9th Class Physics Chapter 6 Mechanical Properties of Matter Long Questions

Question 1

What is Hooke's law? Give three applications of this law.

Accepted Answer

Statement Hooke's law: Within the elastic limit, the extension (or compression) of a spring is directly proportional to the applied force. F ∝ x, so F = kx Spring constant: k = F ÷ x, the force per unit extension; SI unit N m⁻¹. Graph Applications Spring balance: the extension of the spring is a measure of the weight hung on it, read by a pointer on a scale. In a compression balance the load squeezes the spring instead.; Balance wheel of a mechanical clock: a fine spring makes the wheel swing back and forth regularly, controlling the speed of the hands.; Galvanometer: a hair spring brings the pointer back to zero; the deflection is proportional to the current. k = 40 ÷ 0.02 = 2000 N m⁻¹. so a 16 mm stretch means 2000 × 0.016 = 32 N

Question 2

Describe the working and applications of a simple mercury barometer and a manometer.

Accepted Answer

Mercury barometer: construction A glass tube about 1 m long, closed at one end, is filled with mercury and turned upside down in a dish of mercury. The mercury falls until its column is about 76 cm high, leaving a vacuum above it. A scale beside the tube measures the height. Working Point A in the tube and point B on the open surface are at the same level, so they have the same pressure. At B the pressure is atmospheric; at A it is the pressure of the mercury column. So atmospheric pressure = ρgh. At sea level, with P = 1.013 × 10⁵ Pa and ρ = 13.6 × 10³ kg m⁻³, h is about 760 mm. Uses of the barometer Measuring atmospheric pressure, for weather forecasting.; Finding altitude, because pressure falls with height. Manometer A U-tube containing mercury. With both ends open, the levels are equal. A gas supply is connected to one arm and the other is left open. If the mercury in the gas arm is lower (fig. a), the gas pressure is more than atmospheric by ρgh.; If it is higher (fig. b), the gas pressure is less than atmospheric by ρgh. A barometer measures atmospheric pressure; a manometer measures the pressure of a gas compared with it.

Question 3

Describe Pascal's law. State its applications with examples.

Accepted Answer

Statement Pascal's law: Pressure applied at one point of an enclosed fluid is transmitted equally, without loss, to all parts of the fluid. Hydraulic press A force F₁ on the small piston gives a pressure P = F₁ ÷ A₁.; This pressure reaches the large piston unchanged, so F₂ = P × A₂ = F₁ × (A₂ ÷ A₁).; Since A₂ > A₁, F₂ > F₁: the press is a force multiplier. F₂ = F₁ × A₂ ÷ A₁ Cotton bales or metal sheets placed on the large piston are pressed against a fixed plate. The same idea lifts cars at service stations. Hydraulic brakes The brake pedal pushes the small piston of the master cylinder, which is full of brake oil.; The pressure travels through the brake lines to the larger pistons of the wheel cylinders.; These push the brake pads against the discs (or drums); friction slows the wheels.; When the pedal is released, springs pull the pads back. Because the pressure is the same everywhere, all four wheels are braked equally.

Question 4

On what factors does the pressure of a liquid in a container depend? How is it determined?

Accepted Answer

Liquid pressure A liquid presses on everything in it, in all directions, and the pressure increases with depth. Diagram Derivation Consider an area A at depth h. The liquid above it forms a column of volume V = Ah.; Mass of the column: m = ρV = ρAh.; Force on A = weight of the column: F = mg = ρAhg.; Pressure: P = F ÷ A = ρAhg ÷ A. P = ρgh Factors Depth h: the deeper the point, the greater the pressure.; Density ρ: a denser liquid gives more pressure at the same depth.; g: the gravitational field strength. It does not depend on the shape of the container or the area of the surface. P = 1030 × 10 × 10. 1.03 × 10⁵ Pa

Question 5

Explain that the atmosphere exerts pressure. What are its applications? Give at least three examples.

Accepted Answer

Atmospheric pressure The Earth is covered by a layer of air. Air molecules move randomly and keep striking every surface; these collisions produce a force on each unit of area, which is atmospheric pressure. Because the motion is random, it acts equally in all directions. At sea level it is about 1.013 × 10⁵ Pa. Experiment: the collapsing can Boil a little water in a tin can so that steam drives out the air.; Close the can tightly and cool it with cold water.; The steam condenses, so the pressure inside becomes very low.; The atmospheric pressure outside, now much larger, crushes the can. Applications Barometer: measures atmospheric pressure by the height of mercury it holds up.; Weather forecasting: changes in pressure signal changes in the weather.; Altimeter: pressure falls with height, so it tells the altitude.; Tyre pressure gauge: measures the air pressure in tyres.; Straws and syringes: atmospheric pressure pushes the liquid in when the pressure inside is lowered. We do not feel the atmosphere crushing us because the pressure of the fluids inside our bodies balances it.

Question 6

Define density. How would you find the density of (a) a regular solid (b) an irregular solid (c) a liquid?

Accepted Answer

Definition Density: Mass per unit volume: ρ = m ÷ V. SI unit kg m⁻³. (a) Regular solid Measure the mass on a balance.; Measure the length, breadth and height with a ruler or vernier callipers; volume = l × b × h.; ρ = m ÷ V. (b) Irregular solid Measure the mass on a balance.; Put water in a measuring cylinder and note the level V₁.; Lower the solid in on a thread and note the new level V₂.; Volume = V₂ − V₁; ρ = m ÷ (V₂ − V₁). (c) Liquid Find the mass of an empty beaker.; Pour in a measured volume of liquid from a measuring cylinder and find the new mass.; Mass of liquid = difference; ρ = mass ÷ volume. V = 4 cm³; ρ = 60 ÷ 4 = 15 g cm⁻³. 15 × 10³ kg m⁻³

Question 7

What is pressure? Explain how pressure depends on area, with examples where it is increased and where it is decreased.

