Understanding Mechanics
$56.25

Understanding Mechanics

By Thorning, Sadler
US$ 56.25
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Book Description

One of the clearest and most straightforward texts ever published, Understanding Mechanics covers all the topics required in the single-subject A Level.

It is equally appropriate for those preparing for other Mathematics examinations at A Level and for students on technical courses in further and higher education.

Table of Contents
  • 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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