TOPIK 3 (T4)

TOPIK 3:  DAYA DAN TEKANAN (FORCE AND PRESSURE)

3.1 UNDERSTANDING PRESSURE

• Pressure is force per unit area
• The SI unit for pressure is Nm ^-2  =  Pascal  (Pa)

 

 Relationship between pressure and area

• The pressure of a given force decreases as the surface area increases.
• The pressure of a given force increases as the surface area decreases.

Applications involving High Pressure

• Increasing the pressure by reducing the area

 

• A sharp knife has a very small surface area on its cutting edge so that high pressure can be exerted to cut the meat.
• 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.
• 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.

Application involving Low Pressure

• Reducing the pressure by increasing the area

• 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.

3.2  UNDERSTANDING PRESSURE IN LIQUIDS

• A liquid in a container exerts pressure because of its weight.

Characteristics of Pressure in a liquid

• The pressure at any point in a liquid, at a particular depth, acts equally in all directions.
• The pressure in a liquid does not depend on the area of its surface.
• The pressure in a liquid acts equally in all directions and does not depend on the shape of the container.

Relate depth to pressure in a liquid .

• The pressure in a liquid is directly proportional to the depth.
• The pressure in a liquid increases with depth.

Relate density to pressure in a liquid

• The pressure in a liquid is directly proportional to  the density of the liquid.

Formula for the pressure in a liquid.

Applications of pressure in liquids

• 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.

• Normally a water tank is placed at higher level so as to supply water at greater pressure.

• Submarine is built with thick wall so as to withstand enormous pressure at greater depth.

• A patient receiving intravenous drips of a certain fluid from a bottle. In order for the fluid to flow into the vein, the bottle must be placed at a height above the injection site.
• The liquid solution is at a higher pressure so it has sufficient pressure to flow into the veins of the patient.

Example

1. If the density of sea water is 1150 kgm^-3, calculate the pressure below 40m of sea water due to the water alone. (Pressure in liquid = ρgh).

2. The figure shows a cylinder containing liquid mercury.  What is the pressure caused by the liquid mercury at the point P?

[Density of liquid mercury is 1.36 x 10⁵ kg m-3 ]

3.3 UNDERSTANDING GAS PRESSURE AND ATMOSPHERIC PRESSURE

Gas pressure

• is the force per unit area exerted by the gas molecules as they collide with the walls of their container.

Atmospheric pressure

• is the pressure caused by the weight of the air above us.
• acts equally in all directions.
• varies with the height of the object above sea level.
• decreases with the altitude or the height above sea level.

At higher altitudes,

• the density of the air are lower 
• the temperature of the air are lower

Existence of atmospheric pressure

• Atmospheric pressure acts under the surface of the cardboard is greater than the weight of the water in the glass.

•  Pressure inside the metal can decrease. The atmospheric pressure outside the metal can  is higher. Hence it compresses the metal can.

Applications of atmospheric pressure

Drinking straw

Suck through a straw,

• the air pressure in the straw is lowered. 
• the atmospheric pressure  acting on the surface of the drink pushes the water up the straw and into our mouth.

Rubber sucker

 

The sucker is pressed into place

• The air behind it is squeezed out.
• The atmospheric pressure outside the rubber sucker held it in position.

Syringe

• Pulling up the piston
• Reduces the atmospheric pressure inside the cylinder.
• Atmospheric pressure on the liquid surface then pushes the liquid up into the syringe.

Vacuum cleaner

The fan inside the cylinder blows air out of the vents

• less air inside
• air pressure there drops.
• atmospheric pressure outside pushes air up the cleaner hose ,carrying dust and dirt with it.

MEASURING  ATMOSPHERIC PRESSURE AND GAS PRESSURE

Measuring atmospheric pressure

Using Fortin Barometer

1.    The mercury column rises or falls according to the pressure of air on the mercury in the dish.

2.    The space above the mercury column is vacuum so it exerts no pressure on the top of the mercury column.

3.    If the vertical height of the mercury is h cm, the atmospheric pressure reading  is “ h cm mercury ”.

4.    The height, h unchanged when the glass tube

a)    diameter increases

b)   is tilted

c)    lowered further into the dish

d)   lifted up from the dish

5.    The height, h will increases when the barometer is slowly submerged in water.

6.    The height, h will decreases when

a)    the vacuum space in the glass tube is filled with gas

b)   the barometer is carried out to a mountain

Using Aneroid Barometer

 1.    Is used as an altimeter by mountaineers or in an aero plane to determine its altitude.

2.    When the atmospheric pressure

a)    decreases , the container will expand.

b)   increases, the container will constrict.

3.    The slight movement of the container is magnified by a lever system which is connected to a pointer.

Measuring gas pressure

Using Manometer

 

 

 

  

 Using Bourdon Gauge

1.    When the gas supply is connected, the pressure in the gas acts to straighten the curved metallic tube.

2.    The movement is transferred to the lever system which actuates a pointer to move across the scale.

3.    Suitable for measuring higher pressure.

3.4 APPLYING PASCAL’S PRINCIPLE

•  Pascal’s Principle states that when pressure is applied to an enclosed fluid, the pressure will be transmitted equally throughout the whole enclosed fluid.

