Physics Notes Chapter 3-7
Content
Chapter 4: Mass, Weight and Density
Mass and Weight
1) Definition SI Unit Mass Weight Measure of the amount Amount of gravitational of matter in a body. force acting on a body. Kilogram (kg) Newton (N) Dependent on the mass of the object and the gravitational field strength.
Dependen Dependent on the t on number and composition of atoms making up the body.
Properties Mass has only Weight has both magnitude, and is magnitude and direction constant (unaffected by (towards the centre of gravitational field Earth). strength). Measuring Beam balance, Instrumen electronic balance t Relationsh ip Spring balance, compression balance
Weight of an object is directly proportional to its mass. Weight = Mass x Gravitational field strength (W=mg)
Gravitational field strength 7) Gravitational field is the region where an object experiences gravitational force. 8) Gravitational field strength, g, is the gravitational force acting per unit mass on an object. SI unit= N/kg. 9) The gravitational force pulls objects to the centre of the Earth and gets weaker with increasing altitude.
10 A 1kg object will experience a 10N gravitational force due to Earth’s ) gravitational pull (gravity).
Inertia
14 Inertia is the resistance of an object to change in its state of motion or ) rest. (The larger the mass, the greater the inertia) Note: Inertia is not a force. 15 The inertia of an object is directly proportional to is mass. ) 16 Explain how seatbelts can prevent a driver from injury during a ) sudden stop. Initially, the driver is in motion. During a sudden stop, the driver will continue to move forward due to his inertia. Without seatbelts, the driver will be thrown forward and crash into the windscreen. Seatbelts will pull the driver back onto is seat and stop him from moving forward, thus preventing him from crashing into the windscreen and injury.
Density
17 Density is the mass per unit volume of a substance. SI unit= ) kg/m3 The density of a substance is dependent on the composition and number of atoms making up the substance (mass). Metals have high 18 densities as the atoms are closely packed. The large number of atoms ) in 1kg the metal contributes to the higher mass and hence density, compared to gases where the molecules are spaced further apart.
19 Use the kinetic particle theory to explain why solids have ) higher densities than gases. Solids have higher densities than gases as their particles are packed closer together. The number of particles per unit mass in a solid is higher than in gases. Of the same mass, solids have a lower volume hence a higher density; while gases have higher volumes hence a lower density.
Chapter 5: Turning Effect of Forces Moment of a force about a point is the product of the force and the perpendicular distance from the pivot to the line of action of the force. Moments (Nm)= Force (N) x Distance travelled (m) Conditions for object in equilibrium: 1) Fnet= 0 2) Net moments due to external forces= 0 Principle of Moments When a body is in equilibrium, the sum of clockwise moments about the balanced point is equal to the sum of anticlockwise moments about the same point (pivot). Total clockwise moment = Total anticlockwise moment When the clockwise moment is not equal to the anticlockwise moment, there is a resultant moment and the object will rotate in the direction of resultant moment. If there is no resultant moment, the object is balanced. Centre of gravity The centre of gravity (CG) of a body is the point through which the whole weight of the object appears to act. The CG of a regular object is at the centre. The CG of an irregular object is determined using a plumb line. If a body is hanging freely at rest, its CG is always vertically below the pivot, thus the plumb line method works. It can only be used for flat, irregular objects. Stability Stability is a measure of the body's ability to return to its original position after being displaced slightly. 3 types of stability: 1. Stable equilibrium
Object will return to original position after slight disturbance. Line of action of the weight passes through the base area of the object, the moment due to its weight will cause it to return to its original position. 2. Unstable equilibrium Object will topple over after being tilted slightly. If the line of action of the weight is outside the base area of the object, the moment due to its weight will cause the object to topple. 3. Neutral equilibrium Object remains in new position after being tilted slightly. To increase the stability of a body, its base area should be increased, and by lowering the centre of gravity.
