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Mechanics (Model types and assumptions (Particle- dimensions of the object…
Mechanics
Model types and assumptions
Particle- dimensions of the object are negligible. Assumptions- mass of the object is concentrated at a single point
Rod- all dimensions but one are negligible. Assumptions- mass is concentrated along a line, no thickness, rigid
Lamina- object with area but negligible thickness. Assumptions- mass is distributed across flat surface
Uniform body- mass distributed evenly. Assumptions- mass of object is concentrated at the centre of mass
Light object- mass is small compared to another mass eg. string or pulley. Assumptions- treat object as no mass, tension is same at both sides of the string
Inextensible string- string doesn't stretch under load. Assumptions- acceleration is the same in objects connected by the string
Smooth surface assumptions- there is no friction
Rough surface assumptions- object and surface have some friction
Wire- thin rigid length of metal. Assumptions- treated as one dimensional
Smooth and light pulley assumptions- it has no mass, tension is same on either side of pulley
Bead- particle with a hole in it. Assumptions- move freely along wire/string, tension is same on either side of the bead
Peg- support where objects can be suspended/rested. Assumptions- dimensionless and fixed, can be rough or smooth
Gravity- force of attractions between all objects, denoted as g if acceleration is involved. Assumptions- all object with mass are attracted towards earth, earth's gravity is uniform and vertically down and g=9.8ms-2 unless otherwise stated
Air resistance- resistance as an object moves to the floor. Assumptions- modelled as negligible
Vectors
Examples are
Displacement
Velocity
Acceleration
Force/weight
Its a quantity with both magnitude and direction
When considering motion in a straight line, vectors can be positive or negative
Scalar quantity
It has a magnitude only
Examples are
Distance
Speed
Time
Mass
Scalar quantities are always positive
Constructing a model
Mathematical models can be constructed to simulate real life situations
Mechanics deals with the motion and action of forces on objects
Modelling assumptions
Understand significance of modelling assumption and how they affect calculations
Can simplify a problem and allow you to analyse a real life situation
Quantities and units
Derived units
Acceleartion- metre per second per second or ms-2
Speed/velocity- metre per second or ms-1
Weight/force- newtons or N (=kgms-2)
Base units
Mass- kilograms or kg
Length/displacement- metre or m
Time- seconds or s
Modelling process
Real world problem
Set up mathematical model. What assumptions? What variables?
Solve and interpret
Is answer reasonable? If yes report solution and interpret in context. If no reconsider assumptions and go back to stage 2