动力和脉冲

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is another way of looking at how objects affect each others' motion.  Rather than looking at how forces change over the time of the interaction, we can look at how objects are moving before they interact and then after they interact. 
::这是另一种观察物体如何影响彼此运动的方法。与其看物体在互动期间的变化力,不如看物体在互动之前和互动之后如何移动。

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Momentum and Impulse
::动力和脉冲

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If a bowling ball and a ping-pong ball are each moving with a of 5 mph, you intuitively understand that it will require more effort to stop the bowling ball than the ping pong ball because of the greater mass of the bowling ball.  Similarly, if you have two bowling balls, one moving at 5 mph and the other moving at 10 mph, you know it will take more effort to stop the ball with the greater . It is clear that both the mass and the velocity of a moving object contribute to what is necessary to change the motion of the moving object. The product of the mass and velocity of an object is called its  momentum .  Momentum is a vector quantity that has the same direction as the velocity of the object and is represented by a lowercase letter p .
::如果保龄球和乒乓球每个移动5米,你直觉地理解,由于保龄球的重量较大,它需要比乒乓球更努力地阻止保龄球。同样,如果保龄球有两个保龄球,一个在5米,另一个在10米,你就会知道,要用更大的球来阻止球,需要付出更多努力。很明显,移动对象的质量与速度都有助于改变移动对象的动作。一个物体的质量与速度的产物称为其动量。动因是一种矢量,其方向与物体的速度相同,并以小写字母p表示。

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$\begin{array}{r}p=mv\end{array}$
::p=mv =p=mv =pp =mv =pmv =pp=mv =pmv

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The momentum of a 0.500 kg ball moving with a velocity of 15.0 m/s will be
::移动速度为15.0米/秒的0.500公斤球的动力将是

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::p=mv=(0.500公斤)(15.0米/秒)=7.50千克/秒

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You should note that the units for momentum are kg·m/s.
::请注意,动量单位为千克/米/秒。

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According to Newton’s first law , the velocity of an object cannot change unless a force is applied. If we wish to change the momentum of a body, we must apply a force. The longer the force is applied, the greater the change in momentum.   A common misconception is that when two objects collide, the smaller object is hit harder or experiences more force than the larger object. Play around with the simulation below to dispel this misconception:
::根据牛顿的第一部法律,一个物体的速度不能改变,除非使用武力。如果我们想改变一个身体的动力,我们必须使用一种力量。 力量的运用时间越长,动力的变化越大。 一种常见的误解是,当两个物体相撞时,小物体受到的打击比更大的物体更重,或者受到的力更大。 玩弄下面的模拟来消除这种误解:

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The  is the quantity defined as the force multiplied by the time it is applied. It is a vector quantity that has the same direction as the force.  The units for impulse are N·s but we know that Newtons are also kg·m/s ² and so N·s = (kg·m/s ² )(s) = kg·m/s. Impulse and momentum have the same units; when an impulse is applied to an object, the momentum of the object changes and the change of momentum is equal to the impulse.
::是指在应用时所定义的功率乘以乘以时的功率。它是一个与功率方向相同的矢量。脉冲的单位为 N / NS。但我们知道牛顿的功率也是 kg / m/ s2, 所以N = (kg / m/ s2 (s) = kg / m (s) / s。 脉冲和动量具有相同的功率;当脉冲应用到物体时,物体变化的势头和动力的改变与脉冲相等。

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$\begin{array}{r}Ft=\mathrm{\Delta }mv\end{array}$
::Ftmv

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Example 1
::例1

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A 0.15 kg ball is moving with a velocity of 35 m/s.  Find the momentum of the ball.
::0.15公斤的球正在以35米/秒的速度移动,找到球的动力。

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  $\begin{array}{r}p=mv=(0.15\text{kg})(35\text{m/s})=5.25\text{kg}\cdot \text{m/s}\end{array}$
::p=mv=(0.15公斤)(35米/秒)=5.25公斤/秒)

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Example 2  
::例2

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If a ball with mass 5.00 kg has a momentum of $\begin{array}{r}5.25\text{kg}\cdot \text{m/s}\end{array}$ , what is its velocity?
::如果一个质量为5.00公斤的球的体积为5.25千克/秒,其速度是多少?

