P = pressure, Pascal (Pa) F = forces, N A = area, m 2 ( Unit: N m -2 ) State relationship between pressure and area.
Pressure depends on 2 factors:
a) forces acting
b) area of surface
Pressure increases as surface area decreases.
APPLICATION INVOLVING HIGH PRESSURE A sharp knife has a very small surface area on its cutting edge so that high pressure can be exerted to cut the meat. Nails, needles and pins have very sharp ends with very small surface areas . When a force is applied to the head of a nail, the pressure will drive its sharp end into a piece of wood easily. The studs on a football boot have only a small area of contact with the ground . The pressure under the studs is high enough for them to sink into the ground , which gives extra grip.
APPLICATION INVOLVING LOW PRESSURE Skis have a large area to reduce the pressure on the snow so that they do not sink in too far. A tractor moving on soft ground has wide tires to reduce the pressure on the ground so that they will not sink into the ground. A wide shoulder pad of a heavy bag will reduce the pressure exerted on the shoulder of the person carrying the bag.
A pressure of 2000 Pa is applied on a floor with an area of 0.2 m 2 . What is the forced produced?
A butcher uses a knife with the surface area of 0.2 m 2 to cut a piece of meat. If the butcher uses 20 N to cut the meat, what is the pressure produced?
MASTERY PRACTICE 3.1 (page 81)
UNDERSTANDING PRESSURE IN LIQUID
A liquid in a container exerts pressure because of its weight .
For example, if you try to put your finger over the end of a tap when it is turned on, you can feel the pressure of the water in the pipe.
What is pressure in liquid? P = pressure, Nm -2 / Pa h = depth, metre (m) = density, kgm -3 g = gravitational field strength, Nkg -1 Formula pressure in liquid
The pressure in a liquid is directly proportional to the depth .
The pressure in a liquid increases with depth.
Pressure in liquid doesn’t depends on shape or size of container.
Relate depth to pressure in a liquid .
Liquid in container has weight.
The weight exerts a pressure on liquid below it.
The pressure at any point in liquid acts in all direction and will increase with depth .
Relate density to pressure in a liquid
A liquid with higher density exerts a higher pressure.
This is because a liquid with higher density has a larger weight .
The pressure in a liquid is directly proportional to the density of the liquid.
900 kg/m 3 1000 kg/m 3
The pressure of sea water at the bottom of an ocean is 1.7 × 10 8 Nm -2 . What is the depth of the ocean? [ Density of sea water = 1.02 × 10 3 kgm -3 ]
The surface area of submarine is 200 m 2 .
a) at what depth below the sea level will the water pressure of 6.18 × 10 5 Pa exerted on the submarine.
b) calculate the force which acts on the submarine at the depth.
[ Density of sea water= 1030kgm -3 ; g = 10 Nkg -1 ]
Characteristics of Pressure in Liquid
Pressure increase with depth .
Pressure acts in all direction .
Pressure at 2 points at the same level in same liquid are equal .
Pressure doesn’t depends on area of surface.
Pressure doesn’t depends on the shape or size of container.
The wall of a dam is much thicker at the bottom than at the top.
Because it must withstand the increased lateral pressure in depths of the water.
The higher the depth , the higher the pressure exerted, thus the much thicker the wall of the dam at bottom .
Application of pressure in liquid a) Construction of dam
The deeper the submarine submerge into the water, the greater the pressure exerted.
Submarine is built with thick wall so as to withstand enormous pressure at greater depth.
Application of pressure in liquid b) Thick wall built in submarine
The bottle is hung at a higher position to increase the pressure of liquid.
So it has sufficient pressure to flow into the veins of the patient.
Application of pressure in liquid c) Blood transfusion
UNDERSTANDING GAS PRESSURE AND ATMOSPHERIC PRESSURE
UNDERSTANDING GAS PRESSURE AND ATMOSPHERIC PRESSURE
Air inside the balloons are in random motion which collide all over inner surface of ball.
Forces of collision pushes the wall of the balloons outwards results in air pressure in the balloons.
What you feel when you squeezed a balloon filled with air?
Gas pressure is the force per unit area exerted by the gas molecules as they collide with the walls of their container .
a) Gas Pressure Wall of container
Gas molecules are always colliding with the wall of container and produced force.
The force will acts on an area of the wall of container and produced pressure .
b) Atmospheric Pressure
Atmosphere is a thick layer of air surrounds the Earth.
The air has mass and weight.
The weight of atmosphere acts on surface of objects and atmospheric pressure is produced .
