Class 9 Physics Chapter 6 Complete Guide Book — Mechanical Properties of Matter | PunjabTest.com

A deforming force changes a body's size or shape. Elastic materials regain their original form when the force is removed, up to the elastic limit; beyond it the deformation becomes permanent. Clay and plasticine are inelastic (they stay deformed).

Hooke's law: within the elastic limit, extension is directly proportional to the applied force: F = kx, where k is the spring constant (stiffness) = F ÷ x, equal to the slope of a force–extension graph. Example: a 40 N load stretching a spring 20 mm gives k = 40 ÷ 0.020 = 2000 N m⁻¹ (2 kN m⁻¹); a 16 mm extension then needs F = 2000 × 0.016 = 32 N. Springs are made of steel, not iron, because steel is more elastic (higher elastic limit, returns to shape reliably).

Which is more elastic? Iron is more elastic than rubber (rubber stretches more but has a lower modulus — elasticity means regaining shape, and stiffness matters); water is more elastic than air (its bulk modulus is far larger — air compresses easily).

Density ρ = mass ÷ volume (unit kg m⁻³). Density is a property of the material, not of the object made from it: a small and a large piece of the same material have the same density, though their masses differ.

Examples: 5 litres of milk (0.005 m³) of mass 4.5 kg has density 4.5 ÷ 0.005 = 900 kg m⁻³ (0.9 × 10³ kg m⁻³). A 60 g solid displacing water from 40 cm³ to 44 cm³ has volume 4 cm³ and density 60 ÷ 4 = 15 g cm⁻³ = 15 × 10³ kg m⁻³. A block of density 8 × 10³ kg m⁻³ and volume 60 cm³ has mass 8 × 10³ × 60 × 10⁻⁶ = 0.48 kg.

Pressure P = F ÷ A (unit pascal, Pa = N m⁻²). Force vs pressure: force is a push/pull (N); pressure is force per unit area — the same force gives more pressure on a smaller area. That is why heavy animals like elephants have large feet (spreading weight lowers pressure), fast animals like deer have small feet (higher pressure for grip/push), and walking barefoot on pebbles hurts (tiny contact area → huge pressure).

Liquid pressure P = ρgh: it depends on the liquid's density, the depth, and g — not on the container's size or shape. So water pressure 1 m below the surface is the same in a swimming pool and in a very large deep lake. At the same depth, two plates of areas 2 m² and 3 m² feel the same pressure — ratio 1:1. The pressure at any point in a liquid is proportional to density, depth and g — all of the above.

Pascal's law: pressure applied at one point in an enclosed fluid is transmitted unchanged to every part of the fluid and the walls of the container. If pressure is increased in one part of a confined liquid, it increases equally everywhere.

Applications: hydraulic press, hydraulic brakes, car lifts at service stations. In a hydraulic brake, a 500 N force on a 5 cm² piston gives pressure 500 ÷ (5 × 10⁻⁴) = 1.0 × 10⁶ N m⁻², transmitted to a 20 cm² piston giving force 1.0 × 10⁶ × 20 × 10⁻⁴ = 2000 N — force multiplied by the area ratio. A hydraulic press lifting a 4000 N car with a 10 cm² small piston needs only 400 N if the large piston is 100 cm². If pressure rises by an extra 10 N cm⁻² on a 50 cm² platform, the extra load supported is 500 N. The basic principle of hydraulic brakes is Pascal's law.

Pressure ideas explain many everyday things. A giraffe raising its long neck suddenly is not harmed because valves in its neck veins stop blood flowing back, and its strong heart and elastic arteries manage the large pressure changes. Engineers estimate a large structure's load by its total weight (dead load + live load) spread over the foundation area — the pressure on the ground must stay below what the soil can bear, so heavy buildings get wide foundations.

Hot-air balloon graph (book's problem): plotting altitude against pressure shows pressure falling with height; extending the line back to sea level (0 m) gives about 1.01 × 10⁵ Pa, and the height where pressure is 90 kPa is about 1.02 km. Deep-sea diver at 10 m in seawater (ρ = 1030 kg m⁻³): P = ρgh = 1030 × 10 × 10 = 1.03 × 10⁵ N m⁻² (gauge pressure, besides atmospheric pressure).