Modelling Assumptions (Edexcel International A Level Maths: Mechanics 1)

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 types of modelling assumptions are there?

• Gravity is constant and vertical 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 should be treated as a long, rigid particle
• A uniform object’s mass is distributed evenly
• A light object has zero mass
• An inextensible object cannot be stretched

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.