Work - Work is the product of the force on a body and the distance it moves in the direction of the force - Work done = force x distance moved in the direction of the force - Work is done whenever energy is changed from one form into another. - SI unit is joule (J) - Work is a scalar quantity Energy - energy is defined as the ability to do work - SI unit is joule (J) - Energy is a scalar quantity - kinetic energy is the energy possessed by an object due to its motion. - kinetic energy can be classified into - kinetic energy= 1/2 mv2 - potential energy is the energy a body possesses due to its position or state - potential energy can be classified into: --gravitational potential energy: possessed by a body due to its position = mgh -elastic potential energy: possessed by a body due to its strained state of being stretched or compressed Eg. A ball of mass 500g is moving at a velocity of 5m/s. What is the kinetic energy of the ball? kinetic energy = 1/2 mv2 = 1/2 x 0.5 x 5 x 5 = 6.25 J Eg. Billy has a mass of 40kg. He runs up a flight of 20 steps, each of height 0.25m. Calculate his gain in gravitational potential energy gain in gravitational potential energy = mgh = 40 x 10 x (20 x 0.25) = 2000 J Principle of Conservation of Energy: States that energy can neither be created not destroyed but can be converted from one form into another with no change in its total amount.
Power and efficiency - Power is defined as the rate of work done. - Power = work done/time taken (P=W/t) - SI unit is watt (W) - Efficiency is the ratio of useful output energy to the total input energy or the ratio of useful power to the total input power. efficiency = (useful output energy / input energy) x 100% Eg. A crane can lift a 200kg mass through a vertical height of 5m in 4s. Calculate i. the power output of the motor driving the crane ii. the efficiency of the motor if the power input is 5kW i. power output = work done/time taken = (200 x 10 x 5)/4 = 2500W ii. efficiency of motor = (power output/power input) x 100% = (2500/5000) x 100% = 50% Friction 1. Static friction - related to objects which are not moving. - amount of force applied = amount of friction 2. Moving friction - applied force does not affect friction - it can be affected by surface or sudden change in mass Advantages of friction - enables walking - brakes of vehicles Disadvantages - reduce efficiency of machinery - energy wasted as heat Methods to reduce friction - lubricants - ball bearings -----> so that moving parts are made smoother Energy, Work, Power
Work
Energy
Power
Definiti Work done on an on object is when a constant force is applied on the object producing a distance moving in the direction of the force. SI unit Joule (J)
Energy is the Power is defined as capacity to do work. the rate of doing work There are many different types of - Rate of energy energy like transfer / translational, conversion rotational and vibrational kinetic energy. Joule (J) One joule of work is done when an object with 1kg moves at 1m/s. Watt (W) One watt is produced when 1 joule of work is done for 1 second.
Definiti One joule of work is on of SI done when a force unit of one Newton moves through a distance of one metre in the direction of the force. Equatio Work = Force x n Distance
K.E. = (1/2)(mv2) m = mass v = velocity P.E. = mgh m = mass g = gravitational acceleration h = height
Power = Work/Time Power = Energy/Time
Remark Work is done on an s object only when the force applied on it produces motion.
The principle of Efficiency = (useful conservation of energy output/total energy states that energy input) x 100 energy cannot be created or destroyed, but can only change from one form to another.
Terminal velocity
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The greater the velocity of an object, the higher the air resistance.
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Definition: The constant maximum velocity reached by a body falling through the atmosphere under the attraction of gravity. When an object reaches terminal velocity, the force of gravity and air resistance are balanced, the object falls at a constant speed and doesn’t accelerate. Factors affected: Size, surface area, weight and nature of medium where object is flying. If an object is falling through a vacuum, there would be no air resistance, thus acceleration is due to gravity alone.
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Pressure - Pressure is force acting normally per unit area.
