AS Mechanics Flashcards
define particle
dimensions of the particle are negligible
what are the modelling assumptions for a particle?
mass of the object is concentrated at a single point
rotational force & air resistance are ignored
define rod
all dimensions except 1 are negligible, like a pole or beam
what are the modelling assumptions for a rod?
mass is concentrated along a line
no thickness
rigid (does not bend or buckle)
define lamina
object with area but negligible thickness, like sheet of paper
what are the modelling assumptions for a lamina?
mass is distributed across a flat surface
define uniform body
mass is distributed evenly
what are the modelling assumptions for a uniform body?
the mass of the object is concentrated at a single point at the geometrical centre of the body = the centre of mass
define light object
mass of the object is small compared to other masses, like a string or pulley
what are the modelling assumptions for a light object?
treat object as having 0 mass
tension is the same at both ends of a light string
define inextensible string
a string that does not stretch under load
what are the modelling assumptions for an inextensible string?
acceleration is the same in objects connected by a taut inextensible string
what are the modelling assumptions for a smooth surface?
there is no friction b/w the surface & any object on it
define rough surface
surface that is not smooth
what are the modelling assumptions for a rough surface?
objects in contact with the surface experience a frictional force if they are moving or acted on by a force
define wire
rigid, thin length of metal
what are the modelling assumptions for a wire?
treated as one-dimensional
define smooth & light pulley
all pulleys
what are the modelling assumptions for a smooth & light pulley?
pulley has no mass
tension is the same on either side of the pulley
define bead
particle with hole in it for threading on a wire or string
what are the modelling assumptions for a bead?
bead moves freely along a wire or string
tension is the same on either side of the string
define peg
a support from which a body can be suspended or rested
what are the modelling assumptions for a peg?
no dimensions & fixed
can be rough or smooth - depends on Q
define air resistance
resistance experienced as an object moves through air (opposite direction to motion)
what are the modelling assumptions for air resistance?
usually modelled as negligible
define gravity
force of attraction b/w all objects
acceleration due to gravity = g = 9.8
what are the modelling assumptions for gravity?
assume all objects with mass are attracted towards Earth
Earth’s gravity is uniform & acts vertically downwards
g is constant & = 9.8ms-2, unless otherwise states in Q
how is a model involving gravity improved?
use a more accurate value of g
what are the common labels for force diagrams & the directions they act in?
weight - acts vertically downwards
normal reaction - acts perpendicular to the surface when an object is in contact with the surface
friction - opposes motion b/w 2 rough surfaces
tension - in string
thrust/compression - object pushed by light rod
buoyancy - upward force on body that allows it to float in liqui
air resistance - opposes motion
define vector
quantity which has both direction & magnitude
define displacement, velocity, acceleration & force/weight
displacement - distance in a particular direction (m)
velocity - rate of change of displacement (ms-1)
acceleration - rate of change of velocity (ms-2)
force/weight - described by magnitude, direction & point of application (N)
define scalar
has magnitude only (no direction)
define distance, speed, time & mass
distance - measure of length (m)
speed - measure of how quickly a body moves (ms-1)
time - measure of ongoing events taking place (s)
mass - measure of the quantity of matter contained in an object (kg)
if +ve direction is right & particle is moving to the left & speed is increasing…
velocity = -ve
acceleration = -ve
if +ve direction is right & particle is moving to the left & speed is decreasing…
velocity = -ve
acceleration = +ve
distance is the magnitude of the displacement vector
speed is the magnitude of the velocity vector
describe displacement-time graphs
time on x-axis
displacement on y-axis
gradient = velocity
straight line = constant velocity
curve = velocity is increasing/decreasing = object is accelerating
average velocity =
displacement from start point / time taken
average speed =
total distance travelled / time taken
describe velocity-time graphs
time on x-axis
velocity on y-axis
gradient = acceleration
straight line = constance acceleration
area under graph = v.t = displacement - for motion in straight line with +ve velocity
describe how to derive SUVAT equations for constant acceleration
see Y1 textbook pg 137
velocity-time graph
a = gradient
u = y-intercept
shaded area = displacement
using SUVAT equations
describe vertical motion under gravity
force of gravity causes objects to accelerate towards Earth
acceleration is constant (if air resistance is ignored)
acceleration does not depend on mass of object
constant downwards acceleration = g=9.8ms-2
define time of flight
the total time that an object is in motion from the time it is projected to the time it hits the ground
define speed of projection
initial speed
at greatest height,
v = 0
what is Newton’s 1st law of motion?
an object at rest will stay at rest
& an object moving with constant velocity will continue to move with constant velocity unless an unbalanced/resultant force acts on the object
what is the effect of a resultant force?
it causes the object to accelerate in the same direction as it’s acting in
how to find the resultant of 2 or more forces given as vectors
add the vectors
what is Newton’s 2nd law of motion?
the force needed to accelerate a particle = the product of the mass of the particle & the acceleration
F=ma
weight =
mg
F = ma with vectors
see OneNote
solving problems involving connected particles
can consider the particles separately or as a single particle/system if they are moving in the same straight line
see OneNote
what is Newton’s 3rd law?
for every action, there is an = & opposite reaction
solving problems involving a scale pan with multiple weights stacked on top of each other
remember reaction forces
solving problems involving smooth pulleys
tension in the string is the same on both sides of the pulley
DO NOT treat the system involving the pulley as a single particle - bc the particles are moving in different directions
how can displacement, velocity & acceleration be expressed?
as functions of time
how to go from s —> v —> a
differentiation
maxima & minima
dy/dx = 0
how to go from a —> v —> s
integration
remember +c
how to derive formula for motion with constant acceleration
calculus
see Y1 textbook pg 192
