Modelling Assumptions (AQA A Level Maths: Mechanics): Revision Note
Exam code: 7357
Modelling assumptions
What is modelling in Mechanics?
Mechanics uses modelling to solve problems in real life situations
We use assumptions to simplify real life problems in order to turn them into equations or graphs that can be solved
We will sometimes need to criticise or refine our assumptions to improve the model
What is a modelling assumption?
There are many different modelling assumptions that can be made to simplify real life situations
Different assumptions will be needed for different models
The assumptions you make will affect the calculations in each problem differently
What types of modelling assumptions do I need to know?
Gravity is constant and acts vertically downwards
Air resistance is usually modelled as negligible and can be ignored
A smooth surface has no friction
A rough surface has a frictional force between the surface and any object that makes contact with it
A particle has negligible dimensions, therefore forces will all act on a particle at the same point
A rod or a beam has negligible thickness bit not negligible length, it is rigid and its mass lies along a line
A uniform object’s mass is distributed evenly
A light object has zero mass
An inextensible object cannot be stretched
Worked Example
Two blocks, A and B are attached by means of a light inextensible string running over a smooth pulley. Block A has mass 0.7 kg and is accelerating along a smooth horizontal surface, block B has a mass 0.2 kg. Both A and B are modelled as particles. State how the following modelling assumptions can be used in your calculations.
(a) A and B are both particles.
(b) The string is light.
(c) The string is inextensible.
(d) The pulley is smooth.
(e) The surface A is moving along is smooth.
Answer:
(a)
Modelling an object as a particle means its size and shape are ignored, so all of its mass is treated as being at a single point
The dimensions of A and B can be ignored, so all the forces on each block act at a single point and there is no rotation
This does not remove air resistance: ignoring air resistance is a separate modelling assumption
(b)
A light string has zero mass
The tension is the same throughout the string, so it is the same at A and at B
(c)
An inextensible string cannot stretch
A and B move with the same speed and the same acceleration
(d)
A smooth pulley has no friction
The tension in the string is the same on both sides of the pulley
(e)
A smooth surface has no friction
There is no frictional force between block A and the surface
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