CHAPTER 3 : FORCE AND PRESSURE Pressure Pressure is defined as force acting perpendicular on a surface area area.. Formula of Pressure
Factors affecting the magnitude of Pressure: 1. Magnitude of the force force:: The larger the force, the higher the pressure. 2. Contact area 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 •
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Foundation of Building Snow Shoes Tyre of Tractor Feet of Elephant
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 = Pressure h = 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/m 3) Answer: Pressure caused by water, P = hρg P = (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. 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 Dam
The wall of the dam is built thicker at the bottom to withstand a higher pressure. The generator generator is 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 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 Atmospheric pressure exerted exerted on the surface surface of any objects 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) - centimet centimetre/milimetre re/milimetre mercury (cmHg/mmHg) - atmosphere (atm) - metre water Notes: - Atmospheric Pressure at Sea Level = 1atm - 1 atm = 76cmHg Atmospheric Pressure and Altitude
Atmospheric Atmosphe ric pressure decreases decreases as as the altitude altitude increases. 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:: 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) = P air + 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 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
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Difference of gas pressure at different level can be ignored.
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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.
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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/m 3] Answer:
i) Gas Pressure, P = Patm + P water 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 can be used used to determine determine density 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/cm 3. Find the density of liquid X. Answer:
Gas Pressure In A Capillary Tube
P gas gas = gas pressure in the capillary tube P atm atm = 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/m 3] Answer:
Gas Pressure, P = Patm + hρg P = 100,000 + (0.005)(13600)(10) P = 100680Pa Bourdon Pressure Gauge
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If pressure is applied, the copper tube will be straightened slightly.
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The copper tube pushes the lever system and hence rotates the pointer.
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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. magnitude . Pascal's Priciple - 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 water. Hydraulic System
F1 = Force exerted on the small piston A1 = area of the small piston F2 = Force exerted on the big piston A2 = area of the big piston
The hydraulic system acts as a force multiplier. In a hydraulic system the large piston has cross-sectional area A 2 = 200 cm2 and the small piston has cross-sectional area A 1 = 5 cm2. If a force of 250 N is applied to the small piston, what is the force F, on 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 c ylinder.
-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 Brake
When the brake pedal is pressed, the piston of the master cylinder applies a pressure on the brake fluid. 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 vehicle to slow down and stop.
Bernoulli's Principle
Bernoulli's principle, physical principle formulated by Daniel Bernoulli that states that
"as the speed of a moving fluid (liquid or gas) increases increases,, the pressure within the fluiddecreases fluid decreases." ." Experiment 1
Water flows from high pressure region to low region.
Pressure at A > Pressure at B > Pressure at C. Experiment 2
Pressure at B becomes lowest because the speed of the water is the highest.
Experiment 3
Pressure at B becomes lowest because the speed of the water is the highest. Bunsen Burner
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When the burner is connected to a gas supply, the gas flows at high
velocity through a narrow passage in the burner, creating a region of low pressure. •
The outside air, which is at atmospheric
pressure, is drawn in and mixes with the gas.
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The mixture of gas and air enables the gas to burn completely to produce
a clean, hot, and smokeless flame Aeroplane
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When a wing in the form of an aerofoil moves in air, the flow of air over
the top travels faster and creates a region of low pressure. The flow of air below the wing is slower resulting in a region of higher pressure. •
The difference between the pressures at the top and underside of the
wing causes a net upward force, called lift, which helps the plane to take-off. Insect Spray
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When the plunger is pushed in, the air flows at a high velocity through a
nozzle.
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The flow of air at high velocity creates a region of low pressure above the
metal tube. The higher pressure of the atmospheric air acts on the surface of the liquid insecticide causing it to rise up the metal tube. •
The insecticide leaves the top of the metal tube through the nozzle as a
fine spray.
