chapter 3 forces and pressure 2011

7/30/2019 CHAPTER 3 Forces and Pressure 2011

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Hoo Sze Yen www.physicsrox.com Physics SPM 2011

Chapter 3: Forces and Pressure of 8

CHAPTER 3:

FORCES AND PRESSURE

3.1 Pressure

Pressure is the force

which acts normal per

unit area of contact.

A

F P =

where P = pressure [Pa]

F = force [N]

A = area [m2]

3.2 Pressure in Liquids

Pressure in liquids are not dependent on the size or shape of the container; only on its depth.

ghP ρ =

where P = pressure [Pa]

h = height of liquid [m]

ρ = density of liquid [kg m-3

]

g = gravitational acceleration [m s-2

]

3.3 Atmospheric and Gas Pressure

3.3.1 Atmospheric Pressure

• Atmospheric pressure is measured by barometers.

Mercury barometer Aneroid barometer

Units of pressure

Unit Note

Pa SI unit

N m-2

Equivalent to Pa

N cm-2

cm Hg

m water

atm 1 atm = atmospheric pressure at sea level

bar 1 bar = 1 atm

For

atmospheric

pressure

only





Atmospheric pressure measured by a simple mercury barometer can be calculated using the

formula P=h ρg.

Standard atmospheric pressure at sea level is usually 76 cm Hg or 10 m water. It can also be

expressed as 1 bar.

Note: cm Hg is an accepted unit of atmospheric pressure. Other similar units involving different

liquids are also accepted.

For example:

Given that h = 76 cm and the density of mercury is

13 600 kg m-3

:

Answer:

Atmospheric pressure = 76 cm Hg

State the answer in Pascal:P = h ρg = 0.76(13 600)(10) = 103 360 Pa

3.3.2 Gas Pressure

• Gas pressure can be measured using manometers and Bourdon gauges.

Manometer Bourdon gauge

In manometers, pressure can be calculated based on pressure equilibrium.

For example:

Pressure at point A = Pressure at point C

Gas pressure = Atmospheric pressure + h ρg





3.4 Pascal’s Principle

Pascal’s Principle dictates that pressure which is exerted onto the surface of a fluid in a closed

container will be transferred uniformly throughout the entire fluid.

2

2

1

1

AF

AF =

All hydraulic systems are built based on Pascal’s Principle.

3.4.1 Hydraulic jack

• When the lever is pushed downwards, valve A closes while valve B opens.

• Pressure is transferred to the larger cylinder and creates a large force to lift the car.

• When the lever is pulled upwards, valve B closes while valve A opens. The hydraulic oilflows out from the tank to fill the space in the small cylinder.

• As every movement downwards by the lever creates a small movement upwards for the large

piston, the lever needs to be pushed and pulled repeatedly before the car can be raised to a

certain height required.

• The car can be lowered down by opening the release valve so that the hydraulic oil can flow

back into the tank.

A2 A1

F 2 F 1





3.4.2 Hydraulic brake

• When the driver steps on the brake pedal, the piston in the main cylinder transfers pressure

through the hydraulic oil in the cylinders.

• Pressure is transferred uniformly through the hydraulic oil.

• The pistons in the slave cylinders are larger, therefore a large amount of force is transferred

to the brake pads.

• The brake pads transfer the large amount of force onto the disc so that the rotation of the tire

is slowed down.

3.4.3 Hydraulic pump

• A hydraulic machine uses a hydraulic pump to transfer hydraulic liquid from one vessel into

a large cylinder to create a movement.

• The above diagram shows a hydraulic pump used to move the arm of a crane.





3.5 Archimedes’ Principle

Archimedes’ principle dictates that when an object is partially or fully immersed in a fluid, the

object undergoes a buoyant force which is equal to the weight of the fluid displaced

Buoyant force = Weight of fluid displaced= V ρg

where V = volume of fluid displaced [m3]

ρ = density of fluid [kg m-3

]


]

If the object is floating stationary:

Weight of object = Weight of fluid displacedmg = V ρg

3.5.1 Submarine

The buoyant force acting on the submarine is always the same because the weight of fluid

displaced is always the same.

When water is pumped into the ballast tank,

the weight of the submarine increases. When

the weight of the submarine is greater than thebuoyant force, the submarine sinks.

When water is pumped out of the ballast tank

and replaced with air, the weight of the

submarine decreases. When the weight of thesubmarine is less than the buoyant force, the

submarine floats.

Weight of object

Buoyant force





3.5.2 Hydrometer

A hydrometer is used to measure the relative density of a liquid.

When the hydrometer floats stationary on the surface of the liquid,

Weight of the hydrometer = Weight of the liquid displaced

mg = V ρg

where m = mass of the hydrometer [kg]V = volume of liquid displaced [m3]

ρ = density of liquid [kg m-3

]


]

The higher the hydrometer floats, the denser the liquid.

The lower the hydrometer floats, the less dense the liquid.

3.5.3 Hot air balloon

• A hot air balloon displaces a large volume of air.

• When the weight of the balloon is less than the upward thrust, thehot air balloon will move upwards.

3.5.4 Ships

Ships are marked with Plimsoll lines at the sides as a guide on

the maximum load the ship can bear in different conditions.

TF = Tropical freshwater

F = FreshwaterT = Tropical ocean

S = Summer ocean

W = Winter ocean

WNA = Winter in North

Atlantic Ocean





3.6 Bernoulli’s Principle

Bernoulli’s principle dictates that when the velocity of a flowing fluid increases, the pressure at

that point decreases.

Uniform tube:

(a) When a uniform tube with one end stopped is filled with water, the levels in all three vertical

tubes are the same.

Water pressure at A = Water pressure at B = Water pressure at C

(b) When the stopper is removed, it is found that the water levels are decreasing from P to Q to

R.

Water pressure at A > Water pressure at B > Water pressure at C

This is because water flows from high pressure to low pressure.

Venturi tube:

(a) When a Venturi tube with one end stopped is filled with water, the levels in all three vertical

tubes are the same.

Water pressure at X = Water pressure at Y = Water pressure at Z

(b) When the stopper is removed, it is found that the water levels are the lowest at Y and the

highest at X .

Water pressure at X > Water pressure at Z > Water pressure at Y

The tube cross-section at Y is the smallest, therefore water travels at the fastest velocity at

tube Y . Therefore, the pressure at Y is the lowest.

The water velocity in tube X and Z are the same because they have the same cross-section

area. However, the pressure gradient still decreases from D to E to F, which is why the water

level at Z is lower than at X .





3.6.1 Aerofoil

• As the aerofoil shape cuts through the air, the air is forced

to travel at a higher speed on top of the aerofoil compared

to below the aerofoil.

• The high velocity area causes the air to have low pressure.• Therefore, the higher pressure area pressures against the

aerofoil towards the lower pressure area causing a lifting

force.

3.6.2 Carburetor• Carburetor mixes petrol and air for burning in the

engine cylinder.

• When air flows through the narrower part of the

tube, the velocity increases thus the pressure

decreases. An area with low pressure is formed atX.

• The atmospheric pressure, which is greater, pushes

the petrol out from the jet.

• Petrol and air are mixed to create a spray.

3.6.3 Bunsen Burner

• Gas flows out through the narrow jet at a very high velocity.

• A low-pressured area is formed at X.

• The air outside at atmospheric pressure flows in and mixes with gasto light it.

• Oxygen supply which is enough from the air will ensure a complete

burning to produce a hotter flame and less luminous.

END OF CHAPTER

chapter 3 forces and pressure 2011

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