# Mechanics - Models > Source: https://ollybritton.com/notes/a-level/maths/topics/mechanics/models/ · Updated: 2020-09-08 · Tags: ankify, school, mechanics, year-1 # Models ##### What is a model?? A model is a simplified representation of a physical situation, made by accepting assumptions. ##### What's an example of a common assumption?? * No air resistance * Constant gravity * Uniform mass ##### What two questions need to be asked when setting up a mathematical model?? * What are your assumptions? * What are the variables? ##### If the answer presented by a mathematical model is unreasonable, what should be done?? You should reconsider your assumptions. ## Modelling Assumptions ##### When should a _particle_ model be used?? When the dimensions of an object don't matter. ##### What are the two modelling assumptions for a _particle_?? * mass of the object is concentrated at a single point * rotational forces and air resistance can be ignored ##### How is mass thought of in a _particle_ model?? Concentrated at a single point. ##### Should air resistance be taken into account using a _particle_ model?? No. ##### Should rotational forces be taken into account using a _particle_ model?? No. ##### Should gravity be taken into account using a _particle_ model?? Yes. ##### When should a _rod_ model be used?? When all dimensions of an object except one don't matter, like a pole or a beam. ##### What are the three modelling assumptions for a _rod_?? * mass is concentrated along a line * no thickness * rigid (does not bend or buckle) ##### How is mass thought of in a _rod_ model?? Concentrated along a line. ##### How is thickness thought considered in a _rod_ model?? There is no thickness. ##### How is rigidity considered in a _rod_ model?? The rod is completely rigid, it does not bend or buckle. ##### How many dimensions do you care about when using a rod?? 1. ##### When should a _lamina_ model be used?? When the object has a surface area, but negligible thickness, like a sheet of paper. ##### What is the modelling assumption for a _lamina_?? * mass is distributed across a flat surface ##### How is mass thought of in a _lamina_ model?? As distributed across a flat surfae. ##### When is an object said to be a _uniform body_?? When the mass is distributed evenly. ##### How is mass considered in a _uniform body_?? As concentrated at a single point at the geometrical centre of the body, the centre of mass. ##### In a _uniform body_, where is the centre of mass?? At the geometric centre of the body. ##### When is an object said to be a _light object_ in mechanics?? When the mass of the object is small compared to the other masses, like a string or a pulley. ##### What modelling assumption can you make for a _light object_?? That it has no mass. ##### When a string is a _light object_, what can be said about the tension along the string?? That it is the same at both ends of the string. ##### What is the _inextensible string_ model?? A string that does not stretch under load. ##### What modelling assumption can be made for an _inextensible string_?? Acceleration is the same in objects connected by a tight inextensible string. ##### What can be said about the acceleration for objects at the end of a tight inextensible string?? It is constant, i.e. they cannot stretch the string and slow down. ##### When should a _smooth surface_ model be used?? When the surface in question is smooth, like ice. ##### What is the modelling assumption for a _smooth surface_?? There is no friction between the surface and any objects on it. ##### When should a _rough surface_ model be used?? When the surface is not smooth, like tarmac. ##### What modelling assumption do you make for a _rough surface_?? Objects on the surface experiece friction when: * They are moving * They are being acted on by another force ##### When should a _wire_ model be used?? To represent a rigid, thin length of metal. ##### What is the modelling assumption for a _wire_?? The object is one dimensional. ##### In mechanics A-level, what assumption do we make about all pulleys?? That they are smooth and light. ##### What two modelling assumptions do you make for a _smooth and light pulley_?? * Pulley has no mass * Tension is the same on either side of the pulley ##### What is a _bead_ model?? A particle with a hole in it for threading on a wire or a string. ##### What two modelling assumptions do you make for _beads_?? * Moves freely along a wire or a string * Tension is the same on either side of the bead ##### What is air resistance?? Friction or resistance experienced as an object moves through the air. ##### What usually occurs when modelling air resistance?? It is treated as negligible and not accounted for. ##### What is gravity?? A force of attraction between all objects. ##### What is the symbol for acceleration due to gravity?? $g$ ##### What does the symbol $g$ mean in mechanics?? The acceleration due to gravity. ##### What is the value of $g$ in mechanics?? $9.8ms^{-2}$ ##### What is the value of $g$ in physics?? $9.81ms^{-2}$ ##### What two assumptions do we make about gravity in mechanics?? * Gravity is uniform across the Earth's surface * Gravity acts vertically downwards --- Olly Britton — https://ollybritton.com. 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