Characteristics of Atmospheric Pressure
1. Varies with the height of the object above sea level .
At higher altitude, the temperature and density of air are lower .
As a result, the frequency of collision of molecules is lower .
Thus, atmospheric pressure is lower .
2. Atmospheric pressure acts in all direction .
At sea level , the atmospheric pressure is about 100 000 Pa (1×10 5 Pa) 1 atmosphere (1 atm) = 10 5 Pa / 10 5 Nm -2 At 5600 m above sea level, the atmospheric pressure is about 50 000 Pa (5×10 4 Pa) The pressure in the space around satellite is almost zero . An aircraft travelling at an altitude of 11000 m will experience an atmospheric pressure of 25 000 Pa (2.5×10 4 Pa) Atmospheric pressure varies with height
Activities to show existence of atmospheric pressure
The water remains in the glass.
This is due to the atmospheric pressure acts on the cardboard pushing it up.
Application of atmospheric pressure
a) Drinking straw
When sucked, air inside straw is removed , leaving a low pressure area .
The higher atmospheric pressure acts on the surface of water and pushed drinks into the straw.
b) Sucker hook
When the sucker hook is press, the air inside is forced out and leaving a low pressure area .
The higher external atmospheric pressure outside pressed down on the hook and makes its stick firmly to the wall.
1) The fan sucks out the air when it is switched on. 2) Space in x become partially vacuum. 3) The higher atmospheric pressure forces the air and dust particles into the dust bag 4) Dust particles are trapped but the air still can flow through the exit. x c) Vacuum cleaner
Instrument for measuring Gas Pressure a) Bourdon Gauge
Instrument for measuring Atmospheric Pressure a) Aneroid barometer
The Aneroid barometer can be used as an altimeter by mountaineers or in an aeroplane to determine its altitude.
b) Fortin barometer
Operation based on mercury barometer.
Measures atmospheric pressure in mm Hg.
c) Mercury barometer
Mercury barometer contains mercury enclosed in a tube.
Glass tube that has been filled with mercury then inverted into a bowl of mercury.
At sea level or 1 atmospheric pressure, mercury level is at 76 cm Hg or 760 mm Hg.
The level does not drop further because the mercury column is held up by atmospheric pressure .
Atmospheric pressure and its units a) At a sea level, the atmospheric pressure : 1 atm = 760 mm Hg = 76 cm Hg = 0.76 m Hg b) Atmospheric pressure in unit Nm -2 or Pa : = h g =0.76 × 13600 × 9.8 =10 5 Nm -2 / 10 5 Pa
h = height of mercury column
= density of mercury (13600 kgm -3 )
g = gravitational field strength, Nkg -1
c) Atmospheric pressure in unit metre water: P atm = 10 m water
Archimedes’ Principle Archimedes’ Principle state that “ When an object is wholly or partially immersed in a fluid, the buoyant force is equal to the weight of fluid displaced by the object.
When in fluid, the object experiences two forces : (a)The actual weight which acts downwards (b) The buoyant force which acts upwards .
F b = weight of fluid displaced
= mg ; from ( =m/V)
F b = V g
Fb = buoyant force
= density of fluid displaced
V = Volume of fluid displaced = Volume of part immersed
V F b
Apparent weight, W 2 Actual weight, W 1 0.40 N 0.67 N Buoyant force, F b //Upthrust = Actual weight, W 1 – Apparent weight, W 2 = Weight of water displaced
F b > W : Object will rise up in fluid.
F b < W : Object will sink in fluid.
F b = W : Object will float
If the object is floating :
Fb = Weight of fluid displaced = Weight of the object
If the object is submerged :
Volume of liquid displaced = Volume of object
Examples 35 N 35 N 3.5×10 -3 m 3 3.5×10 -3 m 3
1200 kgm -3
A submarine has a large ballast tank , which is used to control its position and depth from the surface of the sea.
When the ballast tanks are filled with water , the buoyant force is smaller than the weight of the submarine . The submarine sinks .
Application of Archimedes’ Principle a) Submarine How does a submarine sink? How does a submarine rises?
When the ballast tanks are filled with air (removed all water) , the buoyant force is larger than the weight of the submarine . The submarine rises .
Ship made by a steel do not sink in water because:
- contains air space which is hollow inside thus increase the volume of ship and lower its density .
Upthrust is great enough to support the weight of ship.
However ship may sink too deep into water if it is overload and enter a low density water .
Ship submerge deeper in fresh water because of fresh water has low density .
