Stats & Mechs - Chapter 8: Modelling Assumptions Flashcards
Particle Model
Dimensions of the object are negligible
Particle Modelling Assumptions
- Mass of the object is concentrated at a single point
- Rotational forces and air resistance can be ignored
Rod Model
All dimensions but one are negligible, like a pole or a beam.
Rod Model Assumptions
- Mass is concentrated along a line
- No thickness
- Rigid (doesn’t bend)
Lamina Model
Object with area but negligible thickness, like a sheet of paper
Lamina Modelling Assumptions
- Mass is distributed across a flat surface
Uniform Body Model
Mass is distributed evenly
Uniform Body Model Assumptions
- Mass of the object is concentrated at a single point at the geometrical centre of the body - the centre of mass
Light object Model
Mass of the object is small compared to other masses, like a string or a pulley
Light object Model Assumptions
- Treat object as having zero mass
- tension the same at both ends of a light string
Inextensible string Model
A string that does not stretch under load
Inextensible string Model Assumptions
- Acceleration is the same in objects connected by a taut inextensible string.
Smooth Surface Model Assumptions
- Assume that there is no friction between the surface and any object on it.
Rough Surface Model
If a surface is not smooth, it is rough
Rough Surface Model Assumptions
- Objects in contact with the surface experience a frictional force if they are moving or are acted on by a force
Wire Model
Rigid thin length of metal
Wire Model Assumptions
- Treated as one dimensional
Smooth and light pulley Model
A pulleys you consider will be smooth and light
Smooth and light pulley Model Assumptions
- Pulley has no mass
- Tension is the same on either side of the pulley
Bead Model
Particle with a hole in it for threading on a wire or string
Bead Model Assumptions
- Moves freely along a wire or string
- Tension is the same on either side of the bead
Peg Model
A support from which a body can be suspended or rested
Peg Model Assumptions
- Dimensionless and fixed
- Can be rough or smooth as specified in question
Air resistance Model
Resistance experienced as an object moves through the air
Air resistance Model Assumptions
- Usually modelled as being negligible
Gravity Model
Force of attraction between all objects. Acceleration due to gravity is denoted by g
Gravity Model Assumptions
- Assume that all objects with mass are attracted towards the Earth
- Earth’s gravity is uniform and acts vertically downwards
- g is constant and is taken as 9.8 ms^-2, unless otherwise stated in the question
