Mechanics - Modelling in Mechanics Flashcards
What is the “particle” model and the modelling assumptions?
Particle - Dimensions of the object are negligible.
Modelling Assumptions:
- mass of the object is concentrated at a single point
- rotational forces and air resistance can be ignored
What is the “rod” model and the modelling assumptions?
Rod - All dimensions but one (length) are negligible, like a pole or a beam.
Modelling Assumptions:
- mass is concentrated along a line (mass is negligible)
- no thickness
- rigid (does not bend or buckle)
What is the “lamina” model and the modelling assumptions?
Lamina - Object with area but negligible thickness, like a sheet of paper.
Modelling Assumptions:
- mass is distributed across a flat surface
What is the “uniform body” model and the modelling assumptions?
Uniform Body - Mass is distributed evenly.
Modelling Assumptions:
- mass of the object is concentrated at a single point at the geometrical centre of the body - the centre of mass
What is the “light object” model and the modelling assumptions?
Light Object - Mass of the object is small compared to other masses, like a string or a pulley.
Modelling Assumptions:
- treat object as having zero mass
- tension the same at both ends of a light string
What is the “inextensible string” model and the modelling assumptions?
Inextensible String - A string that does not stretch under load.
Modelling Assumptions:
- acceleration is the same in objects connected by a taut inextensible string
What is the “smooth surface” model and the modelling assumptions?
Smooth Surface - The surface is completely flat/smooth.
Modelling Assumptions:
- assume that there is no friction between the surface and any object on it
What is the “rough surface” model and the modelling assumptions?
Rough Surface - If a surface is not smooth, it is rough.
Modelling Assumptions:
- objects in contact with the surface experience a frictional force if they are moving or are acted on by a force
What is the “wire” model and the modelling assumptions?
Wire - Rigid thin length of metal.
Modelling Assumptions:
- treated as one-dimensional
What is the “smooth and light pulley” model and the modelling assumptions?
Smooth and Light Pulley - All pulleys you consider will be smooth and light.
Modelling Assumptions:
- pulley has no mass
- tension is the same on either side of the pulley
What is the “bead” model and the modelling assumptions?
Bead - Particle with a hole in it for threading on a wire or string.
Modelling Assumptions:
- moves freely along a wire or string
- tension is the same on either side of the bead
What is the “peg” model and the modelling assumptions?
Peg - A support from which a body can be suspended or rested.
Modelling Assumptions:
- dimensionless and fixed
- can be rough or smooth as specified in question
What is the “air resistance” model and the modelling assumptions?
Air Resistance - Resistance experienced as an object moves through the air.
Modelling Assumptions:
- usually modelled as being negligible
What is the “gravity” model and the modelling assumptions?
Gravity - Force of attraction between all objects. Acceleration due to gravity is denoted by g.
Modelling 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 9.8ms-2, unless otherwise stated in the question
What is the weight?
The weight (or gravitational force) of an object acts vertically downwards.
What is the normal reaction?
The normal reaction is the force which acts perpendicular to a surface when an object is in contact with the surface.
What is the friction?
The friction is a force which opposes the motion between two rough surfaces.
What is the tension?
If an object is being pulled along by a string, the force acting on the object is called the tension in the string.
What is the thrust or 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.
What is buoyancy?
Buoyancy is the upward force on a body that allows it to float or rise when submerged in a liquid.
What is air resistance?
Air resistance opposes motion.
What is a vector quantity?
A vector is a quantity which has both magnitude and direction.
What are examples of vector quantities?
- displacement: distance in a particular direction
- velocity: rate of change in displacement
- acceleration: rate of change of velocity
- force/weight: described by magnitude, direction and point of application
What is a scalar quantity?
A scalar quantity has magnitude only,
What are examples of scalar quantities?
- distance: measure of length
- speed: measure of how quickly a body moves
- time: measure of ongoing events taking place
- mass: measure of the quantity of matter contained in an object
Are vector and scalar quantities positive or negative?
Scalar quantities are always positive. When considering motion in a straight line (1-dimensional motion), vector quantities can be positive or negative.
What is distance?
Distance is the magnitude of the displacement vector.
What is speed?
Speed is the magnitude of the velocity vector.
