Chapter 5 : Pressure and Deformation in Solids

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Chapter Overview & SLOs

What is pressure? Chapter 5, "Pressure and Deformation in Solids," explores the mechanics of fluids (liquids and gases) and the deformational properties of solids. This chapter answers fundamental questions about how pressure behaves in different states of matter and how materials respond to forces. What is pressure and how is it calculated? You will learn that pressure is defined as force per unit area: - Formula: $P = \frac{F}{A}$ (Pressure = Force / Area) - Units: Pascal (Pa) = N/m², also atm (atmosphere), bar, mbar, torr, mmHg - Important concept: For the same force, pressure increases when area decreases (sharp knife cuts better) and decreases when area increases (snowshoes prevent sinking) - Pressure in different states of matter: Highest in solids, lower in liquids, lowest in gases How does liquid pressure vary with depth and density? You will study the derivation of liquid pressure formula: - Derivation: Pressure at depth h = weight of liquid column above / area = (m × g) / A = (ρ × V × g) / A = (ρ × A × h × g) / A = ρgh - Formula: $P = ρgh$ (Pressure = density × gravitational acceleration × depth) - Key findings: Liquid pressure increases with depth (deeper = higher pressure), increases with density (mercury is denser than water → higher pressure), acts equally in all directions at a given point, independent of the shape or size of the container What is atmospheric pressure and how is it measured? You will learn about atmospheric pressure (pressure exerted by Earth's atmosphere): - Standard value: 1 atm = 101,325 Pa ≈ 101.3 kPa ≈ 760 mmHg ≈ 14.7 psi - Mercury barometer: Device to measure atmospheric pressure. A glass tube filled with mercury inverted into a mercury reservoir. Height of mercury column (about 76 cm at sea level) indicates atmospheric pressure. - Variation with altitude: Atmospheric pressure decreases as altitude increases (there is less air above to exert pressure). Why mountaineers need oxygen cylinders at high altitudes. - Applications: Weather forecasting (high pressure = clear skies, low pressure = storms), altitude measurement, straw/siphon operation What is Pascal's law and how does it apply to hydraulic systems? A major focus is Pascal's Law: - Statement: Pressure applied to an enclosed fluid is transmitted equally and undiminished to all parts of the fluid and to the walls of the container. - Hydraulic Lift (Force Multiplier): Uses Pascal's law to multiply force. Formula: $\frac{F_1}{A_1} = \frac{F_2}{A_2}$ or $F_2 = F_1 × \frac{A_2}{A_1}$ - How it works: Small force applied on small piston (A₁) creates pressure transmitted equally. This pressure acts on large piston (A₂) producing larger force. - Applications: Hydraulic car lifts, hydraulic brakes, hydraulic jacks, hydraulic presses - Why atmospheric pressure prevents sipping on the moon: On Earth, sucking on a straw reduces pressure in the straw, and atmospheric pressure pushes liquid up. On the moon (no atmosphere), no pressure to push liquid. What is elasticity and Hooke's law? The second half of the chapter covers deformation in solids and elasticity: - Elasticity: Property of a material to return to its original shape and size after the deforming force is removed. - Elastic Limit: Maximum stress a material can withstand without permanent deformation. Beyond this point, material undergoes plastic deformation (does not return to original shape). - Stress: Deforming force per unit area. Formula: $σ = \frac{F}{A}$ (units: Pa or N/m²) - Strain: Ratio of change in dimension to original dimension (dimensionless, no units). For length: $ε = \frac{ΔL}{L}$ - Hooke's Law: Within the elastic limit, extension (or compression) of a spring is directly proportional to the applied force. Formula: $F = -kx$ (negative sign indicates restoring force opposite to displacement) - Spring constant (k): Measure of spring stiffness. Formula: $k = \frac{F}{x}$ (units: N/m). Stiffer springs have larger k values. - When a spring is cut: The spring constant increases (each piece becomes stiffer) - Force-extension graph: Straight line through origin within elastic limit (slope = k). Beyond elastic limit, graph becomes curved (non-linear) and permanent deformation occurs. These notes are strictly aligned with the Student Learning Outcomes (SLOs) for the FBISE 2026 annual examination.

• What is pressure and how does it vary in liquids and atmosphere? Define pressure as force per unit area (P = F/A) with units Pascal (Pa = N/m²), and explain how liquid pressure varies using P = ρgh (depends on depth, density, and gravitational acceleration), and how atmospheric pressure varies with altitude (decreases as height increases due to less air above).
• What is a barometer and how does it work? Describe the construction and working of a mercury barometer (glass tube filled with mercury inverted into mercury reservoir, height of mercury column indicates atmospheric pressure, about 76 cm or 760 mmHg at sea level), and its applications in weather forecasting (high pressure = clear skies, low pressure = storms) and altitude measurement.
• What is Pascal's law and how does it apply to hydraulic systems? State Pascal's law (pressure applied to enclosed fluid is transmitted equally to all parts of the fluid and container walls), and explain its application in hydraulic systems including hydraulic lifts and hydraulic brakes as force multipliers using the formula F₂ = F₁ × (A₂/A₁) or F₁/A₁ = F₂/A₂.
• What is elasticity, stress, strain, and Hooke's law? Define elasticity (ability to return to original shape after deforming force removed), elastic limit (maximum stress without permanent deformation), stress (σ = F/A), strain (ε = ΔL/L), and apply Hooke's law (F = -kx) within elastic limit, including calculation of spring constant (k = F/x) and interpretation of force-extension graphs.

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