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  • Define pressure.
  • Explain the relationship between pressure and force.
  • Calculate force given pressure and area.

You have no doubt heard the word pressure    being used in relation to blood (high or low blood pressure) and in relation to the weather (high- and low-pressure weather systems). These are only two of many examples of pressures in fluids. Pressure P size 12{P} {} is defined as

P = F A size 12{P= { {F} over {A} } } {}

where F size 12{P} {} is a force applied to an area A size 12{P} {} that is perpendicular to the force.

Pressure

Pressure is defined as the force divided by the area perpendicular to the force over which the force is applied, or

P = F A . size 12{P= { {F} over {A} } } {}

A given force can have a significantly different effect depending on the area over which the force is exerted, as shown in [link] . The SI unit for pressure is the pascal , where

1 Pa = 1 N/m 2 . size 12{1`"Pa"=1`"Nm" rSup { size 8{2} } } {}

In addition to the pascal, there are many other units for pressure that are in common use. In meteorology, atmospheric pressure is often described in units of millibar (mb), where

100 mb = 1 × 10 5 Pa  . size 12{"100"`"mb"=1 times "10" rSup { size 8{5} } `"Pa"} {}

Pounds per square inch lb/in 2 or psi size 12{ left ("lb/in" rSup { size 8{2} } `"or"``"psi" right )} {} is still sometimes used as a measure of tire pressure, and millimeters of mercury (mm Hg) is still often used in the measurement of blood pressure. Pressure is defined for all states of matter but is particularly important when discussing fluids.

In figure a, the person is poked with a finger exerting a small pressure due to the large area of contact and, in b, he is poked with a syringe exerting a large pressure due to the small area of contact.
(a) While the person being poked with the finger might be irritated, the force has little lasting effect. (b) In contrast, the same force applied to an area the size of the sharp end of a needle is great enough to break the skin.

Calculating force exerted by the air: what force does a pressure exert?

An astronaut is working outside the International Space Station where the atmospheric pressure is essentially zero. The pressure gauge on her air tank reads 6 . 90 × 10 6 Pa size 12{6 "." "90" times "10" rSup { size 8{6} } `"Pa"} {} . What force does the air inside the tank exert on the flat end of the cylindrical tank, a disk 0.150 m in diameter?

Strategy

We can find the force exerted from the definition of pressure given in P = F A size 12{P= { {F} over {A} } } {} , provided we can find the area A size 12{A} {} acted upon.

Solution

By rearranging the definition of pressure to solve for force, we see that

F = PA . size 12{F= ital "PA"} {}

Here, the pressure P size 12{P} {} is given, as is the area of the end of the cylinder A size 12{A} {} , given by A = πr 2 size 12{A=πr rSup { size 8{2} } } {} . Thus,

F = 6.90 × 10 6 N/m 2 3.14 0.0750 m 2 = 1.22 × 10 5 N. alignl { stack { size 12{F= left (6 "." "90" times "10" rSup { size 8{6} } `"N/m" rSup { size 8{2} } right ) left (3 "." "14" right ) left (0 "." "0750"`m right ) rSup { size 8{2} } } {} #=1 "." "22" times "10" rSup { size 8{5} } `N "." {} } } {}

Discussion

Wow! No wonder the tank must be strong. Since we found F = PA size 12{F= ital "PA"} {} , we see that the force exerted by a pressure is directly proportional to the area acted upon as well as the pressure itself.

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The force exerted on the end of the tank is perpendicular to its inside surface. This direction is because the force is exerted by a static or stationary fluid. We have already seen that fluids cannot withstand shearing (sideways) forces; they cannot exert shearing forces, either. Fluid pressure has no direction, being a scalar quantity. The forces due to pressure have well-defined directions: they are always exerted perpendicular to any surface. (See the tire in [link] , for example.) Finally, note that pressure is exerted on all surfaces. Swimmers, as well as the tire, feel pressure on all sides. (See [link] .)

The forces inside a tire are shown by arrow lines. An inset shows an enlarged view of the valve in the tire. Air pressure in the tire keeps the valve closed.
Pressure inside this tire exerts forces perpendicular to all surfaces it contacts. The arrows give representative directions and magnitudes of the forces exerted at various points. Note that static fluids do not exert shearing forces.
A man swimming underwater has many arrows pointing toward him to represent the directions and magnitudes of the forces exerted on him at various points.
Pressure is exerted on all sides of this swimmer, since the water would flow into the space he occupies if he were not there. The arrows represent the directions and magnitudes of the forces exerted at various points on the swimmer. Note that the forces are larger underneath, due to greater depth, giving a net upward or buoyant force that is balanced by the weight of the swimmer.

Phet explorations: gas properties

Pump gas molecules to a box and see what happens as you change the volume, add or remove heat, change gravity, and more. Measure the temperature and pressure, and discover how the properties of the gas vary in relation to each other.

Gas Properties

Section summary

  • Pressure is the force per unit perpendicular area over which the force is applied. In equation form, pressure is defined as
    P = F A . size 12{P= { {F} over {A} } "." } {}
  • The SI unit of pressure is pascal and 1 Pa = 1 N/m 2 size 12{1`"Pa"=1`"N/m" rSup { size 8{2} } } {} .

