A2 Mechanics Flashcards
what is a moment?
the turning effect of the force on a rigid body
when do moments occur?
around a point
when object has size & force is not acting through the centre of mass
what is the formula for moment with units?
moment (Nm) = force (N) x perpendicular distance (m)
moment = |F| x dsinθ
d = distance from point
define equilibrium
when the resultant force = 0
& when the resultant moment = 0
describe how to solve equilibrium problems
- resolve forces vertically
- resolve forces horizontally
- resolve moments around a point you choose that will eliminate a variable
what is the difference b/w a uniform & non-uniform mass?
uniform mass - the centre of mass is at the middle of the object
non-uniform mass - the centre of mass is not necessarily at the centre of the object
describe the ‘point of tilting’
one support is the pivot, one support has 0 reaction force or 0 tension
Ra = 0N
see Wilson OneNote
describe resolving forces
components of the force in the direction of motion - perpendicular & parallel using
y = Fsinθ
x = Fcosθ
–> always choose triangle that creates these equations
F = (Fcosθi + Fsinθj) N
see Wilson OneNote
F = ma
F - resultant force
if F = 0, a = 0
when to use F = ma?
if equilibrium in a certain direction, equate forces in opposing directions
if no equilibrium in certain direction, use F=ma
describe resolving forces along a plane
perpendicular & parallel to the plane
Fr =
max. friction at limiting equilibrium
μR
μ = roughness of plane, if μ = 0, plane is smooth
R = reaction force
if pulling force < Fmax?
object won’t move & Fr will = pulling force
define static particle
at equilibrium
no moments
a = 0
F=ma=0
describe how to solve problems in statics
draw diagram
resolve the forces in horizontal & vertical directions or, if the particle is on an inclined plane, in perpendicular & parallel directions
set the sum of components in each direction = to 0
solve the resulting equilibrium to find the unknown forces
what is true about a rigid body in static equilibrium?
the body is stationary
the resultant force in any direction is 0
the resultant moment is 0
modelling with static particles
weight
tension - force of string in both directions
pulleys
wires
planes
strings
beads - tension on each side is the same (see OneNote)
pegs
+ skills from static particles
define light, inextensible string
light - no mass
inextensible - no stretch
practice modelling with static particles & tension, friction
define lamina
like a piece of paper - 2d surface with area & thickness = 0
mass is distributed across the 2d surface
what point should you resolve forces about in static rigid bodies?
a point that eliminates a force
draw diagram for inclined rod & peg with reaction & friction forces, resting on rough ground
see Wilson OneNote
draw diagram for ladder on rough wall & rough ground with reaction & friction forces
see Wilson OneNote
draw diagram for suspended rod & rough wall with reaction, tension & friction forces
see Wilson OneNote
ask - where is the friction??
particle = no moments
what equations do dynamics questions involve?
SUVAT
F = ma
resolving forces
Fmax = μR
how do you find the position vector of an object, given the initial position vector?
r = r0 + ut + 1/2at^2
bc r = ut+1/2at^2 is displacement from the original point
with dynamic particles, friction is…
at max.
Fmax = μR
with dynamic particles what is the resultant force?
not 0
with dynamic particles what is the acceleration?
not 0
describe how to solve problems with dynamic particles
draw diagram
state which direction is +ve
include friction if rough surface
use F=ma to resolve horizontally & vertically or parallel & perpendicular if on an inclined plane
solve the resulting equations.
SUVAT if required
find force on pulley if required
describe how to find the force acting on the pulley
use angle in triangle
split it in half
resolve forces to middle line
see OneNote ‘connected particles’ pg
key points with projectiles
horizontal acceleration = 0
vertical acceleration = g
Ux & Uy are the horizontal & vertical components of the initial velocity
it can be useful to make +ve direction downwards
describe how to solve problems with projectiles
draw diagram
state +ve direction
list initial velocities - ux and uy.
resolve vertically or horizontally
apply SUVAT
does the answer make sense?
refer/link back to question - reject non-sensical answers
what are the formulae for Ux & Uy?
Ux = Ucosα
Uy = Usinα
α is the angle of projection
when does a projectile reach its point of greatest height?
when Uy = 0
for deriving projectile motion formulae, what is assigned to each letter of SUVAT?
sketch, positive directions, Ux & Uy
resolve horizontally (take x = Sx)
resolve vertically (take y = Sy)
eliminate the variable t
use trig. identities to reach formulae as required
derive time of flight formula
derive time to reach greatest height formula
derive range on horizontal plane formula
derive equation of trajectory
in kinematics, acceleration is
not constant
describe how to get from s to v to a when acceleration is variable
differentiate
describe how to get from a to v to s when acceleration is variable
integrate
what is the position vector of a particle that starts from point with position vector r0 & moves with constant velocity
& what is its displacement from its initial position at time t?
r = r0 + vt
this is distance = speed x time for vectors
its displacement from its initial position at time t is: vt
what formulae can be used with vector questions involving constant acceleration?
v = u + at
r = ut + 1/2at^2
r is displacement
be careful of where r is being measured from
solve projectile problems involving vectors
describe how to differentiate vectors
differentiate each function of time separately
what is dot notation?
short-hand for differentiation with respect to time
1 dot = first derivative
2 dots = 2nd derivative
describe how to integrate vectors
integrate normally with +c
make +c a column vector with i & j components:
(p
q)