• When the piston is pushed into the glass sphere the jet of water is shot out from the holes in the glass sphere with the same speed.
• This is because the pressure acting on the water is transferred uniformly throughout the water.

Hydraulic system

 

• A small input force, F1 is applied to the small piston resulting in a large output force, F2.
• The magnitude of the force at the large piston depends on:

           - the force, F1, applied to the small piston,

           - the ratio of the surface area of the piston,

• 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.

Application of Pascal’s Principle

Hidraulik Jack

• By moving the push-pull handle a number of times , the large piston can be raised carrying a heavy load.

 Hidraulik Brake

 

•  A small force acting at the pedal can transmit a large force to all wheels simultaneously to stop the car.
• It is because the pressure will be transferred through the pedal brake liquid to car’s tyre

3.5 APPLYING ARCHIMEDES’ PRINCIPLE

Archimedes’ Principle state that

When an object is immersed in a fluid, the buoyant force (uptrust) on the

object is equal to the weight of fluid displaced by the object.

Buoyant force is an upward force resulting from an object being wholly

or partially immersed in a fluid

Actual weight       =  Weight of an object in air

Apparent weight  =  Weight when the object is immersed in a fluid

                                        

Buoyant force makes thing seem to be lighter

 

 Buoyant force = actual weight – apparent weight

                        = 25 – 15

                        = 10 N

  In water, the object experiences two forces:

(a) The actual weight which acts downwards.

(b) The buoyant force which acts upwards.

The object displaces a volume of liquid.

Volume of liquid displaced

         = volume of the submerged part of the object.

         = weight of liquid displaced

Buoyant Force, F_B   =  Weight of fluid displaced

                                      =   mg   

                                      =   ρVg  

F_B = ρVg

F_B = Bouyant Force or Upthrust

ρ   = Density of fluid

V  = Volume of fluid displaced (volume of the object that immersed  in the fluid)

      

Applications of Archimedes Principle

A ship float in sea water.

• Weight of the ship equal to the weight of sea water displaced
• Although a ship has a larger density than water, its shape is hollow so that the overall density of the ship is smaller than the sea water.

 Boat made of steel will float in water, but a block of steel will sink.

• A block of steel will displaced a small volume of water. So buoyant force acting on it is smaller than its weight. Therefore it sinks
• The volume of water displaced by the ship is sufficiently large. The weight of water displaced is large so the buoyant force acting on the ship is also greater. Therefore it float.

 Same boat sailing in the sea water and the river

• The buoyant forces in the sea and in the river are the same because the buoyant force is equal to the weight of the boat.
• The density of fresh water is lower than sea water.
• The lower the density of the water, the larger the volume of water displaced.
• The larger the volume of water displaced, the larger the buoyant force
• Therefore  the boat float lower in the river compare to the sea.

The purpose of Plimsoll line mark on a ship.

• Plimsoll line marked on the body of the ship acts as a guide, to ensure that a ship is loaded within safe limits.

Submarine

Hydrometer

• Used to measure the relative density of liquids in accumulators, such as milk or acid.
• 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 to equal the weight. The hydrometer is submerged more.
• In a liquid of higher density, the hydrometer floats higher.

Hot air balloon

• A hot-air balloon displaces a large volume of air.
• The buoyant force =  the weight of the air  displaced
• When:

buoyant force  <  the total weight of the balloon:  the balloon will rise.

buoyant force  =  the total weight of the balloon:  the balloon floating in the air. 

3.6  UNDERSTANDING BERNOULLI’S PRINCIPLE

 Bernoulli’s  Principle states that

“The pressure of a moving liquid decreases as the speed of the fluid increases 

and vice versa.”

Activities relate to Bernoulli’s Principle

(a)

The air is blown up above the surface of a piece of paper,

- the paper moves up.

- because the air moved at a very high velocity.

According to Bernoulli’s Principle,

- the pressure of the moving air decreases as the speed of the air increases.

- atmospheric pressure which acts at the bottom of the paper is higher and 

  pushes up the paper.

(b)

When the air is blown harder through the straw ,

- the two ping-pong balls will move closely to each other.

- the air moved at a very high velocity between the balls.

- the pressure of the moving air decreases as the speed of the air increases.

- the higher atmospheric pressure caused the ping-pong balls closer to 

  each other.

(c)

When the air blows harder,

- the ball is not falling down.

- the air moved at a very high velocity between the balls and the wall of 

  the filter funnel.

- the pressure of the moving air decreases as the speed of the air increases.

- the bottom of the ball has the higher atmospheric pressure which can 

  hold the ball from falling down.

Applications of Bernoulli’s Principle

Aerofoil

- the speed of air is greater on the upper surface.

- the pressure of the moving air is lower.

- the bottom of the aerofoil  has the higher atmospheric pressure 

  because of the slower airflow.

- the different in air pressure produces the lifting force which cause

  the aerofoil to rise.

The tube has different diameters at different positions.

When the water is static,

- the  water level in the vertical tube is equal

- the pressure of water at position A. B and C is the same

When the water is flowing from X to Y,

- the  speed of water at B > C > A

- the pressure of water at B < C < A

- the water level at B is the lowest