Physics Form 4 : Force And Pressure

   Physics  

                                                           

Chapter 3 : Force And Pressure.

3.1 Understanding Pressure.

• Pressure is defined force per unit area applied in a direction perpendicular to the surface of an object
• The unit of pressure is Pascal.

A force, F, applied normally to the surface with an area, A, will result in a PRESSURE, P, which can be defined as :

Pressure is measured in newtons per square metre ( N m -2 ). The SI unit for pressure is the pascal ( Pa ).

1 pascal ( Pa ) is equal to 1 newton per square metre ( N m -2 ).

3.2 Understanding pressure in liquids.

Pressure in Liquids

• Pressure in liquid is owing to the weight of the liquid acting on the surface of any objects in the liquid.

• Pressure of a liquid is directly proportional to
• the gravitational field strength
• the depth
• density of the liquid.

• Pressure in liquids is not affected by the size or shape of the object.

• The pressure caused by a liquid and the pressure in a liquid can be determined by using the equation below:

Pressure Caused by Liquid

Pressure in Liquid

3.3 Understanding gas pressure and atmospheric              pressure.

Gas Pressure

• Gas pressure is the force per unit area exerted by the gas molecules as they collide with the surface of an object.

Atmospheric Pressure

• On the surface of the earth, there is a thick layer of gas called the atmosphere. The atmosphere consists of various types of gas called the atmospheric gas.

• The atmospheric gases collide on the surface of the earth and hence exert a pressure on the surface of the earth, called the atmospheric pressure.

• The atmospheric pressure can be measured in the unit of atm, mmHg or Pa. The atmospheric pressure at sea level is taken to be 1 atm, which is approximately 760 mmHg or 101,000 Pa.

Characteristics of Atmospherics Pressure

• Decreases with altitude

The atmospheric pressure changes accordingly to the altitude. Altitude is the height above sea level. The greater the altitude, the lower the atmospheric pressure.

• Act equally in all direction

The atmospheric pressure acts on every object in the atmosphere. It acts equally in all direction.

• Atmospheric pressure is ~ 100,000Pa at sea level

On the surface of the earth, the atmospheric pressure can be as high as 101,000 Pa.

Unit Used to Measure Atmospheric Pressure

• The following are the unit used to measure atmospheric pressure

• Pascal (Pa)
  1 Pa = 1 N/m²

• Standard Atmospheric Pressure (atm)
  1 atm = Atmospheric Pressure at sea level ( = 101,325 Pa)

• mmHg (also known as torr)
  1 mmHg = 1/760 atm (roughly equal to the liquid pressure exerted by a millimetre of mercury).

• milibar 

• In SPM, usually we use the unit cmHg, instead of mmHg.

Applications of Atmospheric Pressure

Syringe

1. When the piston is pulled up, the atmospheric pressure inside the cylinder will decrease.
2. The atmospheric pressure outside pushes the liquid up into the syringe.

Lift Pump

Siphon

Working Mechanism of Siphon

Sucker Hook

When the sucker is pressed into place, the air inside is forced out. As a result, the pressure inside the sucker become very low. The sucker is then held in position by the high atmospheric
pressure on the outside surface.

Straw

When a person sucks 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.

Rubber Sucker

Vacuum Cleaner

3.4 Pascal’s Principle

• Pascal's principle states that in a confined fluid, an externally applied pressure is transmitted uniformly in all directions.

• Pascal's principle is also known as the principle of transmission of pressure in a liquid.

Hydraulic System

1. A hydraulic system applies Pascal's principle in its working mechanism. It can be used as a force multiplier.
2. In this hydraulic system, a small force, F_l is applied to the small piston X results in a large force, F₂ at the large piston Y. The pressure, due to the force, F₁, is transmitted by the liquid to the large piston.
3. According to Pascal’s principle,

F1A1=F2A2

Change of Oil Level in a Hydraulic System

In the diagram to the left, when piston-X is pressed down, piston-Y will be push up. The change of the piston levels of the 2 pistons is given by the following equation:

h1A1=h2A2

Applications of Pascal's Principle

Hydraulic Braking System

In most vehicle, hydraulic system is used in the braking system, as shown in the figure below.

Usually, a disc brake is used in the front wheel of a car while a drum brake is used in the back wheel of a car.

Working Mechanism of Hydraulic 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 cylinder 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

Hydraulic Jack

Working mechanism of a hydraulic jack.

1. 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.
   
2. 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.
   
3. This process is repeated until the load is sufficiently lifted up.
4. The large piston can be lowered down by releasing the hydraulic fluid back to the buffer tank through the release vale.

3.5 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.

• Upthrust/Buoyant force is an upward force exerted by a fluid on an object immersed in it.

