Chapter 8 - Modelling in Mechanics Flashcards
Particle:
Dimensions of the object are negligible
Modelling assumptions of a particle:
- Mass of the object is concentrated at single point
- Rotational forces and air resistance can be ignored
Rod:
All dimensions but one are negligible, like a pole or a beam
Modelling assumptions of a rod:
- Mass is concentrated along a line
- No thickness
- Rigid (does not bend or buckle)
Lamina:
Object with area but negligible thickness, like a sheet of paper
Modelling assumptions of a lamina:
- Mass is distributed across a flat surface
Uniform body:
Mass is distributed evenly
Modelling assumptions for a uniform body:
- Mass of the object is concentrated at a single point at the geometrical centre of the body - the centre of mass
Light object:
Mass of the object is small compared to other masses, like a string or a pulley
Modelling assumptions of a light object:
- Treat the object as having zero mass
- Tension the same at both ends of a light string
Inextensible string:
A string that does not stretch under load
Modelling assumptions of an inextensible string:
- Acceleration is the same in objects connected by a taut inextensible string
Modelling assumptions of a smooth surface:
- Assume that there is no friction between the surface and any object on it
Rough surface:
If a surface is not smooth, it’s rough
Modelling assumptions of a rough surface:
- Objects in contact with the surface experience a frictional force if they are moving or are acted on by a force
Wire:
Rigid thin length of metal
Modelling assumptions of a wire:
- Treated as one-dimensional
Smooth and light pulley:
All pulleys you consider will be smooth and light
Modelling assumptions of a smooth and light pulley:
- Pulley has no mass
- Tension is the same on either side of the pulley
Bead:
Particle with a hole in it for threading on a wire or a string
Modelling assumptions for a bead:
- Moves freely along a wire or string
- Tension is the same on either side of the bead
Peg:
A support from which a body can be suspended or rested
Modelling assumptions of a peg:
- Dimensionless and fixed
- Can be rough or smooth (specified in question)
Air resistance:
Resistance experienced as an object moves through the air
Modelling assumptions for air resistance:
- Usually modelled as being negligible
Gravity:
Force of attraction between all objects. Acceleration due to gravity is denoted by g. g = 9.8ms-2
Modelling assumptions for gravity:
- 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 9.8ms-2, unless otherwise stated in the question
SI Units
gravitational force vs normal reaction
Friction:
Friction is a force which opposes the motion between two rough surfaces
Tension:
If an object is being pulled along by a string, the force acting on the object is called the tension in the string
Thrust/Compression:
If an object is being pushed along using a light rod, the force acting on the object is called the thrust or compression in the rod
Buoyancy:
Buoyancy is the upward force on a body that allows it to float or rise when submerged in a liquid
Air resistance (in a force diagram):
Air resistance opposes motion
What is a vector quantity?
A vector is a quantity which has both magnitude and direction
What is a scalar quantity?
A scalar quantity has magnitude only
Vector quantities:
Scalar quantities:
Magnitude (length)
- Distance is the magnitude (length) of the displacement vector
- Speed is the magnitude (length) of the velocity vector
How can you describe vectors?
You can describe vectors using i, j notation, where i and j are positive 1 unit vectors in the x and y direction respectively