If the amount of applied force is the same, then Larger area --> Lower pressure Smaller area --> Higher pressure
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Examples of Pressure
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Skis have a large area to hold up the weight of the skier on the snow Flat bottomed shoes are comfortable to wear due to reduced pressure acting on our feet A sharp knife can cut easily because the very high pressure under the cutting surface is more than the object can withstand Atmospheric Pressure Atmospheric pressure exists because of MOLECULAR BOMBARDMENT of energetic air molecules (from the air around us) Under normal conditions, there are large numbers of air molecules and these molecules move with high velocities. They make frequent collisions with things around us The pressure exerted by the air molecules is almost equivalent to putting a 1 kg mass on an area of 1 cm2 Normal atmospheric pressure= 1 atm (about 1.013 x 105 pa or 101300 pa) 101300 Nm-2 = 10.13 Ncm-2 = 1.013 kgcm-2
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Applications of atmospheric pressure
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Drinking with a straw Drawing a liquid into a syringe by withdrawing the plunger Holding a rubber sucker on a smooth surface
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Removing dust with vacuum cleaner
Pressure due to a liquid column
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The taller the liquid column (with narrow base), the larger the amount of liquid contained, the greater the weight of the liquid to exert pressure The amount of pressure in the SAME liquid column is DIFFERENT at DIFFERENT DEPTHS. The greater the depth, the greater the weight of the liquid above it, the greater the pressure
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The pressure in a liquid depends on the HEIGHT of the liquid The amount of pressure increases with DEPTH
2 cases of liquid pressure 1. With atmospheric pressure
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p = p0 + ρgh Pressure at bottom = atmospheric pressure + pressure due to liquid column In this case, when the container is open, there is atmospheric pressure acting on the liquid as well.
2. Without atmospheric pressure
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p = ρgh
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Pressure at bottom = pressure due to liquid column only In this case, when the container is closed, air is removed (vacuum), so there is no atmospheric pressure.
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Factors affecting pressure in a liquid
1.Density of liquid 2.Depth of liquid 3. Gravitational acceleration When it is at equilibrium, pressure must be the same at any point along the same depth (h). Note: pressure does not depend on the shape of the liquid column.
Measurement of pressure Simple Mercury Barometer - Used to measure atmospheric pressure How to construct
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A thick-walled glass tube (about 1m long) is filled with mercury completely The open end of the tube is covered with a finger and inverted Place the inverted tube in a trough of mercury
Observation: The height of the mercury column found to be about 760mm or 76cm Atmospheric pressure = 1 atm or 760 mmHg or 76 cmHg Reasons for using mercury in a barometer
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Mercury does not wet glass Mercury has a high density
Manometer - Used to measure gas pressure How to construct
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The manometer consists of a U-tube containing a column of liquid The liquid can be mercury, water or oil
How to measure?
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When both arms are open, same atmospheric pressure is exerted on the liquid surfaces (same horizontal level) To measure the pressure of a gas, left side is connected to a gas supply The gas exerts pressure on the surface at L. The gas pressure must be greater than atmospheric pressure to cause the right side to rise Pressure at L given by p = p0 + ρgh
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Hydraulic System
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Pressure can be transmitted throughout a liquid in hydraulic presses When a small force is applied to the smaller piston, pressure is exerted on the liquid This pressure is transmitted in the liquid (oil) and is the same everywhere within the oil. Thus the pressure at the bigger piston must also be p. Since area at the bigger piston is bigger, force must also be greater
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A small force applied to the smaller piston can lift a greater load on the bigger piston
Additional Notes
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Pressure is the force acting normal or perpendicularly per unit area SI unit: Pascal (Pa) or N/m2
Pressur Solid
Liquid
Gas
e in: Equatio Pressure = n Force/Area Pressure = hpg The air surrounding us h = depth of liquid exerts a pressure (m) in all directions p = density of which is about 105 3 liquid (kg/m ) Pa. g = gravitational field strength - A liquid exerts pressure because of its weight. - Liquid pressure acts equally in all directions. This is because particles of the water can flow and wrap around the object. - A barometer is used to measure pressure. It consists of an inverted tube in a dish of mercury. The space above the mercury in the tube is vacuum. - Liquid mercury is used as its density is very high and a shorter barometer can be used to show atmospheric pressure. - An object can be bent/sucked in due to the production of vacuum and due to the difference in pressure; the atmospheric pressure will press on the object.
