Pressure Pressure is defined as force acting perpendicular on a surface area. Formula of Pressure Factors affecting the magnitude of Pressure: 1. Magnitude of the force: The larger the force, the higher the pressure. 2. Contact area: The larger the contact area, the lower the pressure. 3. S.I. Unit of Pressure: The S.I. unit of pressure is : Pascal Notes: 1Pa = 1 Nm -2 Other units: cmHg, atm Application Involving High Pressure CHAPTER 3 : FORCE AND PRESSURE
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Pressure
Pressure is defined as force acting perpendicular on a surface area.
Formula of Pressure
Factors affecting the magnitude of Pressure:
1. Magnitude of the force:The larger the force, the higher the pressure.
2. Contact area:The larger the contact area, the lower the pressure.
3. S.I. Unit of Pressure: The S.I. unit of pressure is : Pascal
Notes: 1Pa = 1 Nm-2
Other units: cmHg, atm
Application Involving High Pressure
Application Involving Low Pressure
Foundation of Building
Snow Shoes Tyre of Tractor Feet of Elephant
CHAPTER 3 : FORCE AND PRESSURE
Pressure in Liquid
Pressure in liquid is due to the weight of the liquid acting on the surface of any objects in the liquid.
Formula: Pressure Caused by Liquid
P = Pressureh = depth
ρ = density of liquid
Example 1
Figure above shows a fish in a lake. Find the pressure of water exerted on the fish. (Density of water = 1000kg/m3)
Answer:
Pressure caused by water,P = hρgP = (3-1.8)(1000)(10)=12000Pa
Formula: Pressure in Liquid
P = Pressure
Patm = Atmospheric Pressure
h = Depth
ρ = Density of liquid
g = Gravitational Field Strength
Characteristic 1:
The pressure in a liquid increases with depth.
Characteristic 2:
The pressure at any point of a liquid acts equally in all direction.
Characteristic 3:
For a given liquid, the pressure at a point within it varies only with the vertical depth of the point below the surface of the liquid.
Pressure in liquid does not depends on- the shape of the container.- the size of the container.- the area of its surface
Characteristic 4:
Pressure in liquid depends only on its vertical distance from the surface of the liquid.
Pressure at A = Pressure at B
Application of Pressure in Liquid:
1. Construction of Dam
The wall of the dam is built thicker at the bottom to withstand a higher pressure.
The generator is placed at the lower part so that the pressure of the water is high enough to drive the turbine.
2. Public Water Supply System
The water tower is built at high place so that the water has sufficient pressure to
flow to consumer’s house.
What is Atmospheric Pressure?
Atmospheric pressure is the pressure exerted on the surface of any objects by the atmospheric gas.
It is caused by the weight of the atmospheric gas above the earth surface.
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
Atmospheric pressure decreases as the altitude increases.
Conversion of Pa and cmHg
h = height of mercury column
ρ = density of mercury
g = gravitational field strength
Example 1:
Given that the atmospheric pressure at Genting Highland is 72cmHg. Find the equivalent
value of this pressure in the unit of Pascal (Pa). [density of mercury = 13600 kgm-3]
Answer:
h = 72cm = 0.72m
ρ = 13600 kgm-3
g = 10 ms-2
Pressure in the unit of Pascal,
P = hρg
P = (0.72)(13600)(10) = 97920 Pa
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:
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.
Crushing Can
When a can filled with hot water is closed and is cooled down rapidly by pouring cold
water on it, it will crash 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.
Magdeburg Hemisphere
Figure above shows a Magdeburg Hemisphere. When the air inside the hemisphere is
pumped out so that it becomes a vacuum, the hemisphere cannot be separated even by
a very great force.
Explanation:
The atmospheric pressure exerts a strong force on the outer surface of the hemisphere,
holding the hemisphere tightly together.
Instrument Used to Measure Atmospheric Pressure
-Simple Barometer
-Fortin Barometer
-Anaroid Barometer
Simple Barometer
Pa = 0cmHg
Pb = 26cmHg
Pe = 76cmHg
Pf = 84 cmHg
For a given liquid, the pressure will be the same at same level. Therefore,
Pd = Pe = 76cmHg
The difference of gas pressure at different level can be ignored if the difference of the
height is not too large. Therefore,
Pc = Pd = 76cmHg
Example 2
Figure above shows a simple barometer. Find the atmospheric pressure in the unit of
a) cmHg
b) Pa
[Density of mercury = 13,600 kgm-3]
Answer:
a) The atmospheric pressure,
P = 76cmHg
b) The atmospheric pressure,
P = hρg
P = (0.76)(13,600)(10) = 103,360 Pa
Example 3
Figure above shows a column of mercury in a glass tube. Some air is trapped in the
glass tube. If the atmospheric pressure is 76cmHg, what is the pressure of the gas
inside the tube?
Answer:
Patm = Pair + Pmercury
(76) = Pair + 50
Pair= 76 - 50 = 26cmHg
More About Simple Barometer
The height, h will remains unchanged when
i) 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 increased
Rubber Sucker
-When the sucker is pressed into place, the air inside is forced out.
-The sucker is held in position by the high atmospheric pressure on the outside surface.
Syringe
When the piston is pulled up, the atmospheric pressure inside the cylinder will decrease.
The atmospheric pressure outside pushes the liquid up into the syringe.
Straw
-When a person suck through the straw, the pressure in the straw become low.
-The atmospheric pressure outside which is higher will force the water into the straw and
consequently into the mouth.
Vacuum Cleaner
When a vacuum cleaner is switched on, it sucks out the air inside the cleaner, causes
the pressure inside the cleaner become low.
The atmospheric pressure which is higher in magnitude, forces the air and duct particles
into the cleaner.
How gas pressure is produced?
Gas molecules are at constant and random movements.
When the molecules collide with the wall of the container and bounce back, they
experience a change in momentum.
The momentum change exerts a force on the wall.
Force per unit area is the pressure exerted on the wall of the container.
instruments used to measure gas pressure
-Manometer
- Bourdon Gauge
Using Manometer
Difference of gas pressure at different level can be ignored.
Pessure on the surface of a liquid is equal to the pressure of the gas in contact.
For a given liquid (same liquid), the pressure at any point of the same level is the
same.
For different liquid with different density, pressure will be different at the same
level.
Pgas = Patm + Pliquid
Pgas = Patm + hρg
Pgas = Gas Pressure
Patm = Atmospheric Pressure
g = Gravitational Field Strength
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 = 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
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 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
Example 3
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]