Understanding Mechanics

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Description

Contents

Reviews

Language

English

ISBN

9781382018197

Front Cover

IFC

Title Page

Preface

Contents

1 Vectors

Resultant of vectors

Vector representation

Unit vectors

Addition of vectors

The magnitude of a vector

Resolving a vector

Scalar product

Scalar product from vectors in component form

2 Distance, velocity and acceleration

Constant speed and constant velocity

Average speed

i–j notation

Uniform acceleration formulae

Free fall under gravity

Graphical representation

Setting up a mathematical model of a real situation

3 Force and Newton’s laws

Newton’s First Law

Newton’s Second Law

Newton’s Third Law

Connected particles

Pulley systems

4 Resultants and components of forces

Resultant of two forces

Parallelogram of forces

Resultant of any number of forces

Components

Resultant from sum of components

5 Equilibrium and acceleration under concurrent forces

Triangle of forces

Polygon of forces

Three forces in equilibrium: solution by calculation

Lami’s Theorem

Particle in equilibrium under more than three forces: solution by calculation

Systems involving more than one particle

Motion of a particle on a plane

6 Friction

Rough and smooth surfaces

Limiting eqilibrium

Coefficient of friction

Laws of friction

Rough inclined plane

Angle of friction

7 Moments

Moment of a force

Parallel forces and couples

Replacement of parallel forces by a single force

Parallel forces in equilibrium

Non-parallel forces in equilibrium

Equivalent systems of forces

8 Centre of gravity

Attraction of the Earth

Centre of gravity of a system of particles

Centre of gravity of a rigid body

Composite laminae

Standard results

Toppling

Equilibrium of a suspended lamina

Use of calculus

Solids of revolution

9 General equilibrium of a rigid body

Three forces

General method

Ladder problems

10 Resultant velocity and relative velocity

Resultant velocity

Components of velocity

The modelling process

Relative velocity

True velocity

Interception and collision

Closest approach

Course for closest approach

11 Work, energy and power

Work done by a constant force

Work done against gravity

Work done against gravity and friction

Energy

The Principle of Conservation of Energy

Equivalence of work and energy

Work done by a force acting in a direction different to that of the motion of the body

Power

Pump raising and ejecting water

Vehicles in motion

12 Projectiles

Horizontal projection

Modelling real objects as “particles”

Particle projected at an angle to the horizontal

Symmetrical path

General results

Equation of trajectory

Projectile on an inclined plane

13 Circular motion

Radians

Linear and angular speed

Motion on a circular path

Conical pendulum

Motion of a car rounding a banked curve

Motion of a train rounding a banked curve

Motion in a vertical circle

Conditions for a particle to perform complete circles

14 Momentum and impulse

Momentum

Changes in momentum

Impulse

Force on a surface

Impact

Loss of energy

Recoil of a gun

15 Elasticity

Elastic strings

Hooke’s Law

Elastic springs

Potential energy stored in an elastic string

Elastic impact

Impact with a surface

16 Use of calculus

Acceleration as a function of time

Motion in the i–j plane

Motion in i–j–k space

Velocity as a function of displacement

Acceleration as a function of displacement

Acceleration as a function of velocity

Variable force

Resisting medium

Motion under gravity

Appendix of useful standard integrals

Further examples

Work done by a variable force

Variable force acting along a curved path

17 Simple harmonic motion

Circular representation of SHM

Springs and SHM

More examples involving strings

The simple pendulum

18 Compound bodies and frameworks

Jointed rods in equilibrium

Further examples

Light rods

Answers

Index

IBC

Back Cover

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