$60.57

# Understanding Mechanics

By Thorning, Sadler

US$ 60.57

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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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