Mechanics Chapter 8 Modelling in Mechanics Flashcards
What are the modelling assumptions for a particle (negligible dimensions)?
- mass of the object is concentrated at a single point
- rotational forces and air resistance can be ignored
What are the modelling assumptions for a rod (all dimensions but 1 are negligable)?
- mass is concentrated along a line
- no thickness
- rigid (doesnt bend)
What are the modelling assumptions for a lamina (object with area but negligable thickness, like a sheet of paper)?
- mass is distributed across a flat surface
What are the modelling assumptions for a uniform body (mass is distributed evenly)?
- mass of the object is concentrated at a single point at the geometrical centre of the body (the centre of mass)
What are the modelling assumptions for a light body (mass of the object is small compared to other masses)?
- treat object as having zero mass
- tension is the same at both ends of a light string
What are the modelling assumptions for an inextensible string (does not stretch under load)?
- acceleration is the same in objects connected by a taut inextensible string
What are the modelling assumptions for a smooth surface?
- assume there is no friction between the surface and any object on it
What are the modelling assumptions for a rough surface (if a surface is not smooth it is rough)?
- objects in contact with the surface experience a frictional force if they are moving or are acted on by a force
What are the modelling assumptions for a wire (rigid thin length of metal)?
- treated as one-dimensional
What are the modelling assumptions for a smooth and light pulley?
- pulley has no mass
- tension is the same on either side of the pulley
What are the modelling assumptions for a bead (particle with a hole in it for threading on a wire or a string)?
- moves freely along a wire or string
- tension is the same on either side of the bead
What are the modelling assumptions for a peg (a support from which a body can be suspended or rested)?
- dimensionless and fixed
- can be rough or smooth as specified in the question
What are the modelling assumptions for air resistance?
- usually modelled as being negligable
What are the 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 9.8 m s-2 unless otherwise stated in the question
What is the unit for mass?
kilogram, kg
What is the unit for length/displacement?
metre, m
What is the unit for time?
seconds, s
What is the unit for speed/velocity?
metres per second, m s-1
What is the unit for acceleration?
metres per second per second, m s-2
What is the unit for weight/force?
newton, N
At which direction does the weight act?
vertically downwards
At which direction does the normal reaction force act?
perpendicular to a surface when an object is in contact with the surface
At which direction does the frictional force act?
opposing to the motion between two rough surfaces
At which direction does the tension force act?
if an object is being pulled along by a string, the force acting on the object is the tension
At which direction does the thrust act?
if an object is being pushed, the force acting on it is called the thrust or compression
At which direction does the buoyancy act?
upwards if an object is submerged in liquid
At which direction does the air resistance act?
opposing motion
What is a vector?
a quantity with both magnitude and direction
What are examples of vector quantaties?
Displacement, velocity, acceleration, force/weight
What is a scalar quantity?
a quantity with only magnitude
What are examples of a scalar quantity?
Distance, speed, time, mass
Are scalar quantities always positive or negative?
Positive
What is distance equivalent to?
The magnitude of the dispacement vector
What is speed equivalent to?
The magnitude of the velocity vector