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  $\begin{array}{r}v=\frac{p}{m}=\frac{5.25\text{kg}\cdot \text{m/s}}{5.00\text{kg}}=1.05\text{m/s}\end{array}$

::v=pm=5.25 kgm/s5.00kg=1.05m/s

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It should be clear from the equation relating impulse to change in momentum, $\begin{array}{r}Ft=\mathrm{\Delta }mv\end{array}$ , that any amount of force would (eventually) bring a moving object to rest. If the force is very small, it must be applied for a long time, but a greater force can bring the object to rest in a shorter period of time. 
::从与改变动力的冲动有关的方程式Ftmv中应该可以清楚地看出,任何武力的量都会(甚至)使移动物体止步。 如果武力非常小,必须长期使用,但更大的力量可以在较短的时间内使物体消亡。

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If you jump off a porch and land on your feet with your knees locked in the straight position, your motion would be brought to rest in a very short period of time and thus the force would need to be very large – large enough, perhaps, to damage your joints or bones.
::如果你从门廊跳下,膝盖紧紧地跪在地上, 你的动作就会在很短的时间内得到休息, 因此部队需要非常大 — — 也许足够大,足以破坏你的关节或骨头。

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Suppose that when you hit the ground, your velocity was 7.0 m/s and that velocity was brought to rest in 0.05 seconds.  If your mass is 100. kg, what force was required to bring you to rest?
::假设当你撞击地面时,你的速度是7.0米/秒,而速度在0.05秒后得到休息。如果质量是100公斤,那么需要何种力量才能使你休息?

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$\begin{array}{r}F=\frac{\mathrm{\Delta }mv}{t}=\frac{(100.\text{kg})(7.0\text{m/s})}{0.050\text{s}}=14,000\text{N}\end{array}$
::Fmvt=(100公斤)(700米/秒)0.050秒=14 000奈

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If, on the other hand, when your feet first touched the ground, you allowed your knees to flex so that the period of time over which your body was brought to rest is increased, then the force on your body would be smaller and it would be less likely that you would damage your legs.
::另一方面,如果,当你的脚第一次触碰地面时,你允许你的膝盖伸缩,以便增加你身体被送去休息的时间,那么,你身体上的力量就会小一些,而你的腿也不太可能受损。

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Suppose that when you first touch the ground, you allow your knees to bend and extend the stopping time to 0.50 seconds. What force would be required to bring you to rest this time?
::假设你第一次接触地面时,你的膝盖可以弯曲,把停止时间延长到0.50秒。这次需要用什么力量来使你休息?

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$\begin{array}{r}F=\frac{\mathrm{\Delta }mv}{t}=\frac{(100.\text{kg})(7.0\text{m/s})}{0.50\text{s}}=1400\text{N}\end{array}$
::-mvt=(100公斤)(700米/秒)0.50秒=1400奈

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With the longer period of time for the force to act, the necessary force is reduced to one-tenth of what was needed before.
::随着部队行动时间的延长,必要的武力将减少到以前需要的十分之一。

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Extending the period of time over which a force acts in order to lessen the force is a common practice in design. Padding in shoes and seats allows the time to increase. The front of automobiles are designed to crumple in an accident; this increases the time the car takes to stop. Similarly, barrels of water or sand in front of abutments on the highway and airbags serve to slow down the stoppage time. These changes all serve to decrease the amount of force it takes to stop the momentum in a car crash, which consequently saves lives. Use the Crash Dummy simulation below to learn more:
::延长部队为减少兵力而采取行动的时间是设计上的一种常见做法。 穿鞋和坐椅可以增加时间。 汽车前部的设计是为了在事故中折叠;这增加了汽车停车的时间。 同样,在高速公路和气囊的挡板前的一桶水或沙子有助于减缓停机时间。 这些变化都有助于减少它为阻止汽车撞车而需要的力气量,从而挽救生命。 下面用克拉舍堆肥模拟来学习更多的东西:

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Example 3  
::例3

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An 0.15 kg baseball is thrown horizontally at 40. m/s and after it is struck by a bat, it is traveling at -40. m/s.
::0.15公斤的棒球在40米/秒时水平投出,在被蝙蝠击中后,球速为-40米/秒。

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(a) What impulse did the bat deliver to the ball?
:a) 蝙蝠给球带来了什么动力?

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(b) If the contact time of the bat and bat was 0.00080 seconds, what was the average force the bat exerted on the ball?
:b) 如果蝙蝠和蝙蝠的接触时间为0.0080秒,球上蝙蝠的平均作用是什么?

