11.4 从武力和质量中加速计算

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  从力和质量加速计算

  

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  Zeke  goes airborne on his  skateboard as he exits a half-pipe at Newton’s Skate Park. How did he gain enough in the half-pipe to fly into the air when he got to the top? His increase in speed was due partly to the force of gravity.  
  ::Zeke在从牛顿滑板公园的半排气管出口时登上滑板。 当他到达顶端时,他是如何从半排气管中获得足够的气管飞入空中的? 他速度的上升部分是由于重力造成的。

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  Acceleration, Force, and Mass
  ::加速、力和质量

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  A change in an object’s motion—such as  Zeke  speeding up on his s kateboard —is called . Acceleration occurs whenever an object is acted upon by an unbalanced force. The greater the net force acting on the object, the greater its acceleration will be, but the mass of the object also affects its acceleration. The smaller its mass is, the greater its acceleration for a given amount of force. Newton’s second law of motion summarizes these relationships. According to this law , the acceleration of an object equals the net force acting on it divided by its mass. This can be represented by the equation:
  ::物体运动的改变,如Zeke加速滑板上的动作。当物体受到不平衡的力量影响时,加速就会发生。在物体上行动的净力越大,加速力就会越大,但物体的质量也会影响加速力。物体质量越小,其加速力就越大。牛顿的第二个运动法则对这些关系进行了总结。根据这项法律,物体的加速力等于物体上行动的净力除以其质量。这可以用等式表示:

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  $\begin{array}{r}\mathrm{A}\mathrm{c}\mathrm{c}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}=\frac{\mathrm{N}\mathrm{e}\mathrm{t}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{c}\mathrm{e}}{\mathrm{M}\mathrm{a}\mathrm{s}\mathrm{s}}\end{array}$ or $\begin{array}{r}\mathrm{a}=\frac{\mathrm{F}}{\mathrm{m}}\end{array}$
  ::加速 = NetforceMass 或 a = Fm

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  Calculating Acceleration
  ::计算加速加速

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  This equation for acceleration can be used to calculate the acceleration of an object that is acted on by a net force. For example,  Zeke and his scooter have a total mass of 50 kilograms. Assume that the net force acting on  Zeke  and the  skateboard  is 25 Newtons. What is his acceleration? Substitute the relevant values into the equation for acceleration:
  ::这个加速度方程式可用于计算由净力作用的物体的加速度。 例如, Zeke 和他的滑板车总重量为 50 公斤。 假设Zeke 和滑板上的净力为 25 牛顿。 他的加速度是多少? 将相关值替换为加速度 :

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  $$\begin{array}{r}\text{a}=\frac{\text{F}}{\text{m}}=\frac{25\text{N}}{50\text{kg}}=\frac{0.5\text{N}}{\text{kg}}\end{array}$$

  
  ::a=Fm=25 N50公斤=0.5 Nkk

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  The Newton is the SI unit for force. It is defined as the force needed to cause a 1-kilogram mass to accelerate at 1 m/s ² . Therefore, force can also be expressed in the unit kg • m/s ² . This way of expressing force can be substituted for Newtons in Zeke' s acceleration so the answer is expressed in the SI unit for acceleration, which is m/s ² :
  ::牛顿是SI力单位,被定义为使1公斤质量加速1米/秒2所需的力量。因此,也可以用单位单位千克/秒2表示力量。这种表达力量的方式可以取代Zeke加速度中的牛顿,因此答案在SI加速度单位(m/秒2)中表示,加速度为m/秒2:

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  $$\begin{array}{r}\text{a}=\frac{0.5\text{N}}{\text{kg}}=\frac{0.5\text{kg}\cdot {\text{m/s}}^2}{\text{kg}}=0.5{\text{m/s}}^2\end{array}$$

  
  ::a=0.5 Nkg=0.5千克=0.5千克当量/平方米=0.5m/秒2

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  Q : Why are there no kilograms in the final answer to this problem?
  ::问:为什么对这一问题的最后答案没有公斤?