Accepted Answer

Definition Pressure: The force acting normally per unit area: P = F ÷ A. SI unit: pascal (1 Pa = 1 N m⁻²). It is a scalar. Pressure and area For the same force, P ∝ 1/A: a smaller area gives a larger pressure. Where a large pressure is wanted Knives, needles and nails are sharp.; Football boots have studs; deer have small hooves. Where a small pressure is wanted School bags have wide straps.; Tractors have broad tyres; tanks have tracks.; Elephants have large feet; foundations of buildings are wide. Smallest face: 50 ÷ (50 × 10⁻⁴) = 1.0 × 10⁴ Pa. Largest face: 50 ÷ (200 × 10⁻⁴) = 2.5 × 10³ Pa. the same brick gives four times the pressure on its smallest face

Question 8

Describe an experiment to verify Hooke's law and to find the spring constant of a spring.

Accepted Answer

Apparatus A spring hung from a stand; A metre rule fixed beside it; A pointer at the bottom of the spring; Slotted weights of 1 N each Method Note the position of the pointer with no load.; Add 1 N and note the new reading; the difference is the extension x.; Add weights one by one, noting x each time.; Remove the weights one by one and check the pointer returns to the same readings (the elastic limit has not been passed).; Plot force F against extension x. Result The graph is a straight line through the origin, so F ∝ x: Hooke's law is verified. Its slope gives k = F ÷ x. Precautions Do not overload the spring beyond its elastic limit.; Read the scale at eye level to avoid parallax.; Let the spring stop moving before taking a reading.

Question 9

Explain the hydraulic brake system of a car with a labelled diagram.

Accepted Answer

Principle Hydraulic brakes work on Pascal's law: pressure applied to an enclosed liquid is transmitted equally to all parts of it. Diagram Parts Brake pedal connected to the small piston of the master cylinder.; Brake lines (pipes) full of brake oil.; Wheel cylinders with larger pistons, attached to the brake pads. Working The driver presses the pedal; the master cylinder piston pushes on the oil.; The pressure is transmitted equally through the lines to every wheel cylinder.; The larger pistons push the brake pads against the discs with a large force.; Friction slows and stops the wheels. Releasing the pedal lets springs pull the pads back. Advantages All wheels are braked equally at the same moment.; A small push on the pedal gives a large braking force. Air in the brake lines is dangerous: air is compressible and would squash instead of passing on the pressure.

Question 10

Why is mercury used in a barometer? Find the height of a water barometer, and explain the effect of trapped air or a leak.

Accepted Answer

Why mercury It is very dense (13.6 × 10³ kg m⁻³), so the column is only about 76 cm tall.; It does not stick to glass and is easy to see.; It hardly evaporates, so the space above stays a near vacuum. A water barometer ρ(water) × g × h(water) = ρ(mercury) × g × h(mercury). h(water) = 13 600 × 0.76 ÷ 1000. about 10.3 m, far too tall to be practical Trapped air Air above the mercury pushes down on it, so the column is shorter and the reading is too low. A leak Air keeps entering until the pressure above the mercury equals atmospheric pressure; the mercury then falls to the dish level and the barometer stops working.

Question 11

Explain springs joined in series and in parallel. Derive their spring constants.

Accepted Answer

Single spring A load L stretches one spring by x, so its spring constant is k = L ÷ x. Diagram Series Each spring carries the whole load L, so each stretches by x.; Total extension = 2x.; k(series) = L ÷ 2x = k/2. Parallel The load is shared equally, L/2 on each.; Each, and so the pair, stretches by x/2.; k(parallel) = L ÷ (x/2) = 2k. Series, 2x, k/2, Softer; Parallel, x/2, 2k, Stiffer Car suspensions use springs side by side (parallel) to carry heavy loads with little stretch.

	Extension	Spring constant	Behaviour
Series	2x	k/2	Softer
Parallel	x/2	2k	Stiffer

Long Questions with Answers

Set A: Textbook comprehensive questions 5 questions

What is Hooke's law? Give three applications of this law.

Statement

Graph

Applications

Describe the working and applications of a simple mercury barometer and a manometer.

Mercury barometer: construction

Working

Uses of the barometer

Manometer

Describe Pascal's law. State its applications with examples.

Statement

Hydraulic press

Hydraulic brakes

On what factors does the pressure of a liquid in a container depend? How is it determined?

Liquid pressure

Diagram

Derivation

Factors

Explain that the atmosphere exerts pressure. What are its applications? Give at least three examples.

Atmospheric pressure

Experiment: the collapsing can

Applications

Set B: More important long questions 6 questions

Define density. How would you find the density of (a) a regular solid (b) an irregular solid (c) a liquid?

Definition

(a) Regular solid

(b) Irregular solid

(c) Liquid

What is pressure? Explain how pressure depends on area, with examples where it is increased and where it is decreased.

Definition

Pressure and area

Where a large pressure is wanted

Where a small pressure is wanted

Describe an experiment to verify Hooke's law and to find the spring constant of a spring.

Apparatus

Method

Result

Precautions

Explain the hydraulic brake system of a car with a labelled diagram.

Principle

Diagram

Parts

Working

Advantages

Why is mercury used in a barometer? Find the height of a water barometer, and explain the effect of trapped air or a leak.

Why mercury

A water barometer

Trapped air

A leak

Explain springs joined in series and in parallel. Derive their spring constants.

Single spring

Diagram

Series

Parallel

The rest of Chapter 6

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