Conceptual questions

How is pressure related to the sharpness of a knife and its ability to cut?

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Why does a dull hypodermic needle hurt more than a sharp one?

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The outward force on one end of an air tank was calculated in [link] . How is this force balanced? (The tank does not accelerate, so the force must be balanced.)

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Why is force exerted by static fluids always perpendicular to a surface?

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In a remote location near the North Pole, an iceberg floats in a lake. Next to the lake (assume it is not frozen) sits a comparably sized glacier sitting on land. If both chunks of ice should melt due to rising global temperatures (and the melted ice all goes into the lake), which ice chunk would give the greatest increase in the level of the lake water, if any?

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How do jogging on soft ground and wearing padded shoes reduce the pressures to which the feet and legs are subjected?

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Toe dancing (as in ballet) is much harder on toes than normal dancing or walking. Explain in terms of pressure.

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How do you convert pressure units like millimeters of mercury, centimeters of water, and inches of mercury into units like newtons per meter squared without resorting to a table of pressure conversion factors?

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Problems&Exercises

As a woman walks, her entire weight is momentarily placed on one heel of her high-heeled shoes. Calculate the pressure exerted on the floor by the heel if it has an area of 1 . 50 cm 2 size 12{1 "." "50"`"cm" rSup { size 8{2} } } {} and the woman’s mass is 55.0 kg. Express the pressure in Pa. (In the early days of commercial flight, women were not allowed to wear high-heeled shoes because aircraft floors were too thin to withstand such large pressures.)

3.59 × 10 6 Pa ; or 521 lb/in 2 size 12{"521"`"lb/in" rSup { size 8{2} } } {}

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The pressure exerted by a phonograph needle on a record is surprisingly large. If the equivalent of 1.00 g is supported by a needle, the tip of which is a circle 0.200 mm in radius, what pressure is exerted on the record in N/m 2 size 12{"N/m" rSup { size 8{2} } } {} ?

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Nail tips exert tremendous pressures when they are hit by hammers because they exert a large force over a small area. What force must be exerted on a nail with a circular tip of 1.00 mm diameter to create a pressure of 3 . 00 × 10 9 N/m 2 ? (This high pressure is possible because the hammer striking the nail is brought to rest in such a short distance.)

2.36 × 10 3 N size 12{2 "." "36" times "10" rSup { size 8{3} } `N} {}

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Questions & Answers

find the density of a fluid in which a hydrometer having a density of 0.750g/mL floats with 92.0% of its volume submerged.
Neshrin Reply
Uniform speed
Sunday
(a)calculate the buoyant force on a 2.00-L Helium balloon.(b) given the mass of the rubber in the balloon is 1.50g. what is the vertical force on the balloon if it is let go? you can neglect the volume of the rubber.
Neshrin Reply
To Long
Usman
pleaseee. can you get the answer? I can wait till 12
Neshrin
a thick glass cup cracks when hot liquid is poured into it suddenly
Aiyelabegan Reply
because of the sudden contraction that takes place.
Eklu
railway crack has gap between the end of each length because?
Aiyelabegan Reply
For expansion
Eklu
yes
Aiyelabegan
Please i really find it dificult solving equations on physic, can anyone help me out?
Big Reply
sure
Carlee
what is the equation?
Carlee
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Precious
fersnels biprism spectrometer how to determined
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how to study the hall effect to calculate the hall effect coefficient of the given semiconductor have to calculate the carrier density by carrier mobility.
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Michelson Morley experiment
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Calculate the final velocity attained, when a ball is given a velocity of 2.5m/s, acceleration of 0.67m/s² and reaches its point in 10s. Good luck!!!
Eklu Reply
2.68m/s
Doc
vf=vi+at vf=2.5+ 0.67*10 vf= 2.5 + 6.7 vf = 9.2
babar
s = vi t +1/2at sq s=58.5 s=v av X t vf= 9.2
babar
how 2.68
babar
v=u+at where v=final velocity u=initial velocity a=acceleration t=time
Eklu
the answer is 9.2m/s
OBERT
express your height in Cm
Emmanuel Reply
my project is Sol gel process how to prepare this process pls tell me
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the dimension of work and energy is ML2T2 find the unit of work and energy hence drive for work?
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KgM2S2
Acquah
Two bodies P and Quarter each of mass 1000g. Moved in the same direction with speed of 10m/s and 20m/s respectively. Calculate the impulse of P and Q obeying newton's 3rd law of motion
Shimolla Reply
kk
Doc
the answer is 0.03n according to the 3rd law of motion if the are in same direction meaning they interact each other.
OBERT
definition for wave?
Doc Reply
A disturbance that travel from one medium to another and without causing permanent change to its displacement
Fagbenro
In physics, a wave is a disturbance that transfers energy through matter or space, with little or no associated mass transport (Mass transfer). ... There are two main types ofwaves: mechanical and electromagnetic. Mechanicalwaves propagate through a physical matter, whose substance is being deformed
Devansh
K
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AMADI
Note: LINEAR MOMENTUM Linear momentum is defined as the product of a system’s mass multiplied by its velocity: size 12{p=mv} {}
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Study of matter and energy
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physics is the science of matter and energy and their interactions
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Practice Key Terms 1

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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