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  A : The kilogram units in the numerator and denominator of the fraction cancel out. As a result, the answer is expressed in the correct SI units for acceleration.
  ::A: 分数数中的千克单位和分母取消。 因此, 答案以正确的 SI 单位表示, 以便加速 。

   

   

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  Calculating Force
  ::计算力

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  It’s often easier to measure the mass and acceleration of an object than the net force acting on it. Mass can be measured with a balance, and average acceleration can be calculated from and time. However, net force may be a combination of many unseen forces, such as gravity, with surfaces, and air . Therefore, it may be more useful to know how to calculate the net force acting on an object from its mass and acceleration. The equation for acceleration above can be rewritten to solve for net force as:
  ::测量物体的重量和加速度往往比测量物体的强度和加速度要容易得多。 质量可以用平衡来衡量,平均加速度可以从时间和时间上计算出来。 但是,净力可能是许多看不见的力量(如重力、表面和空气)的组合。 因此,知道如何从物体的重量和加速度来计算物体上作用的净力可能更有用。 以上加速度的方程式可以重新写成,以解决净力问题,例如:

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  Net Force = Mass × Acceleration, or
  ::净力=质量x加速,或

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  F = m × a
  ::F = m = a = m = a

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  Look at Zeke's friend Eren in the Figure . He’s riding his s kateboard  down a ramp. Assume that his acceleration is 0.8 m/s ² . How much force does it take for him to accelerate at this rate? Substitute the relevant values into the equation for force to find the answer:
  ::看看Zeke的朋友Eren在图中。他骑着滑板滑板滑坡下坡。假设他的加速度为0.8米/秒。 假设他的加速度以这种速度加速需要多少力量? 将相关的数值转换为找到答案的方程式:

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  F = m × a = 50 kg × 0.8 m/s ² = 40 kg • m/s ² , or 40 N
  ::F = m = m × a = 50公斤 × 0.8 m/s2 = 40公斤 = m/s2 或 40 N

  

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  Q : If  Eren and his s kateboard  actually had a mass of 40 kg instead of 50 kg, how much force would it take for him to accelerate at 0.8 m/s ² ?
  ::问:如果Eren和他的滑板实际上质量为40公斤,而不是50公斤,那么他加速0.8m/s2的速度需要多少力?

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  A : It would take only 32 N of force (40 kg × 0.8 m/s ² ).
  ::A:只需要32牛顿(40公斤x0.8米/秒)。

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  Summary
  ::摘要

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  • According to Newton’s second law of motion, the acceleration of an object equals the net force acting on it divided by its mass, or $\begin{array}{r}\mathrm{a}=\frac{\mathrm{F}}{\mathrm{m}}\end{array}$ .
    ::根据牛顿的第二项运动法则,物体加速速度等于物体上作用的净力除以质量,或a=Fm。
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  • This equation for acceleration can be used to calculate the acceleration of an object when its mass and the net force acting on it are known.
    ::加速度的这个方程式可以用来计算物体质量和作用力净值已知时的加速度。
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  • The equation for acceleration can be rewritten as F = m × a to calculate the net force acting on an object when its mass and acceleration are known.
    ::加速度方程式可以重写为 F = m × a ,以计算当物体质量和加速度为已知值时该物体的动力净额。

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  Review
  ::回顾

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  1. What is the equation for calculating the acceleration of an object when its mass and the net force acting on it are known?
     ::当一个物体的重量和作用的净力已知时,计算该物体加速度的方程式是什么?
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  2. Zeke' s friend Eren has a skateboard that he rides at Newton’s Skate Park. That’s  Eren  doing a jump in the Figure . The combined mass of  Eren and his skateboard is 60 kg. At the top of his jump, the net force acting on him is 30 Newtons. What is his acceleration at that moment? 

     

     
     ::Zeke的朋友Eren在牛顿滑板公园有一个滑板。那就是Eren跳进图中。Eren和滑板的总质量是60公斤。在他跳跃的顶端,他身上的净额力量是30牛顿。 当时他的加速度是多少?
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  3. What net force would have to act on  Eren for him to have an acceleration of 1 m/s ² ?
     ::艾连要加速1m/s2的速度 需要多少力量才能对艾连采取行动?