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CIE AS & A Level Physics 4.3 Density and pressure Study Notes

CIE AS & A Level Physics 4.3 Density and pressure Study Notes- 2025-2027 Syllabus

CIE AS & A Level Physics 4.3 Density and pressure Study Notes – New Syllabus

CIE AS & A Level Physics 4.3 Density and pressure Study Notes at  IITian Academy  focus on  specific topic and type of questions asked in actual exam. Study Notes focus on AS/A Level Physics  Study Notes syllabus with Candidates should be able to:

  1. define and use density
  2. define and use pressure
  3. derive, from the definitions of pressure and density, the equation for hydrostatic pressure Δp = ρgΔh
  4. use the equation Δp = ρgΔh
  5. understand that the upthrust acting on an object in a fluid is due to a difference in hydrostatic pressure
  6. calculate the upthrust acting on an object in a fluid using the equation F = ρgV (Archimedes’ principle)

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4.3.1 define and use density

  • Density is the measurement of how tightly a material is packed.
  • It is defined as the mas per unit volume.

                                                                                 \(Density = \frac{Mass}{Volume}\)

  • Iron, platinum, and lead are examples of dense materials. 
  • Density: Solids > Liquids > Gases. 
  • This is due to the fact that solids have densely packed particles, liquids are materials where particles can slide around one another, and gases have particles that are free to move all over the place.

4.3.2 define and use pressure

  • Pressure is defined as the force applied perpendicular to the surface of an object per unit area over which that force is distributed.

                                                                                \(Pressure = \frac{Force}{Area}\)

  • The SI unit of pressure is Pascal.
  • A pascal can be defined as a force of one newton applied over a surface area of a one-meter square.
  • Hydrostatic pressure: The hydrostatic pressure is the pressure exerted by a fluid at equilibrium at any point of time due to the force of gravity. Hydrostatic pressure is proportional to the depth measured from the surface as the weight of the fluid increases when a downward force is exerted.
  • Pressure exerted by a fluid can be given as P = ρgh.
  • Fluids exert pressure in all directions equally. 

4.3.3 derive, from the definitions of pressure and density, the equation for hydrostatic pressure Δp = ρgΔh

It is a well-known fact that pressure increases with depth of liquid. The relation between the pressure $p$ due to a fluid (liquid or gas) at depth $h$ is given by the equation
                                                                                                P = ρgh
where ρ is the density of the fluid and g is the acceleration of free fall. The equation can be derived as follows:

                         

Consider a flat horizontal surface at a depth h in a fluid of density ρ. Then,

 Mass of fluid on area  = Density × Volume = ρAh

Weight of fluid on area = ρAgh.

This weight of fluid produces a pressure P on the area given by
Pressure  =\(\frac{ force }{ area }\)
 =\(\frac{ρ g A h}{A}\)= ρgh
Note that this equation allows the pressure due to the fluid to be calculated. It should be remembered that the actual pressure at depth $h$ in a liquid would be given by
pressure P = ρgh+ atmospheric pressure at liquid surface.

4.3.4 use the equation Δp = ρgΔh

  • The change in pressure exerted by a column of liquid  after moving from height h1 to h2 is given as 
                                                                                        P1 – P2 = ρg( h1-h2)

                                                                                                                               ΔP = ρgΔh

                                                                                         

4.3.5 understand that the upthrust acting on an object in a fluid is due to a difference in hydrostatic pressure

  • Upthrust is the upward force that a liquid or gas exerts on an object that is partially or fully submerged in it. It is also known as buoyancy. 
  • The pressure of a fluid increases with depth due to the weight of the fluid above it.
  • The pressure on the bottom of an object is greater than the pressure on the top, so the object experiences an upward force. 
  • If the upthrust is greater than the weight of the object, the object will rise. 
  • If an object is denser than the fluid it is submerged in, it will sink. 

4.3.6 calculate the upthrust acting on an object in a fluid using the equation F = ρgV (Archimedes’ principle)

  • Archimedes’ principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether partially or fully submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the center of mass of the displaced fluid.
  • In simple form, the Archimedes law states that the buoyant force on an object is equal to the weight of the fluid displaced by the object.
  • Thus, Force can be given as F = ρgV, where  is the V volume of water displaced.
  • The mass of the water displaced by an object can be written as Mass = Density × Volume = ρV.
  • Weight = Mass × Acceleration = ρVg. 
  • From Archimedes’ principle, we know that the apparent loss of weight is equal to the weight of the water displaced therefore the thrust force is given by the following equation:

                                                                                                              Thurst force =  ρVg.                                             

 
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