• haruspex
In summary, the PF Insights post "Frequently Made Errors in Mechanics - Hydrostatics" discusses some common errors that occur in applying mechanics principles to hydrostatics. The post covers a specific question about the force on a block at the instant before it moves upward, explaining how different levels of detail can lead to different answers. It also mentions the effects of applying an upward force on a rope and taking up slack slowly.
haruspex
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haruspex submitted a new PF Insights post

Frequently Made Errors in Mechanics - Hydrostatics

Continue reading the Original PF Insights Post.

Last edited:
wrobel and Greg Bernhardt
@haruspex is really on a roll with these tutorials. Soon I will be linking them all together.

Qestion 2 is interesting as an example of how one could go into more and more detail into the phenomenon and get different answers for each "level" of detail. This is particularly true here because we ask about the force at the very instant when the block is about to move upward. In practice, there would be no "instant" but there would be a transient process where the force would vary in interesting ways before settling down into ##W-\rhoVg##

If we apply an increasing upward force on the rope, a moment would come when water would try to rush into the gap between the block and the floor. You could think of it as a transient partial vacuum under the block, or as a bernoulli pressure drop that results in a net downward component.

If the slack on the rope is taken up infinitely slowly, then the bernoulli / vacuum effect would always be negligible and the tension would climb smoothly from zero to the archimedes value.

## What is hydrostatics?

Hydrostatics is a branch of mechanics that deals with the study of fluids at rest, specifically in relation to their pressure, density, and buoyancy.

## What are some common errors made in hydrostatics?

Some common errors made in hydrostatics include confusing pressure with force, neglecting atmospheric pressure, and not considering the effects of surface tension.

## How does surface tension affect hydrostatics?

Surface tension is a property of liquids that causes them to have an elastic-like surface. In hydrostatics, surface tension can affect the pressure and buoyancy of a fluid, leading to errors if not taken into account.

## Why is it important to understand hydrostatics?

Understanding hydrostatics is important in many practical applications, such as designing ships and submarines, calculating water pressure in dams and pipes, and predicting weather patterns.

## What are some ways to avoid errors in hydrostatics?

To avoid errors in hydrostatics, it is important to have a clear understanding of the concepts involved and to double-check calculations. It is also helpful to consider real-world factors, such as atmospheric pressure and surface tension, and to use appropriate units and equations.

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