\begin{array}{r}W=Fd\end{array}$ , we can use these formulas to derive a formula relating power to the of the object that is produced by the power.
  ::由于P=Wt和W=Fd,我们可以使用这些公式来得出一个公式,该公式与该动力产生的物体的功率有关。

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  $\begin{array}{r}P=\frac{W}{t}=\frac{Fd}{t}=F\frac{d}{t}=Fv\end{array}$
  ::P=Wt=Fdt=Fdt=Fv

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  The in this formula is the average speed of the object during the time interval.
  ::在此公式中,该公式是时间间隔中对象的平均速度。

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  Example 2  
  ::例2

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  Calculate the power required of a 1400 kg car if the car climbs a 10° hill at a steady 80. km/h.
  ::计算1400公斤汽车在每小时80公里处稳定攀爬10度山丘时所需的功率。

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  First convert 80. km/h to m/s: 22.2 m/s.
  ::首先转换80公里/小时到m/秒:22.2米/秒。

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  In 1.00 s, the car would travel 22.2 m on the road surface but the traveled upward would be (22.2 m)(sin 10°) = (22.2 m)(0.174) = 3.86 m. The force in the direction of the upward motion is the weight of the car: (1400 kg)(9.80 m/s ² ) = 13720 N.
  ::1时,汽车在公路表面行驶22.2米,但向上行驶为22.2米(10°)(22.2米)(10°)=22.2米(0.174)=3.86米。 向上行驶的力是汽车的重量(1400公斤)(9.80米/秒)=13720牛顿。

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  $\begin{array}{r}W=Fd=(13720\text{N})(3.86\text{m})=53,000\text{J}\end{array}$
  ::W=Fd=(13720 N(3.86米)=53 000日元)

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  Since this work was done in 1.00 second, the power would be 53,000 W.
  ::由于这项工作是在1.00秒内完成的,电力为53 000瓦。

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  This problem can be solved a different way; by calculating the upward component of the velocity of the car. The process would be similar, and start with finding the vertical component of the velocity vector : (22.2 m/s)(sin 10°) = (22.2 m/s)(0.174) = 3.86 m/s. Again, calculate the weight of the car: (1400 kg)(9.80 m/s ² ) = 13720 N. Finally, we could use the formula relating power to average speed to calculate power.
  ::这个问题可以通过另一种方式来解决;计算汽车速度的上方部分。这一过程相似,从找到速度矢量的垂直部分开始:22.2m/s (sin 10°) = (22.2m/s)(0.174) = 3.86m/s。再说一次,计算汽车的重量:1400kg (9.80m/s2) = 13720N。最后,我们可以使用以平均速度计算功率的公式来计算功率。

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  $\begin{array}{r}P=Fv=(13720\text{N})(3.86\text{m/s})=53,000\text{W}\end{array}$
  ::P=Fv=(13720 N)(3.86 m/s)=53 000 W

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  The of a is simply the ratio of power used to the power supplied (power output divided by power input). Use the simulation below to determine how to maximize the efficiency of a wind turbine:
  ::a 仅仅是所用功率与所提供功率之比(功率输出除以电输入)。

   

   

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  Further Reading
  ::继续阅读

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  Summary
  ::摘要

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  • Power is defined as the rate at which work is done or the rate at which energy is transformed.
    ::电力的定义是工作速度或能源转换速度。
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  • $\begin{array}{r}\text{Power}=\frac{\text{Work}}{\text{Time}}\end{array}$
    ::Power=工作时间
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  • $\begin{array}{r}\text{Power}=\text{Force}\times \text{velocity}\end{array}$
    ::Power= 力x速度

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  Review
  ::回顾

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  1. If the circumference of an orbit for a toy on a string is 18 m and the centripetal force is 12 N, how much work does the centripetal force do on the toy when it follows its orbit for one cycle?
     ::如果一个字符串上的玩具轨道的周长为18米,而子胎力为12N,那么在按照一个周期的轨道运行时,子胎力在玩具上需要做多少工作?
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  2. A 50.0 kg woman climbs a flight of stairs 6.00 m high in 15.0 s.  How much power does she use?
     ::一位50公斤的女士在15秒内爬上6米高的楼梯。 她用了多少电力?
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  3. Assuming no friction, what is the minimum work needed to push a 1000. kg car 45.0 m up a 12.5° incline?
     ::假设没有摩擦,将一辆1 000公斤45.0米的汽车推上12.5摄氏度的斜坡,最起码需要多少工作?

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  Explore More
  ::探索更多

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  Use  this resource to answer the questions that follow.
  ::使用此资源回答下面的问题 。

   

   

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  1. What is the difference between positive and negative work?
     ::积极工作与消极工作有什么区别?
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  2. What are the standard units for power?
     ::标准电力单位是什么?
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  3. What is horsepower?
     ::什么是马力?
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  4. How many grandfather clocks could you power with the same amount of power as is used by a single light bulb?
     ::你能用一个灯泡使用的 同等量的电力 来给多少个爷爷钟?

   

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  Resources
  ::资源

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  If you could lift 550 pounds a foot in the air in a second, what would you be (other than very strong)? Ever wondered what horsepower really means, and what horses have to do with other modes of transportation? See how engines work in machines all around us, including the surprising ways that they're all related. 
  ::如果你能在一秒钟内把550磅一英尺的空中升起,你会是什么样的人?你是否想知道马力真正意味着什么,马匹与其他运输方式有什么关系?看看引擎如何在我们周围的机器中运作,包括它们之间惊人的联系方式。

   

   

   

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  Watch this video for a Crash Course in Work, Energy and Power:
  ::在工作、能源和电力的崩溃课程中观看这段影片: