Chapter 3: Forces and Pressure CHAPTER 3: FORCES AND PRESSURE ╞╡§¥ Physics
3.1
SPM 2013
Pressure
Pressure is the force which acts normal per unit area of contact. P
F A
where P = pressure [Pa] F = force [N] A = area [m2]
3.2
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
Pressure in Liquids
Pressure in liquids are not dependent on the size or shape of the container; only on its depth.
P hg 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
Atmospheric pressure measured by a simple mercury barometer can be calculated using the formula P=hρg.
Hoo Sze Yen
www.physicsrox.com
Page 1 of 8
Chapter 3: Forces and Pressure
╞╡§¥ Physics SPM 2013 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 = hρg = 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 + hρg
Hoo Sze Yen
www.physicsrox.com
Page 2 of 8
╞╡§¥ Physics
3.4
SPM 2013
Chapter 3: Forces and Pressure
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.
F1 F2 A1 A2
A2
A1 F2
F1
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 oil flows 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.
Hoo Sze Yen
www.physicsrox.com
Page 3 of 8
╞╡§¥ Physics
SPM 2013
Chapter 3: Forces and Pressure
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.
Hoo Sze Yen
www.physicsrox.com
Page 4 of 8
╞╡§¥ Physics
3.5
SPM 2013
Chapter 3: Forces and Pressure
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 = Vρg where V = volume of fluid displaced [m3] ρ = density of fluid [kg m-3] g = gravitational acceleration [m s-2]
If the object is floating stationary: Weight of object = Weight of fluid displaced mg = Vρg
Buoyant force Weight of object
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 the buoyant force, the submarine sinks.
Hoo Sze Yen
When water is pumped out of the ballast tank and replaced with air, the weight of the submarine decreases. When the weight of the submarine is less than the buoyant force, the submarine floats.
www.physicsrox.com
Page 5 of 8
╞╡§¥ Physics
SPM 2013
Chapter 3: Forces and Pressure
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 = Vρg where m = mass of the hydrometer [kg] V = volume of liquid displaced [m3] ρ = density of liquid [kg m-3] g = gravitational acceleration [m s-2] 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, the hot air balloon will move upwards.
3.5.4 Ships TF = Tropical freshwater F = Freshwater T = Tropical ocean S = Summer ocean W = Winter ocean WNA = Winter in North Atlantic Ocean Ships are marked with Plimsoll lines at the sides as a guide on the maximum load the ship can bear in different conditions.
Hoo Sze Yen
www.physicsrox.com
Page 6 of 8
╞╡§¥ Physics
3.6
SPM 2013
Chapter 3: Forces and Pressure
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.
Hoo Sze Yen
www.physicsrox.com
Page 7 of 8
╞╡§¥ Physics
Chapter 3: Forces and Pressure
SPM 2013
3.6.1 Aerofoil
3.6.2 Carburetor
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.
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 at X. 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 gas to 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
Hoo Sze Yen
www.physicsrox.com
Page 8 of 8
