 \$56.25

# Understanding Mechanics

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.

• Front Cover
• IFC
• Title Page
• Preface
• Contents
• 1 Vectors
• Resultant of vectors
• Vector representation
• Unit 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
• 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
• 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
• Index
• IBC
• Back Cover
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