Hence Plimsoll line is painted on ship to show the depth of ship should travel and to ensure the maximum weight limit .
b) Ship (Plimsoll line)
Air in the balloon is heated up to over 100 o C. The gas used is Helium gas.
Hot air has a lower density than surrounding air resulting in a bigger upthrust that cause the balloon to rise .
Its means the buoyant force is larger than the total weight of the balloon .
When the height increase, density of air decreases. Thus, Fb will decrease and the balloon descent when Fb less than weight of the balloon.
When the total weight of balloon is equal to the buoyant force , its remains floating in air .
c) Hot-air balloon
A hydrometer is an instrument used to measure the relative density of liquids such as milk or acid in accumulators.
It consists of a tube with a bulb at one end. Lead shots are placed in the bulb to weigh it down and enable the hydrometer floats vertically in the liquid.
In a liquid of lesser density , a larger volume of liquid must be displaced for the buoyant force to equal the weight. So the more the hydrometer is submerged .
The hydrometer floats higher in a liquid of higher density .
Small reading Large reading
Pascal’s principle states that pressure applied to an enclosed liquid is transmitted equally to every part of the liquid.
What will happen when you squeezed the toothpaste?
So if the liquid is trapped in a container and pressure is applied, this pressure will be transmitted equally in all direction.
According to Pascal principle, all the water that moves out from the holes received the same pressure.
Pascal principle is widely used in a hydraulic system. Hydraulic system Output force = output piston area Input force input piston area F 2 = A 2 F 1 A 1
A 1 d 1 = A 2 d 2
Hydraulic systems acts as a force multiplier . They multiply the input force by a certain factor to gain a larger output force.
A small input force, F 1 is applied to the small piston resulting in a large output force, F 2 .
What will happen to the hydraulic system if the air bubbles exist in the brake fluid?
A hydraulic system must not contain any air bubbles in any position of its hydraulic fluid system.
This will reduce the efficiency of the system as part of the applied force will be used up to compress the air bubbles .
Why oil is prefer to be used in hydraulic system?
Because oil helps to reduce friction and prevent rusting.
Applications of Pascal’s Principle in Everyday Life a) Hydraulic jack
Used to lift and carry heavy loads.
When a small input force is applied, a large output force is produced.
b) Hydraulic brake
C ar brake use liquid pressure to transmit the pressure applied at the brake pedal to the brakes of other wheels simultaneously.
c) Hydraulic pump
Bernoulli’s Principle Bernoulli’s principle states that when the speed of a fluid increases the pressure is decreases and vice versa .
If the fluid is at rest, the pressure is the same at all level.
The pressure in a moving fluid depends on the velocity .
The paper is moves up when air is blown up in the surface.
This because air moved at high velocity.
Thus create a low pressure region at the surface of paper.
Higher atmospheric pressure acts at the bottom pushes up the paper.
When air is blown through the straw between the 2 ping pong balls, it will move close to each other.
This because air moved at high velocity between the balls and create a low pressure region .
Thus the higher atmospheric pressure caused the ping pong balls closer to each other.
V , P V , P Patm Patm
When the air blow harder, ball is not falling down.
It is because the air moved at a very high velocity between the balls and the wall of the filter funnel. And create a low pressure region .
The bottom of the ball has higher atmospheric pressure which can hold the ball from falling .
Applications of Bernoulli’s Principle
Carburettor is a device to controls the speed of car engine .
It works by controlling the quantity of petrol and air that enters the engine.
Air is allowed to flow through carburetor when the choke is open and flow through the narrow section .
The narrow passage increase the velocity of the air stream and cause the pressure to drop .
As a result, the petrol which at higher pressure is forced out of a jet in a fine spray to form a combustion mixture with the air.
Mixture of air and petrol is then drawn into the engine cylinder to be burned.
When the piston is pushed in, air is forced out through the jet at high speed .
Thus create a low pressure region.
The higher atmospheric pressure acts on the surface of the liquid insecticide causing it to rise up the narrow metallic tube.
The insecticide leaves the top of narrow tube through the nozzle as a fine spray .
Bernoulli’s principle applied to fluid flow in tubes
Fluid flow from high pressure region to low pressure region.
When fluid flow through a narrow section , the velocity increase thus create a low pressure region .
When a wing in the form of aerofoil moves through the air, the air at the top has to travel faster to cover a long distance and thus create a low pressure region .
The flow of air below the wing is lower resulting in a higher pressure region .
The pressure difference between the top and below the wing cause a net upward forced called lift .