Pressure
Section: Motion, Forces & Energy | Syllabus: Cambridge AS Level Physics 9702
Pressure and Forces Pressure describes how concentrated a force is when applied over a surface. Pressure The effect of a force acting over a certain area. It tells us how concentrated a force is. p = F/A Where: \(p\) = pressure (Pa), \(F\) = force (N), \(A\) = area (m²) 1 Pascal (Pa) = 1 N/m² Key Concept A smaller area produces a larger pressure for the same force, because the force is concentrated.
Effect of Area on Pressure Two scenarios compared: (1) A person standing on stiletto heels - small area, high pressure on floor. (2) Same person on flat shoes - large area, low pressure. Same force (body weight) but different pressures.
Formula: p = F/A. Example: Pressure and Surface Area Examples: A knife cuts easily because its blade has a small surface area → high pressure Snowshoes prevent sinking because they spread weight over a large area → low pressure Memory Aid "Force spread wide gives gentle pressure; force focused tight gives intense pressure." Applications in Daily Life Hydraulic systems: Use liquids to transmit pressure (e.g., car brakes, hydraulic lifts) Tyres: Air inside supports the vehicle weight by exerting pressure on the road Footwear: High heels create large pressure; flat shoes reduce it Important Points 1 Pa = 1 N / m² Pressure depends on force and area , not on mass alone Changing either force or area changes pressure proportionally Pressure in a Liquid Liquids exert pressure on the walls and bottom of their containers and on any object submerged in them.
p = ρ gh Where: \(p\) = pressure (Pa), \(ρ\) = density (kg/m³), \(g 10\) N/kg, \(h\) = depth (m) Pressure vs. Depth in a Liquid Graph with Depth (m) on x-axis and Pressure (Pa) on y-axis. A straight line through the origin showing linear relationship (p = ρgh).
The deeper you go, the greater the pressure. Also shown: arrows at different depths in a container pointing outward equally in all directions. Understanding Liquid Pressure Pressure in a liquid increases with depth because of the weight of the liquid above Pressure depends on the density of the liquid - denser liquids exert higher pressure at the same depth Pressure acts in all directions at a given depth (Pascal's principle) Key Idea At equal depths in a liquid, pressure is the same in all directions and at all points.
Applications Hydraulic systems: A small force applied at one piston is transmitted through an incompressible liquid to produce a larger force at another piston Submarines: Built to withstand high pressure at great depths Dams: Are thicker at the bottom where water pressure is greatest Example: Calculating Pressure in a Liquid Example Calculation: Find the pressure at a depth of 5 m in water (ρ = 1000 kg/m³).
p = ρgh = 1000 × 9.8 × 5 = 49 000 Pa = 49 kPa Common Misconception Pressure in a liquid does not depend on the shape or total volume of the container - only on the depth and density of the liquid. Pascal's Principle Pascal's Principle explains how hydraulic systems work.
Pascal's Principle Any pressure change applied to an enclosed liquid is transmitted equally and undiminished to all parts of the liquid and the walls of its container. Hydraulic System Diagram Two pistons connected by liquid-filled tube.
Small piston (area A₁) on left receives small input force F₁. Pressure transmitted equally through incompressible liquid. Large piston (area A₂) on right produces large output force F₂. F₁/A₁ = F₂/A₂ (Pascal's Principle).
Formula Connection F₁ / A₁ = F₂ / A₂ (when the same liquid transmits pressure). Key Understanding Liquids are incompressible , so pressure is transmitted efficiently In gases, pressure transmission is similar but less efficient because gases are compressible
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