Course: 10.3 《帕斯卡尔法》

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《帕斯卡尔法》
A person is able to lift the entire rear end of the automobile using only one hand with the hydraulic jack shown in the image. Hydraulic systems are similar to simple machines in that they can produce very large mechanical advantages.
::一个人只能用一只手用图像中显示的液压插件提升汽车的后端。水力系统与简单的机器相似,因为它们可以产生巨大的机械优势。

Pascal’s Law
::帕斯卡尔法

The earth’s atmosphere exerts a pressure on all objects with which it is in contact. acting on a fluid is transmitted throughout that fluid. For example, the water pressure at 100. m below the surface of a lake is 9.8 × 10 ⁵ Pa. The total pressure at that point, however, is the pressure of the water plus the pressure of the air above the water. The pressure of the air at the surface of the water is 1.0 × 10 ⁵ Pa, or 1 atm (atmosphere). Therefore, the total pressure at 100. m below the surface of the water is 9.8 × 10 ⁵ Pa + 1.0 × 10 ⁵ Pa = 10.8 × 10 ⁵ Pa.
::地球大气层对其接触的所有物体施加压力。液压在整个液体中传播。例如,湖表面下方100米的水压为9.8×105帕。然而,当时的总压力是水的压力加上水上方的空气压力。水表面的空气压力是1.0×105帕,或1厘米(大气)。因此,水表面下面100米的总压力是9.8×105帕+1.0×105帕=10.8×105帕。

This is an example of Pascal’s law , which states that pressure applied to a confined liquid increases the pressure throughout by the same amount. A number of practical devices take advantage of this principle. Hydraulic brakes, hydraulic lifts , and hydraulic presses are three useful tools that make use of Pascal’s law.
::这是帕斯卡尔法律的一个例子。帕斯卡尔法律指出,对封闭液体施压会增加同样数量的压力。一些实用装置利用了这一原则。液压刹车、液压电梯和液压压机是利用帕斯卡尔法律的三种有用的工具。

The sketch below is an example of a hydraulic lift . We have a confined liquid in contact with two pistons ( $\begin{aligned} A \end{aligned}$ and $\begin{aligned} B \end{aligned}$ ) of different sizes. The pressure of the liquid on these two pisons is the same (Pascal's law). Therefore, $\begin{aligned} F_{A} = F_{B} \end{aligned}$ ,
::下面的草图是液压电梯的一个例子。我们与两个不同大小的活塞(A和B)接触了一种封闭液体。这两个活塞(Pascal's law)的液体压力是一样的(Pascal's law)。因此, FA=FB,

and $\begin{aligned} \frac{F_{A}}{A_{A}} = \frac{F_{B}}{A_{B}} \end{aligned}$ and $\begin{aligned} \frac{F_{A}}{F_{B}} = \frac{A_{A}}{A_{B}} \end{aligned}$ .
::和FAAA=FBAB和FAFB=AAAB。

Suppose that the area of piston $\begin{aligned} A \end{aligned}$ is 4.0 cm ² and the area of piston $\begin{aligned} B \end{aligned}$ is 200. cm ² . If we place an automobile weighing 10,000 N on piston $\begin{aligned} B \end{aligned}$ , we can lift that car by exerting a force of 200 N on piston $\begin{aligned} A \end{aligned}$ . This is another form of simple machine and its ideal mechanical advantage is 50. The ideal mechanical advantage of a hydraulic lift equals the ratio of the large piston area to the small piston area.
::假设活塞A的面积为4.0厘米,活塞B的面积为200厘米。如果我们在活塞B上放置一辆重量为10,000牛顿的汽车,我们可以在活塞B上用200牛顿的力量来提升汽车。这是另一种简单的机器形式,其理想的机械优势是50。液压电梯的理想机械优势相当于大活塞区与小活塞区的比重。

It can be really dangerous if tires are under inflated or over inflated, so it is important to be precise when it comes to measuring tire pressure. Use the simulation below to experiment with different inflation pressures for truck tires:
::如果轮胎被夸大或过度夸大,可能非常危险,因此在测量轮胎压力时必须精确。使用下面的模拟来试验卡车轮胎的不同通胀压力:

Summary
::摘要

Atmospheric pressure acting on a fluid is transmitted throughout that fluid.
::对液体作用的大气压力在整个液体中传播。

Pascal’s law states that pressure applied to a confined liquid increases the pressure throughout by the same amount.
::Pascal的法律规定,对封闭液体施加的压力使整个压力增加同样数量。

Review
::回顾

In a hydraulic lift whose input line has a cross-sectional area of 1.00 cm ² and whose output line has a cross-sectional area of 20.0 cm ² , what is the largest mass (kg) that can be lifted by an input force of 1000. N?
::在液压电梯中,输入线的截面面积为1.00厘米2,其输出线的截面面积为20.0厘米2,最大质量(千克)是1000厘米。 N?

In a hydraulic lift whose IMA is 50, how far (ideally) will the output platform be lifted when the input platform is depressed 100. cm?
::在IMA为50的液压电梯中,当输入平台压抑100厘米时,输出平台将(理想的)提升到多远?

A 20.0 N force is exerted on the small piston of a hydraulic system. The cross-sectional area of the small piston is 0.0500 m ² . What is the magnitude of the weight than can be lifted by the large piston, which has a cross-sectional area of 0.100 m ² ?
::液压系统的小活塞施加了20.0N力,小活塞的横截面面积为0.0500平方米,其重量的大小比大活塞所能提升的重量大多少,而大活塞的横截面面积为0.100平方米?

Explore More
::探索更多

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

What property of liquids allows for the great mechanical advantage of a hydraulic lift?
::液压升降机在机械上有什么优势?

If the ratio of A2 to A1 was 100, what force would be required to lift a 10000 N car?
::如果A2对A1的比率是100,那么需要何种武力才能提升一辆10000N型汽车?

Section outline

General

《帕斯卡尔法》

Pascal’s Law ::帕斯卡尔法

Summary ::摘要

Review ::回顾

Explore More ::探索更多

Pascal’s Law
::帕斯卡尔法

Summary
::摘要

Review
::回顾

Explore More
::探索更多