Remark This formula s can only be used for solids.
Mass and Weight
1) Definition SI Unit Mass Weight Measure of the amount Amount of gravitational of matter in a body. force acting on a body. Kilogram (kg) Newton (N) Dependent on the mass of the object and the gravitational field strength.
Dependen Dependent on the t on number and composition of atoms making up the body.
Properties Mass has only Weight has both magnitude, and is magnitude and direction constant (unaffected by (towards the centre of gravitational field Earth). strength). Measuring Beam balance, Instrumen electronic balance t Relationsh ip Spring balance, compression balance
Weight of an object is directly proportional to its mass. Weight = Mass x Gravitational field strength (W=mg)
Gravitational field strength 7) Gravitational field is the region where an object experiences gravitational force. 8) Gravitational field strength, g, is the gravitational force acting per unit mass on an object. SI unit= N/kg. 9) The gravitational force pulls objects to the centre of the Earth and gets weaker with increasing altitude.
10 A 1kg object will experience a 10N gravitational force due to Earth’s ) gravitational pull (gravity).
Inertia
14 Inertia is the resistance of an object to change in its state of motion or ) rest. (The larger the mass, the greater the inertia) Note: Inertia is not a force. 15 The inertia of an object is directly proportional to is mass. ) 16 Explain how seatbelts can prevent a driver from injury during a ) sudden stop. Initially, the driver is in motion. During a sudden stop, the driver will continue to move forward due to his inertia. Without seatbelts, the driver will be thrown forward and crash into the windscreen. Seatbelts will pull the driver back onto is seat and stop him from moving forward, thus preventing him from crashing into the windscreen and injury.
Density
17 Density is the mass per unit volume of a substance. SI unit= ) kg/m3 The density of a substance is dependent on the composition and number of atoms making up the substance (mass). Metals have high 18 densities as the atoms are closely packed. The large number of atoms ) in 1kg the metal contributes to the higher mass and hence density, compared to gases where the molecules are spaced further apart.
19 Use the kinetic particle theory to explain why solids have ) higher densities than gases. Solids have higher densities than gases as their particles are packed closer together. The number of particles per unit mass in a solid is higher than in gases. Of the same mass, solids have a lower volume hence a higher density; while gases have higher volumes hence a lower density.
Chapter 5: Turning Effect of Forces Moment of a force about a point is the product of the force and the perpendicular distance from the pivot to the line of action of the force. Moments (Nm)= Force (N) x Distance travelled (m) Conditions for object in equilibrium: 1) Fnet= 0 2) Net moments due to external forces= 0 Principle of Moments When a body is in equilibrium, the sum of clockwise moments about the balanced point is equal to the sum of anticlockwise moments about the same point (pivot). Total clockwise moment = Total anticlockwise moment When the clockwise moment is not equal to the anticlockwise moment, there is a resultant moment and the object will rotate in the direction of resultant moment. If there is no resultant moment, the object is balanced. Centre of gravity The centre of gravity (CG) of a body is the point through which the whole weight of the object appears to act. The CG of a regular object is at the centre. The CG of an irregular object is determined using a plumb line. If a body is hanging freely at rest, its CG is always vertically below the pivot, thus the plumb line method works. It can only be used for flat, irregular objects. Stability Stability is a measure of the body's ability to return to its original position after being displaced slightly. 3 types of stability: 1. Stable equilibrium
Object will return to original position after slight disturbance. Line of action of the weight passes through the base area of the object, the moment due to its weight will cause it to return to its original position. 2. Unstable equilibrium Object will topple over after being tilted slightly. If the line of action of the weight is outside the base area of the object, the moment due to its weight will cause the object to topple. 3. Neutral equilibrium Object remains in new position after being tilted slightly. To increase the stability of a body, its base area should be increased, and by lowering the centre of gravity.
