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I have a problem with physical explanation of Pascal’s Law. For example, when I was teaching my sister (a high school student) about force transmitting by a rope, I said her:

“In a very simplified mood, when we pull free end of a rope that is connected to a block, we pull first molecule of the rope, that molecule pulls next one and go on like this and last molecule pull the block. So, our force is transmitted to the block.”

In that case, force is transmitted (and maybe decreases because of loss of energy). In a car hydraulic jack, force not only transmitted but also increases. How can I explain this topic physically (not mathematically)? Additional force comes from where?

lucas
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3 Answers3

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Concerning your wording "force is transmitted (and maybe decreases because of loss of energy)" - no, no, the decrease of force is not easily connected to the loss of energy. Force can be decreased because there is friction, but this does not imply a loss of energy (not if nothing moves). And also energy can be lost (plastic deformation of the rope) without a decrease in force.

To your question... you probably know the famous experiment: take a barrel filled with water and a thin tube connected to it going upward. If you fill the tube with water, the barrel bursts.
The spot below the tube is easy - the whole column of water pushes it. But what with the other spots? Well, they are pushed by the top of the barrel (plus the small column below). So if you cut the barrel in the middle, you have to hold it with the force done by all the water columns, not just the one that actually goes so high.

As to your molecules: it's easier to push someone away when leaning with the back to a wall! :)

Ilja
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Pascal's law states that when there is an increase in pressure at any point in a confined fluid, there is an equal increase at every other point in the container.

To explain this, the hydraulic jack is a better example. Car jack works on mechanical forces. A mechanical jack employs a screw thread for lifting heavy equipment. But hydraulic jacks use force generated from pressure. It's working can be explained using Pascal's law. A hydraulic jack contains two cylinders (one having larger area and the other smaller) connected each other and inside them an in-compressible liquid. Once a force is applied to the small cylinder, a pressure develops on the surface of the cylinder. According to Pascal's law, the same pressure will be transmitted to the entire parts of the fluid. So at the other cylinder the same pressure appears. At the second cylinder, the surface area is large. Since $\displaystyle{pressure=\frac{force}{area}}$ the force acting in the upward direction on the second surface will be larger. So you apply a small force on the cylinder with smaller surface area and you will get a much larger force on the second surface having larger surface area.

As a quantitative example, suppose I have two cylinders $C_1$ and $C_2$. The surface areas of $C_1$ and $C_2$ are denoted as $S_1$ and $S_2$. Let $S_1=1 m^2$ and $S_2=100 m^2$. An in-compressible liquid is present in the cylinders and both are connected. You apply a force of about $600N$ (an average man's weight; suppose you are standing on the first cylinder's surface) on $S_1$. Then it will generate a pressure of $600N/m^2$. By Pascal's law, the same pressure appears on $S_2$. then the force appearing on $S_2$ will be $60000 N$!!!. Impressive, isn't it? That's the weight of 4 cars. you just lifted 4 cars just with your weight. No sweat.

The additional force came from no where. the pressure just remains the same as the liquid is in-compressible. The effect of force comes different when you apply different surface areas connected by the liquid. If you apply two same surface areas, there is no additional force. Here the surface area has great relevance. You cannot just avoid it and think in terms of force alone.

UKH
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You can use the same explanation :

"The first molecule pushes its nearest neighbours (which also push back), the nearest neighbours push their nearest neighbours, and so on until the force is transmitted throughout the fluid."

The total force transmitted to or by a surface is in proportion to the number of molecules pushing, which is proportional to the area.

sammy gerbil
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