CIE A Level Maths: Mechanics复习笔记1.1.5 Modelling Assumptions

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

1.1.5-Modelling-Assumptions-Diagram-2

Modelling Assumptions in Mechanics:

  • There are many different modelling assumptions that can be made when dealing with 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 are there?

  • Gravity is constant and vertical
  • Air resistance is usually modelled as negligible and can be ignored
  • smooth surface has no friction
  • rough surface has a frictional force between the surface and any object that makes contact with it
  • particle has negligible dimensions, therefore forces will all act on a particle at the same point
  • rod or a beam should be treated as a long, rigid particle
  • uniform object’s mass is distributed evenly
  • light object has zero mass
  • An inextensible object cannot be stretched

Worked Example

1.1.5_WE_Modelling-Assumptions_1

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.

1-1-5-worked-example-solution

Exam Tip

  • Make sure you fully understand the definitions of all the words in this section so that you can be clear about what your exam question is asking of you.

 

 

 

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