Ch.8 Modelling in mechanics Flashcards
what axis does the unit vector i travel along?
x
what axis does the unit vector j travel along?
y
what are the 3 base SI units commonly used in mechanics?
- Mass, kilogram, kg
- Length/displacement, metre, m
- Time, second, s
what is a vector quantity?
(mech)
a quantity with both magnitude and direction
what is a scalar quantity?
a quantity with no direction, only magnitude
what are some examples of scalar quantities?
distance and speed
what is a particle model?
an object with negligible dimensions
what are the modelling assumptions made when an object is modelled as a particle?
- the mass of the object is concentrated at a single point
- rotational forces and air resistance can be ignored
what is the rod model?
all dimensions but one are negligible, like a pole or beam
what are the modelling assumptions made when something is modelled as a rod?
- mass is concentrated along a line
- it has no thickness
- it is rigid ( does not bend or buckle )
what is a lamina model?
an object with area but negligible thickness, like a sheet of paper
what are the modelling assumptions made when something is modelled as a lamina?
- it’s mass is distributed across a flat surface
what does uniform body mean in math modelling?
the mass is distributed evenly
what are the modelling assumptions made when something is modelled with a uniform body?
the mass of the object is concentrated at a single point ar the geometrical centre of the body - the centre of mass
what is a light object model?
when the mass of the object is small compared to other masses, like a string or pulley
what are the assumptions made with a light object model?
- treat object as having zero mass
- tension is the same at both ends of a light string
what is an inextensible string model?
a string that does not stretch under load
what is the assumption made with an inextensible string model?
acceleration is the same in objects connected by a taut inextensible string
what is the assumption made with a smooth surface in mechanical modelling?
assume that there is no friction between the surface and any object on it
what is the assumption with a rough surface in mechanical modelling?
objects in contact with the surface experience a frictional force when moving
what is a wire model?
a rigid thin length of metal
what is the modelling assumptions with a wire model?
it is treated as one dimensional
what are the modelling assumptions with a smooth and light pulley?
- the pulley has no mass
- tension is the same on either side of the pulley
what is the bead model?
a particle with a hole in it for threading on a wire or string
