Pressure

Force and area

• The amount of pressure exerted depends on

the size of the force and the area over which it

is exerted.

Exert = to apply a force to an object

• Pressure is measured in newtons per square metre, also known as also known as Pascal.

• One pascal [Pa] is the same as one N/m².

Calculating pressure

Remember that the weight of a body

is equal to the product of its mass

and gravitational acceleration.

W= mg

Applications of increased pressure

• The smaller the area that a given force acts

upon, the greater the pressure that it exerts.

Applications of decreased pressure

• The larger the area that a given force acts

upon, the lower the pressure that it exerts.

• All these objects work by spreading force over

a large area in order to reduce pressure.

Pressure of a liquid

The pressure due to the weight

of a liquid is called

the hydrostatic pressure.the hydrostatic pressure.

• The pressure exerted by a liquid at the bottom

of a cuboid vessel can be calculated in the

same way as the pressure of a cuboid block,

by finding the ratio of the weight of the liquid

to the area of the bottom of the vessel.

• The pressure exerted by a liquid on the

bottom of a container is the product of the

density of the liquid, the gravitational gravitational

accelerationacceleration and the depth of the container.accelerationacceleration and the depth of the container.

Hydrostatic pressure and the density of a liquid

Pressure , depth and density

• For a given liquid, its

pressure:

i. increases with depth

• ii. increases with

density

Pressure of liquids • It is independent of the

- the shape of the container.

- the size of the container.

- the area of its surface

Pressure in liquid depends only

on its vertical distance from

the surface of the liquid.

Applications of pressure in liquids

• Dam holds water at

high altitude. The wall

of the dam has to be

thicker at the base.

Explain.

• The wall of the dam is

built thicker at the

bottom to withstand a

higher pressure.

Explain.

Applications of pressure in liquids

• Water is stored in water

tank at higher level.

Why? • The water tower is

built at high place so

that the water has that the water has

sufficient pressure to

flow to consumer’s

house.

Applications of pressure in liquids

• Submarine is built with

thick wall. Explain.

• Submarine is built with

thick wall so as to

withstand enormous

pressure at greater

depthdepth

Work example 1

Work example 2 Work example 2

Atmospheric Pressure

GAS PRESSURE AND ATMOSPHERIC PRESSURE

GAS PRESSURE AND ATMOSPHERIC PRESSURE

• Gas pressure is the force per unit area

exerted by the gas molecules the gas molecules as they collide

with the walls of their container.

• Atmospheric pressure is the pressure caused • Atmospheric pressure is the pressure caused

by the weight of the air weight of the air above us.

Atmospheric pressure

• Atmospheric pressure decreases with the

altitude or the height above sea level.

• At higher altitudes, the density and the

temperature of the air are lower.

• As a result, the frequency of collisions of the

molecules is lower.

• Hence, atmospheric

pressure is lower

Unit of atmospheric pressure

• The units of atmospheric pressure used in the SPM

syllabus include:

- Pascal (Pa)

- centimetre/milimetre mercury (cmHg/mmHg)

- atmosphere (atm)

- metre water

• Notes:

• - Atmospheric Pressure at Sea Level = 1atm

- 1 atm = 76cmHg

Show existence of atmospheric pressure

• The cardboard does not fall and the

water remains in the glass even

though it’s not supported by

anything.

• Explanation:• Explanation:

The force caused by the

atmospheric pressure acts on the

surface of the cardboard is greater

than the weight of the water in the

glass.

Show existence of atmospheric pressure

• When a can filled with hot

water is closed and is cooled

down rapidly by pouring cold

water on it, it will crash

instantly.instantly.

• Explanation:

When the air inside the can is

cooled, its pressure decreases.

The high atmospheric pressure

outside exerts a great force on

the can and causes it crashes.

Instrument Used to Measure Atmospheric Pressure

-Fortin Barometer

-Anaroid Barometer

-Simple Barometer

Problem solving -> simple barometer Problem solving -> simple barometer

More About Simple BarometerMore About Simple Barometer

The height, h will remains unchanged wheni) the glass tube is lifted up from the dish

ii) the glass tube is lowered further into the dish

iii) the diameter of the glass tube increases

iv) the glass tube is tilted

v) the quantity of mercury in the dish is increasedv) the quantity of mercury in the dish is increased

Spring barometer

Application of atmospheric pressure

• Drinking straw

• Rubber sucker

• Syringe

• Vacuum cleaner• Vacuum cleaner

• Lift pump

Low pressure or high pressure Low pressure or high pressure

• If in some area the pressure is higher than it is

in the surrounding area, we say that it is an

area of high pressure.

Gas pressure

Instruments used to measure gas pressure

- Manometer

- Bourdon Gauge

Using Manometer

Problem solving ManometerProblem solving ����Manometer• Figure above shows the water levels in a water manometer used to measure the

pressure of a gas supply. Find the pressure of the gas in unit of

i) cm water

ii) Pa

[Atmospheric Pressure = 1000cm Water; Density of water = 1000kg/m3]

• Answer:

i)

Gas Pressure,

P = P + PP = Patm + Pwater

P = 1000 + (30-5) = 1025 cm Water

ii)

h = 1025cm = 10.25m

ρ = 1000kgm3

g = 10ms-2

Gas Pressure,

P = hρg

P = (10.25)(1000)(10)

P = 102500 Pa

U-Tube

• A U-tube can be used to determine density

Problem solving U-tube Problem solving� U-tube

• Figure above shows a U-tube filled with 2 liquids X and Y that do not mix.

