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Notes by Category University Engineering

Electronics*
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Mechanics & Stress Analysis*
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  • A-Level Maths

Modelling in Mechanics

The real world of mechanics is incredibly complicated, with hundreds of different factors affecting motion and stability. This would be near impossible to calculate at this stage, so to simplify it we model objects and scenarios in a number of different ways.


Modelling Assumptions

Particle

  • Has negligible dimensions

  • Mass acts about a single point

  • Rotational forces and air resistance can be ignored

Rod

  • The diameter is negligible (so no thickness), only length counts

  • Mass acts along a line

  • It is rigid, so does not bend or buckle

Lamina

  • An object with only area, thickness is negligible (like a sheet of paper)

  • Mass acts across the flat surface

Uniform Body

  • The Mass is distributed evenly throughout the object

  • The mass is modelled to act through one point, the centre of mass, in the geometrical middle of the body

Light Object

  • The mass of the object is negligible

  • Often used for strings or pulleys

  • Allows us to model the tension on each end of a string as equal

Inextensible String

  • A string that does not stretch when a force is applied

  • Allows us to model the acceleration of two connected particles as the same

Smooth Surface

  • There is no friction between the surface and any object on it


Rough Surface

  • There is friction between the surface and any object on it

Wire

  • A rigid length of metal with negligible thickness (only modelled with length)

Smooth and Light Pulley

  • The pulley has no mass

  • No friction in the pulley, so tension is the same either side of it

Bead

  • A particle with a hole in it for string/wire to be threaded through