• Mathematically, we write

F=ρVg

     F = Upthrust/Buoyant Force

     ρ = Density of the liquid

     V = Volume of the displaced liquid

     g = Gravitational field strength

Principle of Floatation

• The principle of floatation states that when an object floats in a liquid the buoyant force/upthrust that acts on the object is equal to the weight of the object.

• As shown in the figure above, if the weight of the object (W) = upthrust (F), the object is in balance and therefore float on the surface of the fluid.

• If the weight of the object > upthrust, the object will sink into the fluid.

Note

• Displaced volume of fluid = volume of the object that immerse in the fluid.

• 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.

Forces Acted on Objects Immersed in Liquid

In order to solve the problem related to object immerse in water, it's important to know the all forces acted on the object.

Case 1:

1. The density of the object is lower than the density of the liquid. The object floats on the surface of the water.
2. The forces acting on the object is
1. the weight of the object(W)
2. the upthrust (F)

Forces are in equilibrium, hence

F = W

Case 2:

1. The density of the object is greater than the density of the liquid. The object sink to the bottom of the water.
2. Lying on the bottom of the water, there is a normal reaction acted on the object.
3. The forces acting on the object is
1. the weight of the object(W)
2. the upthrust (F)
3. Normal reaction (R)

Forces are in equilibrium, hence

F + R = W

Case 3:

1. The density of the object is greater than the density of the liquid. The object is hold by a string so that it does not sink deeper into the water.
2. The forces acting on the object is
1. the weight of the object(W)
2. the upthrust (F)
3. Tension of the string (T)

Forces are in equilibrium, hence

F + T = W

Case 4:

1. The density of the object is lower than the density of the liquid. The object is hold by a string so that it does not move up to the surface of the water.
2. The forces acting on the object is
1. the weight of the object(W)
2. the upthrust (F)
3. Tension of the string (T)

Forces are in equilibrium, hence

F = W + T

Application of Archimedes Principle

Plimsoll Line

• The Plimsoll line is an imaginary line marking the level at which a ship or boat floats in the water.

• It indicates how much load is allowed at different types of water.

Airship

• Air ship is filled with helium gas.

• Helium gas has density lower than the surrounding air, hence an upthrust which higher than the weight of the airship can be produced and cause the airship float in the air.

Hot Air Balloon

• Hot air in the balloon has lower density than the surrounding air.

• As a result, when the buoyant force produced is higher than the weight of the balloon, the balloon will start rising up.

• The altitude of the balloon can be controlled by varying the temperature of the air in the balloon.

Hydrometers

• Hydrometer is used to measure relative density of liquids.

• How deep the hydrometer sink into the liquid is affected by the density of the liquid.

• The lower the density of the liquid, the deeper the hydrometer will sink.

• This is used as the indicator of relative density of a liquid.

Submarine

• A submarine use ballask tank to control its movement up and down.

• To get submerge, water is pumped into the ballast tank to increase the weight of the submarine.

• To surface, the water is pumped out to reduce the weight of the submarine.

3.6 Bernoulli's principle.

Venturi Effect

The Venturi effect is the fluid pressure that results when an incompressible fluid flows through a constricted section of a pipe.

Experiment 1

Figure above shows that when water flow from left to right, the water level decreases from left to right. This indicates that, the water pressure decreases from left to right.

Explanation:
Liquids flow from places with higher pressure to places with lower pressure.

However, if the experiment is repeated by using a Venturi tube where the diameter at B is made smaller than A and C as in the diagram above, the water level become lowest at B.

Explanation:
The pressure at B is the lowest because the liquid flow the fastest at B. According to Bernoulli's Principle, the faster the water flow, the lower the water pressure.

Experiment 2

Figure above shows some air is blow through a tube from left to right. The water level in the capillary tube increases from left to right.
This indicates that the pressure in the tube decreases from left to right.

Explanation:
Gases flow from places with higher pressure to places with lower pressure.

However, if the tube is replaced by a Venturi tube, the water level become highest at B. This indicates that, the pressure of the air is the lowest at B.

Explanation:
The pressure at B is the lowest because the gas flow the fastest at B. According to Bernoulli's Principle, the faster the gas flow, the lower the gas pressure.

Application of Bernoulli’s Principle

Aeroplane

1. 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.
2. 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.

Sports

In some of the sport such as football, a player can make the ball move in a curve path by spinning the ball. This effect can be explained by Bernoulli's Principle.

Insecticide Spray

1. When the plunger is pushed in, the air flows at a high velocity through a nozzle.
2. 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.
3. The insecticide leaves the top of the metal tube through the nozzle as a fine spray.

Bunsen Burner

1. 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.
2. The outside air, which is at atmospheric pressure, is drawn in and mixes with the gas.
3. The mixture of gas and air enables the gas to burn completely to produce a clean, hot, and smokeless flame

Carburetor

A carburetor is a device that blends air and fuel for an internal combustion engine. Figure above shows how Bernoulli's principle is applied in a carburetor to mix the air with the fuel.