Pressure — Cambridge O Level Physics 5054 Revision Notes & Topical Questions

• Pressure
  • the force acting normally per unit area, p = F ÷ A.
    What the symbols mean: p = pressure (Pa = N m⁻²) · F = force acting at right angles to the surface (N) · A = area (m²)
    • (at right angles)
  • Force is in N, area is in m² and pressure is in pascals (Pa), where 1 Pa = 1 N/m².
• Larger units
  • 1 kPa = 1000 Pa and 1 MPa = 10⁶ Pa.
• Reading the equation
  • for a given force, a smaller area gives a larger pressure.
  • For a given area, a larger force gives a larger pressure.
• Force from weight
  • an object resting on a surface exerts a force equal to its weight, F = mg.
  • A 60 kg student exerts about 590 N on the floor.
• Area units
  • convert cm² to m² by dividing by 10 000, because 1 m² = 10 000 cm².

• Increase pressure
  • make the area small.
  • Knives, nails, needles and cutting wires have sharp edges so a modest force produces a large pressure.
• Decrease pressure
  • make the area large.
  • Snowshoes, wide tractor tyres, skis and the broad base of buildings spread the weight so the ground does not sink.
• Table of examples
  • each links force, area and pressure.

• Pressure in a liquid
  • it acts in all directions and increases with depth.
  • A dam wall is thicker at the bottom because the pressure there is greatest.
• Equation
  • the change in pressure with depth is Δp = ρgΔh.
  • ρ is the density of the liquid in kg/m³, g is 9.8 N/kg and Δh is the vertical depth in metres.
• Where it comes from
  • the pressure at depth h is the weight of the column of liquid above divided by the area, p = ρVg ÷ A = ρgh.
• Factors
  • pressure depends on the depth and density but not on the shape of the container or the amount of liquid.
  • A narrow tube and a wide lake with the same depth have the same pressure at the bottom.
• Total pressure
  • the pressure at depth in an open liquid is the sum of atmospheric pressure and ρgh.
• Liquids are almost incompressible
  • they transmit pressure through the whole liquid, which is used in hydraulics.

• Atmospheric pressure
  • the pressure caused by the weight of the air above us.
  • At sea level it is about 100 000 Pa (1.0 × 10⁵ Pa), or 760 mm of mercury.
• Variation with height
  • it decreases as altitude increases because there is less air above.
  • Climbers and aeroplanes experience lower pressure, which is why cabins are pressurised.
• Barometer
  • an instrument that measures atmospheric pressure.
  • A simple mercury barometer has a tube of mercury inverted in a dish and the column height, about 760 mm, shows the pressure.
• Why mercury is used
  • it is very dense, so the column is a manageable height.
  • With water the column would need to be about 10 m high.
• Aneroid barometer
  • it uses a sealed metal box that changes shape with pressure and moves a pointer.
• Effects of atmospheric pressure
  • a drinking straw works because suction lowers pressure and atmospheric pressure pushes the liquid up.

• Manometer
  • a U-tube containing liquid, used to measure the pressure of a gas supply or the difference between two pressures.
• How it works
  • one side is connected to the gas and the other is open to the air.
  • The liquid is pushed down on the gas side and rises on the other side until the pressures balance.
• Equation
  • the gas pressure above atmospheric pressure equals ρgh, where h is the difference in the heights of the liquid levels.
• Using the manometer
  • follow the steps.

1. Connect one arm to the gas supply and leave the other open to the atmosphere.
2. Measure the difference in heights of the liquid surfaces.
3. Calculate Δp = ρgΔh.
4. Add atmospheric pressure to find the absolute gas pressure.

• Same level rule
  • points at the same height in the same continuous liquid have the same pressure.

• Hydraulic system
  • a closed system of liquid in connected cylinders that transmits pressure.
  • The same pressure acts everywhere in the liquid because it is incompressible.
• Principle
  • a small force on a small piston creates a pressure, p = F₁ ÷ A₁, which gives a large force on the large piston, F₂ = p × A₂.
  • So F₁ ÷ A₁ = F₂ ÷ A₂.
• Force multiplier
  • the large piston has a larger force but moves a shorter distance.
  • The work done on both pistons is equal, so energy is conserved.
• Applications
  • car brakes, hydraulic jacks, lifts and excavators.
• Brake fluid
  • a liquid is used rather than a gas because it does not compress, so the force is transmitted immediately.
  • Air bubbles in the pipes make brakes spongy because the air compresses.

• Step-by-step method
  • follow the same pattern for every pressure question.

1. Write the known quantities with units.
2. Identify whether the pressure is due to force on an area or liquid depth.
3. Convert areas to m² and depths to metres.
4. Substitute into p = F ÷ A or p = ρgh.
5. Give the answer in Pa or kPa.

• Link to density
  • liquid pressure questions usually need a density from the table: water 1000 kg/m³, mercury 13 600 kg/m³.
• Link to forces
  • once you know the pressure and area, the force on a surface is F = pA.
  • A submarine window of area 0.20 m² at 5.0 × 10⁵ Pa carries a force of 1.0 × 10⁵ N.

• Pressure acts at right angles
  • the pressure at a surface produces a force at 90° to that surface.
  • A liquid pushes outward on the walls of its container perpendicular to the wall at each point.
• Experiment to show it
  • a tall can of water with small holes at different depths.

1. Make three holes in a vertical line down the side of a plastic bottle and cover them with tape.
2. Fill the bottle with water and keep it topped up.
3. Remove the tape and watch the water jets.
4. Each jet leaves at right angles to the wall, and the lowest jet goes farthest because the pressure there is greatest.

• Second demonstration
  • a thin rubber sheet over a funnel bulges outward in every direction when the funnel is lowered into water.
  • The bulge is greater at greater depth.
• Everyday link
  • water towers are built high so that the pressure in the pipes at the bottom is large enough to push water to taps.

• Method
  • follow the steps to find the atmospheric pressure from a mercury barometer.

1. Fill a long glass tube with mercury and invert it in a dish of mercury.
2. The mercury falls until its column is held up by the atmosphere, and a vacuum forms at the top.
3. Measure the vertical height h of the column above the mercury surface in the dish.
4. Atmospheric pressure = ρgh, or the height of the column in mm of mercury.

-- A column of 760 mm of mercury gives 13 600 × 9.8 × 0.760 = 1.01 × 10⁵ Pa.

• Tilting the tube
  • it does not change the vertical height, so the pressure reading stays the same.