Work - Work is the product of the force on a body and the distance it moves in the direction of the force - Work done = force x distance moved in the direction of the force - Work is done whenever energy is changed from one form into another. - SI unit is joule (J) - Work is a scalar quantity Energy - energy is defined as the ability to do work - SI unit is joule (J) - Energy is a scalar quantity - kinetic energy is the energy possessed by an object due to its motion. - kinetic energy can be classified into - kinetic energy= 1/2 mv2 - potential energy is the energy a body possesses due to its position or state - potential energy can be classified into: --gravitational potential energy: possessed by a body due to its position = mgh -elastic potential energy: possessed by a body due to its strained state of being stretched or compressed Eg. A ball of mass 500g is moving at a velocity of 5m/s. What is the kinetic energy of the ball? kinetic energy = 1/2 mv2 = 1/2 x 0.5 x 5 x 5 = 6.25 J Eg. Billy has a mass of 40kg. He runs up a flight of 20 steps, each of height 0.25m. Calculate his gain in gravitational potential energy gain in gravitational potential energy = mgh = 40 x 10 x (20 x 0.25) = 2000 J Principle of Conservation of Energy: States that energy can neither be created not destroyed but can be converted from one form into another with no change in its total amount.
Power and efficiency - Power is defined as the rate of work done. - Power = work done/time taken (P=W/t) - SI unit is watt (W) - Efficiency is the ratio of useful output energy to the total input energy or the ratio of useful power to the total input power. efficiency = (useful output energy / input energy) x 100% Eg. A crane can lift a 200kg mass through a vertical height of 5m in 4s. Calculate i. the power output of the motor driving the crane ii. the efficiency of the motor if the power input is 5kW i. power output = work done/time taken = (200 x 10 x 5)/4 = 2500W ii. efficiency of motor = (power output/power input) x 100% = (2500/5000) x 100% = 50% Friction 1. Static friction - related to objects which are not moving. - amount of force applied = amount of friction 2. Moving friction - applied force does not affect friction - it can be affected by surface or sudden change in mass Advantages of friction - enables walking - brakes of vehicles Disadvantages - reduce efficiency of machinery - energy wasted as heat Methods to reduce friction - lubricants - ball bearings -----> so that moving parts are made smoother Energy, Work, Power
Work
Energy
Power
Definiti Work done on an on object is when a constant force is applied on the object producing a distance moving in the direction of the force. SI unit Joule (J)
Energy is the Power is defined as capacity to do work. the rate of doing work There are many different types of - Rate of energy energy like transfer / translational, conversion rotational and vibrational kinetic energy. Joule (J) One joule of work is done when an object with 1kg moves at 1m/s. Watt (W) One watt is produced when 1 joule of work is done for 1 second.
Definiti One joule of work is on of SI done when a force unit of one Newton moves through a distance of one metre in the direction of the force. Equatio Work = Force x n Distance
K.E. = (1/2)(mv2) m = mass v = velocity P.E. = mgh m = mass g = gravitational acceleration h = height
Power = Work/Time Power = Energy/Time
Remark Work is done on an s object only when the force applied on it produces motion.
The principle of Efficiency = (useful conservation of energy output/total energy states that energy input) x 100 energy cannot be created or destroyed, but can only change from one form to another.
Terminal velocity
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The greater the velocity of an object, the higher the air resistance.
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Definition: The constant maximum velocity reached by a body falling through the atmosphere under the attraction of gravity. When an object reaches terminal velocity, the force of gravity and air resistance are balanced, the object falls at a constant speed and doesn’t accelerate. Factors affected: Size, surface area, weight and nature of medium where object is flying. If an object is falling through a vacuum, there would be no air resistance, thus acceleration is due to gravity alone.
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Pressure - Pressure is force acting normally per unit area.
