13.2 计算工作

Section outline

• Select section General

  Collapse Expand

  General

  Collapse all Expand all

  • Select activity 新闻通告

    

    新闻通告 Forum
• Select section 计算计算工作

  Collapse Expand

  计算计算工作

  

  播放段落

  Clarissa is cutting the grass in her grandmother’s yard using an old-fashioned push mower. The mower has no motor, so Clarissa is doing all the work. How much work does Clarissa do pushing the mower around the yard? The amount of work depends on how much force she uses and how far she pushes the mower.
  ::Clarissa正在用老式的推土机割草。 割草机没有发动机,因此Clarissa正在做全部工作。 Clarissa在院子周围推开割草机做了多少工作? 工作量取决于她用多少力以及她把割草机推到多远。

  播放段落

  Work, Force, and Distance
  ::工作、力量和距离

  播放段落

  Work  is the use of force to move an object a certain . It is directly related to both the force applied to the object and the distance the object moves. Work can be calculated with this equation when  force and the distance moved are in the same direction:
  ::工作是用武力移动某个物体 。 它与对象的强度和物体移动的距离直接相关。 当动的强度和距离朝同一方向移动时, 工作可以通过此方程式来计算 :

  播放段落

  Work = Force x Distance.
  ::工作=力x距离。

  播放段落

  How Much Work?
  ::多少工作? 多少工作?

  播放段落

  The equation for work can be used to calculate work if force and distance are known. To use the equation, force is expressed in newtons (N), and distance is expressed in meters (m). For example, assume that Clarissa uses 100 newtons of force to push the mower and that she pushes it for a total of 200 meters as she cuts the grass in her grandmother’s yard. Then, the amount of work Clarissa does is:
  ::工作方程式可以用来计算已知强度和距离的工程。 使用方程式时,力法以牛顿( N)表示,距离以米( m)表示。 例如,假设克拉里萨用100牛顿的力量推开割草机,当她切开祖母院子里的草时,她将力法推到总共200米。 然后,Clarissa的工作量是:

  播放段落

  Work = 100 N × 200 m = 20,000 N • m
  ::工作 = 100 N × 200米 = 20 000 N = 千米 = 工作 = 100 N × 200米 = 20 000 N = 千米 = 工作 = 工作 = 工作 = 100 N × 200米 = 20 000 N

  播放段落

  Notice that the unit for work in the answer is the “newton meter” (N • m). A newton meter is equivalent to the SI unit for work and called the joule (J) . One joule equals the amount of work that is done when 1 N of force moves an object over a distance of 1 m.
  ::请注意,回答中的工作单位是“牛顿计” (N • m) 。 牛顿计相当于SI的工作单位,称为Joule (J)。 1 焦耳等于1 N 单位将物体移到1米以外距离时完成的工作量。

  播放段落

  Q : After Clarissa mows her grandmother’s lawn, she volunteers to mow a neighbor’s lawn as well. If she pushes the mower with the same force as before and moves it over a total of 234 meters, how much work does she do mowing the neighbor’s lawn?
  ::问:Clarissa割草坪后,她自愿也修剪邻居的草坪。 如果她用与以前相同的武力推开割草机,并将它移到总共234米,那么她修剪邻居的草坪需要做多少工作?

  播放段落

  A : The work Clarissa does can be calculated as:
  ::A:Clarissa的工作可以计算为:

  播放段落

  Work = 100 N × 234 m = 23,400 N • m, or 23,400 J
  ::工作 = 100 N × 234 m = 23 400 N = 23 400 N = m 或 23 400 J

  播放段落

  Calculating Force or Distance 
  ::强制或距离计算

  播放段落

  The work equation given above can be rearranged to find force or distance if the other variables are known:
  ::如果已知其他变量,上述工作方程式可以重新排列,以找到力量或距离:

  播放段落

  $\begin{array}{r}\mathrm{F}\mathrm{o}\mathrm{r}\mathrm{c}\mathrm{e}=\frac{\mathrm{W}\mathrm{o}\mathrm{r}\mathrm{k}}{\mathrm{D}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}}\end{array}$
  ::强制=工作差异

