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# Illustration 14.2: Pascal's Principle

mass = kg

The animation shows a model of a hydraulic lift (position is given in centimeters, force is given in newtons, and time is given in seconds). A gas or liquid, usually oil (yellow in this animation), fills a container with pistons. Restart.

Notice that because the pressure is the same at the same height in the fluid, the force required for the hand to support the mass is much less than the weight of the mass (10 times less). This is because the areas of the gray circular "lids" on the top of the oil are different by a factor of 10. Now calculate the pressure exerted by the green mass and the pressure exerted by the force arrow. They should be the same. The ratio of the areas is the ratio of the forces required for equilibrium. Enter a new value for the mass (between 100 and 300 kg) and try it.

Now, play the animation. As the arrow moves down, the mass moves up (but the motion is too small to accurately measure how far it moves up). How far up should the mass move and why? The volume of fluid pushed out of the left tube must be the same amount that goes into the right cylinder.

What is the work done by the force arrow? What is the work done on the mass? The work done by the force arrow is exactly the work done on the mass. So what is the advantage of this lift? The advantage is that it allows a small force to raise something much more massive (e.g., lifting up a car in a repair garage). One can think of this as a small force over a large displacement doing the same amount of work as a large force over a small displacement. The force arrow could not directly lift the green mass, but using the hydraulic lift, it can.

In this setup we neglected the change in pressure as a function of depth in the liquid. We assumed the pressure was still the same at the two gray lids on top of the oil at the end of the animation as it was at the beginning of the animation. At the end of the animation, however, the force arrow should actually be larger than that listed because it is some distance below the liquid level of the right side at the end of the animation.

Illustration authored by Anne J. Cox.

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