If the amount of applied force is the same, then Larger area --> Lower pressure Smaller area --> Higher pressure
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Examples of Pressure
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Skis have a large area to hold up the weight of the skier on the snow Flat bottomed shoes are comfortable to wear due to reduced pressure acting on our feet A sharp knife can cut easily because the very high pressure under the cutting surface is more than the object can withstand Atmospheric Pressure Atmospheric pressure exists because of MOLECULAR BOMBARDMENT of energetic air molecules (from the air around us) Under normal conditions, there are large numbers of air molecules and these molecules move with high velocities. They make frequent collisions with things around us The pressure exerted by the air molecules is almost equivalent to putting a 1 kg mass on an area of 1 cm2 Normal atmospheric pressure= 1 atm (about 1.013 x 105 pa or 101300 pa) 101300 Nm-2 = 10.13 Ncm-2 = 1.013 kgcm-2
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Applications of atmospheric pressure
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Drinking with a straw Drawing a liquid into a syringe by withdrawing the plunger Holding a rubber sucker on a smooth surface
•
Removing dust with vacuum cleaner
Pressure due to a liquid column
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The taller the liquid column (with narrow base), the larger the amount of liquid contained, the greater the weight of the liquid to exert pressure The amount of pressure in the SAME liquid column is DIFFERENT at DIFFERENT DEPTHS. The greater the depth, the greater the weight of the liquid above it, the greater the pressure
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The pressure in a liquid depends on the HEIGHT of the liquid The amount of pressure increases with DEPTH
2 cases of liquid pressure 1. With atmospheric pressure
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p = p0 + ρgh Pressure at bottom = atmospheric pressure + pressure due to liquid column In this case, when the container is open, there is atmospheric pressure acting on the liquid as well.
2. Without atmospheric pressure
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p = ρgh
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Pressure at bottom = pressure due to liquid column only In this case, when the container is closed, air is removed (vacuum), so there is no atmospheric pressure.
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Factors affecting pressure in a liquid
1.Density of liquid 2.Depth of liquid 3. Gravitational acceleration When it is at equilibrium, pressure must be the same at any point along the same depth (h). Note: pressure does not depend on the shape of the liquid column.
Measurement of pressure Simple Mercury Barometer - Used to measure atmospheric pressure How to construct
• • •
A thick-walled glass tube (about 1m long) is filled with mercury completely The open end of the tube is covered with a finger and inverted Place the inverted tube in a trough of mercury
Observation: The height of the mercury column found to be about 760mm or 76cm Atmospheric pressure = 1 atm or 760 mmHg or 76 cmHg Reasons for using mercury in a barometer
• •
Mercury does not wet glass Mercury has a high density
Manometer - Used to measure gas pressure How to construct
• •
The manometer consists of a U-tube containing a column of liquid The liquid can be mercury, water or oil
How to measure?
• •
When both arms are open, same atmospheric pressure is exerted on the liquid surfaces (same horizontal level) To measure the pressure of a gas, left side is connected to a gas supply The gas exerts pressure on the surface at L. The gas pressure must be greater than atmospheric pressure to cause the right side to rise Pressure at L given by p = p0 + ρgh
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Hydraulic System
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Pressure can be transmitted throughout a liquid in hydraulic presses When a small force is applied to the smaller piston, pressure is exerted on the liquid This pressure is transmitted in the liquid (oil) and is the same everywhere within the oil. Thus the pressure at the bigger piston must also be p. Since area at the bigger piston is bigger, force must also be greater
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•
A small force applied to the smaller piston can lift a greater load on the bigger piston
Additional Notes
• •
Pressure is the force acting normal or perpendicularly per unit area SI unit: Pascal (Pa) or N/m2
Pressur Solid
Liquid
Gas
e in: Equatio Pressure = n Force/Area Pressure = hpg The air surrounding us h = depth of liquid exerts a pressure (m) in all directions p = density of which is about 105 3 liquid (kg/m ) Pa. g = gravitational field strength - A liquid exerts pressure because of its weight. - Liquid pressure acts equally in all directions. This is because particles of the water can flow and wrap around the object. - A barometer is used to measure pressure. It consists of an inverted tube in a dish of mercury. The space above the mercury in the tube is vacuum. - Liquid mercury is used as its density is very high and a shorter barometer can be used to show atmospheric pressure. - An object can be bent/sucked in due to the production of vacuum and due to the difference in pressure; the atmospheric pressure will press on the object.
Remark This formula s can only be used for solids.