  播放段落

  $\begin{array}{r}\mathrm{D}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}=\frac{\mathrm{W}\mathrm{o}\mathrm{r}\mathrm{k}}{\mathrm{F}\mathrm{o}\mathrm{r}\mathrm{c}\mathrm{e}}\end{array}$
  ::距离=工作单位

  播放段落

  After Clarissa finishes mowing both lawns, she pushes the lawn mower down the sidewalk to her own house. If she pushes the mower over a distance of 30 meters and does 2700 joules of work, how much force does she use? Substitute the known values into the equation for force:
  ::Clarissa修完两片草坪后,她把草坪割草机推下人行道,推到她自己的家。 如果她把割草机推到30米远的地方,并做了2700焦耳的工作,她用了多少力?用已知的数值来代替武力方程式:

  播放段落

  $\begin{array}{r}\text{Force}=\frac{2700\text{J}}{30\text{m}}=90\text{N}\end{array}$
  ::部队=2700 J30 m=90 N

  播放段落

  Q : When Clarissa gets back to her house, she hangs the 200 N lawn mower on some hooks in the garage (see the Figure ). To lift the mower, she does 400 J of work. How high does she lift the mower to hang it?
  ::问:Clarissa回到她家后,她把200个N割草机挂在车库的钩子上(见图 ) 。 要抬起割草机,她要干400J的工作。她把割草机抬高多少?

  播放段落

  A : Substitute the known values into the equation for distance:
  ::A: 在距离方程中替换已知值:

  播放段落

  $\begin{array}{r}\mathrm{D}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}=\frac{\mathrm{W}\mathrm{o}\mathrm{r}\mathrm{k}}{\mathrm{F}\mathrm{o}\mathrm{r}\mathrm{c}\mathrm{e}}\end{array}$
  ::距离=工作单位

  播放段落

  $\begin{array}{r}\text{Distance}=\frac{400J}{200N}=2m\end{array}$
  ::距离=400 J200 N=2米

  

  播放段落

  Getting a piano into a truck isn't easy, so we often use a ramp to lower the amount of required force. A pply the work equation in the  simulation below   to  determine how  much  force it will take to move a piano  up the longest ramp:
  ::将钢琴送进卡车并不容易,所以我们经常使用斜坡来降低所需强度。在下面的模拟中应用工作方程式来确定将钢琴推上最长的斜坡需要多少力:

   

   

  播放段落

  Summary
  ::摘要

  播放段落
  • Work can be calculated with the equation: Work = Force × Distance.
    ::工作可以用公式来计算:工作=部队x距离。
  播放段落
  • The SI unit for work is the joule (J), or newton • meter (N • m). One joule equals the amount of work that is done when 1 N of force moves an object over a distance of 1 m.
    ::SI工作单位为焦耳(J)或牛顿表(N)/米。 焦耳等于1N的力力将物体移到1米远处时完成的工作量。
  播放段落
  • The equation for work can be rearranged to find force or distance if the other variables are known.
    ::如果知道其他变量,可以重新安排工作方程式,以找到力量或距离。

  播放段落

  Review
  ::回顾

  播放段落
  1. Write the equation for calculating work when force and distance are known.
     ::当已知力量和距离时, 写入计算工作的方程式 。
  播放段落
  2. What is the SI unit for work? What does it represent?
     ::SI单位是什么工作单位?它代表什么?
  播放段落
  3. Clarissa helps her mom put the 200 newton lawn mower in the back of her mom’s truck. They lift the mower up from the ground to the truck bed, which is 1.1 meters above the ground. How much work do Clarissa and her mom do?
     ::Clarissa帮助她妈妈把200个牛顿草坪割草机放在她妈妈的卡车后座。 他们把割草机从地上抬到卡车床上,在地面上方1.1米。 Clarissa和她妈妈做了多少工作?
  播放段落
  4. Clarissa climbs into the back of the truck to tie the lawn mower in place. If she does 528 joules of work raising herself to the truck bed, how much  force did she apply?
     ::Clarissa爬上卡车后座,把割草机绑起来。 如果她做了528焦耳的工作,将自己抬到卡车床上,她施了多少力?