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(c) Calculate the of the ball during the time it was in contact with the bat.
:c) 计算与球棒接触时的球体。

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We can calculate the change in momentum and give the answer as impulse because we know that the impulse is equal to the change in momentum.
::我们可以计算出势头的变化,作为动力给出答案,因为我们知道这种冲动等于势头的变化。

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(a)
:a) (a)

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::=mv=(0.15公斤)(-40.m/s-40.m/s)=(0.15公斤)(-80.m/s) =12.m/s)

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The minus sign indicates that the impulse was in the opposite direction of the original throw.
::减号显示 脉冲与最初投出的相反

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(b) $\begin{array}{r}F=\frac{\mathrm{\Delta }mv}{t}=\frac{-12\text{kg}\cdot \text{m/s}}{0.00080\text{s}}=-15000\text{N}\end{array}$
:b) Fmvt12 kg%m/s0.00080 s15000 N

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Again, the negative sign indicates the force was in the opposite direction of the original throw.
::同样,负面迹象表明,武力与最初的投出相反。

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(c) $\begin{array}{r}a=\frac{F}{m}=\frac{-15000\text{N}}{0.15\text{kg}}=-100,000{\text{m/s}}^2\end{array}$
:c) a=Fm15000 N0.15千克 100 000 m/s2

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Further Reading
::继续阅读

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Summary
::摘要

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• The product of the mass and velocity of an object is called momentum, given by the equation  $\begin{array}{r}\rho =mv\end{array}$ . 
  ::方程式 mv 给出的物体质量和速度的产物称为动量。
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• Momentum is a vector quantity that has the same direction as the velocity of the object.
  ::动力是一个与对象速度方向相同的矢量量。
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• The quantity of force multiplied by the time it is applied is called impulse. 
  ::力量乘以施用时的力量,称为脉冲。
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• Impulse is a vector quantity that has the same direction as the force. 
  ::脉冲是一种矢量,其方向与威力方向相同。
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• Momentum and impulse have the same units: kg·m/s.
  ::动力和脉冲的单位相同:千克/米/秒。
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• The change of momentum of an object is equal to the impulse. $\begin{array}{r}Ft=\mathrm{\Delta }mv\end{array}$
  ::物体动力的改变等于脉冲。

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Review
::回顾

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1. A small car with a mass of 800. kg is moving with a velocity of 27.8 m/s.
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   1. What is the momentum of the car?
      ::汽车的动力是什么?
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   2. What velocity is needed for a 2400. kg car in order to have the same momentum?
      ::2400公斤的汽车需要什么速度才能保持同样的车速?
   
   ::一辆质量为800公斤的小型汽车正在以27.8米/秒的速度移动。 汽车的动力是什么? 2400公斤的汽车需要什么速度才能保持同样的动力?
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2. A scooter has a mass of 250. kg. A constant force is exerted on it for 60.0 s.  During the time the force is exerted, the scooter increases its speed from 6.00 m/s to 28.0 m/s.
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   1. What is the change in momentum?
      ::势头的变化是什么?
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   2. What is the magnitude of the force exerted on the scooter?
      ::对摩托车施加的力有多大?
   
   ::摩托车质量为 250 公斤。 对其施加的常力为 6 0.0 秒。 在使用武力期间, 摩托车的速度从 6.00 m/秒升至 28.0 m/秒。 动力变化如何? 对摩托车施加的力有多大?
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3. The brakes on a 15,680 N car exert a stopping force of 640. N.  The car’s velocity changes from 20.0 m/s to 0 m/s.
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   1. What is the car’s mass?
      ::汽车质量是多少?
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   2. What was its initial momentum?
      ::最初的势头是什么?
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   3. What was the change in momentum for the car?
      ::汽车动力的变化是什么?
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   4. How long does it take the braking force to bring the car to rest?
      ::制动部队需要多久才能让车休息?
   
   ::N. 汽车的速度从20米/秒变为0米/秒。 车的质量是什么?车的最初动力是什么?车的动力变化是什么? 车的动力变化是什么? 制动部队需要多长时间才能让车歇息?

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Explore More
::探索更多

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Use this resource to answer the question that follows.
::使用此资源回答以下问题 。

 

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1. Why don't the glasses of water spill when the tablecloth is pulled out from under them?
   ::当桌布从下面拉出来时 为什么不用漏水杯子呢?
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2. How does the video get from momentum to impulse?
   ::视频如何从势头到冲动?