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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