Two objects sliding past each other experience friction forces. For example, a box sliding down a slope. An object moving through the air experiences air resistance. For example, a skydiver falling through the air. When a contact force acts between two objects, both objects experience the same size force, but in opposite directions. Thus for any region within a fluid, in order to achieve static equilibrium, the pressure from the fluid below the region must be greater than the pressure from the fluid above by the weight of the region.
This force which counteracts the weight of a region or object within a static fluid is called the buoyant force or buoyancy. Static Equilibrium of a Region Within a Fluid : This figure shows the equations for static equilibrium of a region within a fluid. Region Within a Static Fluid : This figure is a free body diagram of a region within a static fluid.
In the case on an object at stationary equilibrium within a static fluid, the sum of the forces acting on that object must be zero. As previously discussed, there are two downward acting forces, one being the weight of the object and the other being the force exerted by the pressure from the fluid above the object.
At the same time, there is an upwards force exerted by the pressure from the fluid below the object, which includes the buoyant force. The appearance of a buoyant force in static fluids is due to the fact that pressure within the fluid changes as depth changes. The analysis presented above can furthermore be extended to much more complicated systems involving complex objects and diverse materials.
By exploiting the fact that pressure is transmitted undiminished in an enclosed static liquid, such as in this type of system, static liquids can be used to transform small amounts of force into large amounts of force for many applications such as hydraulic presses.
The cross-sectional area of the bottle changes with height so that at the bottom of the bottle the cross-sectional area is cm 2. Furthermore, the hydrostatic pressure due to the difference in height of the liquid is given by Equation 1 and yields the total pressure at the bottom surface of the bottle. Since the cross-sectional area at the bottom of the bottle is times larger than at the top, the force contributing to the pressure at the bottom of the bottle is N plus the force from the weight of the static fluid in the bottle.
Taking advantage of this phenomenon, hydraulic presses are able to exert a large amount of force requiring a much smaller amount of input force.
Depending on the applied pressure and geometry of the hydraulic press, the magnitude of F 2 can be changed. The difference in height of the fluid between the input and the output ends contributes to the total force exerted by the fluid. For a hydraulic press, the force multiplication factor is the ratio of the output to the input contact areas. Pressure is often measured as gauge pressure, which is defined as the absolute pressure minus the atmospheric pressure.
An important distinction must be made as to the type of pressure quantity being used when dealing with pressure measurements and calculations. Atmospheric pressure is the magnitude of pressure in a system due to the atmosphere, such as the pressure exerted by air molecules a static fluid on the surface of the earth at a given elevation.
In most measurements and calculations, the atmospheric pressure is considered to be constant at 1 atm or , Pa, which is the atmospheric pressure under standard conditions at sea level. Atmospheric pressure is due to the force of the molecules in the atmosphere and is a case of hydrostatic pressure. Depending on the altitude relative to sea level, the actual atmospheric pressure will be less at higher altitudes and more at lower altitudes as the weight of air molecules in the immediate atmosphere changes, thus changing the effective atmospheric pressure.
Atmospheric pressure is a measure of absolute pressure and can be affected by the temperature and air composition of the atmosphere but can generally be accurately approximated to be around standard atmospheric pressure of , Pa.
In this equation p 0 is the pressure at sea level , Pa , g is the acceleration due to gravity, M is the mass of a single molecule of air, R is the universal gas constant, T 0 is the standard temperature at sea level, and h is the height relative to sea level.
Pressure and Height : Atmospheric pressure depends on altitude or height. For most applications, particularly those involving pressure measurements, it is more practical to use gauge pressure than absolute pressure as a unit of measurement. Gauge pressure is a relative pressure measurement which measures pressure relative to atmospheric pressure and is defined as the absolute pressure minus the atmospheric pressure. Most pressure measuring equipment give the pressure of a system in terms of gauge pressure as opposed to absolute pressure.
For example, tire pressure and blood pressure are gauge pressures by convention, while atmospheric pressures, deep vacuum pressures, and altimeter pressures must be absolute. For most working fluids where a fluid exists in a closed system, gauge pressure measurement prevails. Pressure instruments connected to the system will indicate pressures relative to the current atmospheric pressure.
The situation changes when extreme vacuum pressures are measured; absolute pressures are typically used instead. To find the absolute pressure of a system, the atmospheric pressure must then be added to the gauge pressure. While gauge pressure is very useful in practical pressure measurements, most calculations involving pressure, such as the ideal gas law, require pressure values in terms of absolute pressures and thus require gauge pressures to be converted to absolute pressures.
Barometers are devices used for measuring atmospheric and gauge pressure indirectly through the use of hydrostatic fluids. In practice, pressure is most often measured in terms of gauge pressure.