Given that the density of liquid Y is 1.6g/cm3. Find the density of liquid X.

• Answer:

Gas Pressure In A Capillary TubeGas Pressure In A Capillary Tube

Pgas = gas pressure in the capillary

tube

Patm = atmospheric pressure

h = length of the captured mercury

column

ρ = density of mercury

g = gravitational field strength

Problem solving � Capillary Tube

• Figure above shows a capillary containing a column of

mercury. If the atmospheric pressure is 100,000Pa, find the

pressure of the gas trapped in the capillary tube. [Density of

mercury = 13,600kg/m3]

• Answer:

Gas Pressure,

P = Patm + hρg

P = 100,000 + (0.005)(13600)(10)

P = 100680Pa

Bourdon Pressure Gauge

• If pressure is applied, the

copper tube will be

straightened slightly.

• The copper tube pushes the

lever system and hence

rotates the pointer.

• Gas pressure can be read

directly from the scale.

Pascal's Principle

• Pascal's principle states that any change in

pressure applied to an enclosed liquid will be

transmitted to every point of the fluid

without any change in magnitude.without any change in magnitude.

Pascal's Principle - Prove

• When the plunger is pushed in, the water

squirts equally from all the holes. This shows

that the pressure applied to the plunger has

been transmitted uniformly throughout the been transmitted uniformly throughout the

water.

A simple hydraulic machine

• Hydraulic machines make it possible to transfer

forces through pipes filled with a liquid.

• The hydraulic system acts as a force multiplier

Problem solving � Pascal's Principle

• In a hydraulic system the large piston has cross-

sectional area A2 = 200 cm2 and the small piston has

cross-sectional area A1 = 5 cm2. If a force of 250 N is

applied to the small piston, what is the force F, on

the large piston?the large piston?

• Answer

Hydraulic Jack

• When the handle is pressed down, valve A is closed whereas

valve B is opened. The hydraulic fluid is forced into the large

cylinder and hence pushes the piston moving upward.

• When the handle is raised, valve B will be closed while vale A

will be opened. Hydraulic fluid from the buffer tank will be

suck into the small cylinder.suck into the small cylinder.

• This process is repeated until the

load is sufficiently lifted up.

• The large piston can be lowered

down by releasing the hydraulic

fluid back to the buffer tank through

the release vale.

Hydraulic BrakeHydraulic Brake

• When the brake pedal is pressed, the piston of the master

cylinder applies a pressure on the brake fluid.

• This pressure is transmitted uniformly to each cylinders at the

wheel, cause the pistons at the wheels to push the brake

shoes to press against the surface of the brake.

• The friction between the brakes and brake shoes causes the • The friction between the brakes and brake shoes causes the

vehicle to slow down and stop.

Archimedes' Principle

Archimedes' Principle

• Archimedes Principle states that when a body

is wholly or partially immersed in a fluid it

experiences an upthrust equal to the weight

of the fluid displaced.

The upthrust in water

• The upthrust (i.e. buoyant forcebuoyant force) is an upward

force exerted by a fluid on an object immersed

in it.

Thrust=

The force

due to

fluid

pressure.

Principle of Floatation:

• Displaced volume of fluid = volume of the object that

immerse in the fluid.

• If weight of the object > upthrust, the object will sink • If weight of the object > upthrust, the object will sink

into the fluid.

• If weight of the object = upthrust, the object is in

balance and therefore float on the surface of the

fluid.

Partially Immerse

• Density of Object < Density of water

Upthrust = Weight

• Upthrust, F

= ρ V g= ρliquidVliquidg

• Weight, W

= mg

=ρobjectVobjectg

Fully Immerse

• Density of Object < Density of water

F = Upthrust

T = Tension of the string

W = Weight

• Upthrust, F

F = T + W

• Upthrust, F

= ρliquidVliquidg

• Weight, W

= mg

=ρobjectVobjectg

Fully ImmerseFully Immerse

• Density of Object > Density of water

F = Upthrust

T = Tension of the string

W = Weight

• Upthrust, F

T + F = W

= ρliquidVliquidg

Weight, W

= mg

=ρobjectVobjectg

Problem solving � Archemedes Principle

A block that has volume of 0.2 m3 is hanging in a water tank as shown in

the figure above. Find the tension of the string? [ Density of the metal = 8

× 103 kg m-3, density of water = 1 × 103 kg m-3]

Answer:

Volume of metal block, Vblock = 0.2 m3

Density of metal block, ρblock = 8 × 103 kg m-3Density of metal block, ρblock = 8 × 103 kg m-3

Density of metal block, ρwater = 1 × 103 kg m-3

The system is in equilibrium, hence

Upthrust + Tension = Weight

ρwaterVwaterg + T = ρblockVblockg

T = ρblockVblockg - ρwaterVwaterg

T = (8000)(0.2)(10) - (1000)(0.2)(g)

T = 14000 N

Applications of Archimedes' Principle

• Submarine

• Hot air balloon

• Hydrometer

• Hydrometer is an instrument used to measure • Hydrometer is an instrument used to measure

the relative density of liquids.

• Ship – Plimsoil line