Statistics and Mechanics Chapter 8 - Modelling in Mechanics Flashcards
Particle meaning
Dimensions of the objects are negligble.
Particle modelling assumptions
Mass of the object is concentrated at a single point.
Rational forces and air resistance can be ignored.
Rod meaning
All dimensions but one are negligible, like a pole or a beam.
Rod modelling assumptions
Mass is concentrated along a line.
No thickness.
Rigid (does not bend or buckle)>
Lamina meaning
Object with area but negligible thickness, like a sheet of paper.
Lamina modelling assumptions
Mass is distributed across a flat surface.
Uniform body meaning
Mass is distributed evenly
Uniform body modelling assumptions
Mass of the object is concentrated at a single point at the geometrical centre of the body - the centre of mass.
Light object meaning
Mass of the object is small compared to other masses, like a string or a pulley.
Light object modelling assumptions.
Treat object as having zero mass.
Tension the same at both ends of a light strings.
Inextensible string meaning
A string that does not stretch under load.
Inextensible string modelling assumptions
Acceleration is the same in objects connected by a taut inextensible string.
Smooth surface modelling assumptions
Assume that there is not friction between the surface and any objects on it.
Rough surface meaning
If a surface is not smooth, it is rough.
Rough surface modelling assumptions
Objects in contact with the surface experience a frictional force if they are moving or are acted on by a force
Wire meaning
Rigid thin length of metal
Wire modelling assumptions
Treated as one-dimensional
Smooth and light pulley (all pulleys)
Pulley has no mass.
Tension is the same on either side of the pulley.
Bead meaning
Particle with a hole in it for threading on a wire or string
Bead modelling assumptions
Moves freely along a wire or string.
Tension is the same on either side of the bead.
Peg meaning
A support from which a body can be suspended or rested
Peg modelling assumptions
Dimensionless and fixed.
Can be rough or smooth as specified in question.
Gravity meaning
Force of attraction between all objects. Acceleration due to gravity is denoted by g. In maths, g = 9.8. In physics, g = 9.81.
Gravity 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 9.8 ms^-2, unless otherwise stated in the question
Name the 7 forces that you are most likely to find in force diagrams.
1 - weight (mass x acceleration due to gravity)
2 - normal reaction (perpendicular and opposite to the force an object exerts on another object)
3 - friction (opposite to direction of motion)
4 - tension (if an object is being pulled along by a string, the force acting on the object is called the tension in the string)
5 - thrust (if an object is being pushed)
6 - buoyancy (the force that allows an object to float on water)
7 - air resistance
How would you convert km h^-1 to m s^-1?
Set it up as a fraction (distance value over time value). Convert from km to m (multiply by 1000). Convert from h to s (multiply by 60x60). Divide through.
How would you convert 1cm^2 to m^2?
cm to m is divide by 100. cm^2 to m^2 is divide by 100^2.
4 examples of scalar quantities (magnitude and direction)
1 - displacement
2 - velocity
3 - acceleration
4 - force/weight
4 examples of scalar quantities (magnitude only)
1 - distance
2 - speed
3 - time
4 - mass
If right is positive, what does it mean if a particle has negative velocity and negative acceleration?
The particle is moving to the left and its speed is increasing.
(When the direction of the acceleration opposes the direction of motion, the particle is slowing down. This is also called deceleration.)
What does speed = |velocity| mean?
The value for the speed is the absolute value for the velocity.
If the velocity is -9.5ms^1, the speed is 9.5ms^-1.
Which direction is the vector j?
1 unit up.
Which direction is the vector i?
One unit to the right.