Gauge pressure is the pressure of a system above atmospheric pressure. Since atmospheric pressure is mostly constant with little variation near sea level, where most practical pressure measurements are taken, it is assumed to be approximately , Pa. Modern pressure measuring devices sometimes have incorporated mechanisms to account for changes in atmospheric pressure due to elevation changes.
Gauge pressure is much more convenient than absolute pressure for practical measurements and is widely used as an established measure of pressure.
However, it is important to determine whether it is necessary to use absolute gauge plus atmospheric pressure for calculations, as is often the case for most calculations, such as those involving the ideal gas law. Pressure measurements have been accurately taken since the mids with the invention of the traditional barometer. Barometers are devices used to measure pressure and were initially used to measure atmospheric pressure.
Early barometers were used to measure atmospheric pressure through the use of hydrostatic fluids. Hydrostatic based barometers consist of columnar devices usually made from glass and filled with a static liquid of consistent density.
The columnar section is sealed, holds a vacuum, and is partially filled with the liquid while the base section is open to the atmosphere and makes an interface with the surrounding environment.
As the atmospheric pressure changes, the pressure exerted by the atmosphere on the fluid reservoir exposed to the atmosphere at the base changes, increasing as the atmospheric pressure increases and decreasing as the atmospheric pressure decreases. This change in pressure causes the height of the fluid in the columnar structure to change, increasing in height as the atmosphere exerts greater pressure on the liquid in the reservoir base and decreasing as the atmosphere exerts lower pressure on the liquid in the reservoir base.
The height of the liquid within the glass column then gives a measure of the atmospheric pressure. Pressure, as determined by hydrostatic barometers, is often measured by determining the height of the liquid in the barometer column, thus the torr as a unit of pressure, but can be used to determine pressure in SI units. Hydrostatic based barometers most commonly use water or mercury as the static liquid. While the use of water is much less hazardous than mercury, mercury is often a better choice for fabricating accurate hydrostatic barometers.
The density of mercury is much higher than that of water, thus allowing for higher accuracy of measurements and the ability to fabricate more compact hydrostatic barometers.
In theory, a hydrostatic barometer can be placed in a closed system to measure the absolute pressure and the gauge pressure of the system by subtracting the atmospheric pressure. Another type of barometer is the aneroid barometer, which consists of a small, flexible sealed metal box called an aneroid cell. The aneroid cell is made from beryllium-copper alloy and is partially evacuated.
A stiff spring prevents the aneroid cell from collapsing. Small changes in external air pressure cause the cell to expand or contract. This expansion and contraction is amplified by mechanical mechanisms to give a pressure reading. Such pressure measuring devices are more practical than hydrostatic barometers for measuring system pressures. Many modern pressure measuring devices are pre-engineered to output gauge pressure measurements. While the aneroid barometer is the underlying mechanism behind many modern pressure measuring devices, pressure can also be measured using more advanced measuring mechanisms.
Hydrostatic Column Barometer : The concept of determining pressure using the fluid height in a hydrostatic column barometer. Variation of Pressure with Height : The density of the liquid is p, g is the acceleration due to gravity, and h is the height of the fluid in the barometer column. Pressure plays an essential role in a number of critical bodily functions including respiration and blood circulation. Yes, I am simplifying this a bit.
However, the point is that contact area does indeed matter. I am talking about contact area, not surface area. Suppose you put a rubber ball on a glass plate. As you push down on the rubber ball, it will deform such that more of the ball will come in "contact" with the glass. Here is a diagram of this. Greater contact area means greater frictional force. If the contact area is proportional to the normal force, then this looks just like Amontons' Law with the frictional force proportional to the normal force.
Of course this model "breaks" when the contact area can no longer increase. As I add more and more mass onto the friction box, there is less and less available contact area to expand into. In a sense, the contact area becomes saturated. I suppose that if I kept piling on the weight, the friction force would eventually level out and stop increasing.
This really isn't a big deal. The Amontons' Law isn't a law at all ok - it depends on your definition of Law. It's just a model. Let me give an example. Gravitational Model. Near the surface of the Earth, we can calculate the gravitational force on an object using the following model.
The g vector is the local gravitational field. On Earth, it points "down" and has a magnitude around 9. We often call this gravitational force the weight and it's a very useful model.
Even though this model is useful, we still know it's wrong. The above gravitational model says that it doesn't matter how high above the surface of the Earth you are, the weight is the same. Of course that's not true, but it's approximately true when close to the surface.
This says that the gravitational force decreases as the two interacting objects get further away from each other. If you put in the mass of the Earth and the radius of the Earth you get a weight that looks just like the mg version. So, at some point the two versions of gravity agree. The same is true for friction.
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