Non-uniform Objects & Other Problems (Edexcel International A Level Maths) : Revision Note

Non-unform Objects & Other Problems

What is meant by a non-uniform lamina/framework?

• Strictly speaking a non-uniform lamina would be one that has different densities at different points on its surface and a non-uniform framework would be one that is made from rods/wires that have different densities along their lengths.

  • e.g. a plank of wood (timber) may have knots in places on its surface

• However, for the problems you encounter in IAL Mechanics 2 non-uniform means each individual lamina making a composite lamina may be of a different density but each individual lamina is uniform

• Similarly, for a framework, each individual rod/wire will be uniform, but the framework may be made from rods/wires of different densities.

What other problems may I encounter in IAL Mechanics 2 (M2)?

• Non-uniform problems

  • Non-uniform (composite) laminas may be created by having uniform laminas overlapping each other or by taking part of a lamina and folding it back upon itself

  • Non-uniform frameworks would be made from rods/wires that have different (but related) densities or thickness

  • The relationship between the different densities will be explained in a question

    • e.g. part of a (uniform) lamina folded back on itself creates an area of double density

    • e.g. one cable in a framework is twice the thickness of the others

  • In solving problems remember, due to uniformity, we use can use area (laminas) and length (frameworks) rather than mass – so if we have double density, we double the area/length where necessary

• Another type of problem is where a lamina or a framework have an object (or masses) attached to them.

  • This will affect the position of the centre of mass of the lamina or framework

    • e.g. a framework made from metal rods could be holding up spotlights above a stage and so have lights (masses) attached to some (or all) rods

• Problems may involve laminas or frameworks being suspended by more than one string to keep them in a particular position

  • e.g. A sign hanging from a ceiling that needs to be pointing directly left

  • Such problems normally involved finding the position of the centre of mass and/or the tension in the strings, using skills from various parts of the mechanics course