A2 Mechanics

Question 1

what is a moment?

Answer 1

the turning effect of the force on a rigid body

Question 2

when do moments occur?

Answer 2

around a point
when object has size & force is not acting through the centre of mass

Question 3

what is the formula for moment with units?

Answer 3

moment (Nm) = force (N) x perpendicular distance (m)
moment = |F| x dsinθ
d = distance from point

Question 4

define equilibrium

Answer 4

when the resultant force = 0
& when the resultant moment = 0

Question 5

describe how to solve equilibrium problems

Answer 5

1. resolve forces vertically
2. resolve forces horizontally
3. resolve moments around a point you choose that will eliminate a variable

Question 6

what is the difference b/w a uniform & non-uniform mass?

Answer 6

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

Question 7

describe the ‘point of tilting’

Answer 7

one support is the pivot, one support has 0 reaction force or 0 tension
Ra = 0N
see Wilson OneNote

Question 8

describe resolving forces

Answer 8

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

Question 9

F = ma

Answer 9

F - resultant force
if F = 0, a = 0

Question 10

when to use F = ma?

Answer 10

if equilibrium in a certain direction, equate forces in opposing directions
if no equilibrium in certain direction, use F=ma

Question 11

describe resolving forces along a plane

Answer 11

perpendicular & parallel to the plane

Question 12

Fr =
max. friction at limiting equilibrium

Answer 12

μR
μ = roughness of plane, if μ = 0, plane is smooth
R = reaction force

Question 13

if pulling force < Fmax?

Answer 13

object won’t move & Fr will = pulling force

Question 14

define static particle

Answer 14

at equilibrium
no moments
a = 0
F=ma=0

Question 15

describe how to solve problems in statics

Answer 15

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

Question 16

what is true about a rigid body in static equilibrium?

Answer 16

the body is stationary
the resultant force in any direction is 0
the resultant moment is 0

Question 17

modelling with static particles

Answer 17

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

Question 18

define light, inextensible string

Answer 18

light - no mass
inextensible - no stretch

Question 19

practice modelling with static particles & tension, friction

Question 20

define lamina

Answer 20

like a piece of paper - 2d surface with area & thickness = 0
mass is distributed across the 2d surface

Question 21

what point should you resolve forces about in static rigid bodies?

Answer 21

a point that eliminates a force

Question 22

draw diagram for inclined rod & peg with reaction & friction forces, resting on rough ground

Answer 22

see Wilson OneNote

Question 23

draw diagram for ladder on rough wall & rough ground with reaction & friction forces

Answer 23

see Wilson OneNote

Question 24

draw diagram for suspended rod & rough wall with reaction, tension & friction forces

Answer 24

see Wilson OneNote
ask - where is the friction??

Question 25

particle = no moments

Question 26

what equations do dynamics questions involve?

Answer 26

SUVAT F = ma resolving forces Fmax = μR

Question 27

how do you find the position vector of an object, given the initial position vector?

Answer 27

r = r0 + ut + 1/2at^2 bc r = ut+1/2at^2 is displacement from the original point

Question 28

with dynamic particles, friction is...

Answer 28

at max. Fmax = μR

Question 29

with dynamic particles what is the resultant force?

Answer 29

not 0

Question 30

with dynamic particles what is the acceleration?

Answer 30

not 0

Question 31

describe how to solve problems with dynamic particles

Answer 31

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

Question 32

describe how to find the force acting on the pulley

Answer 32

use angle in triangle split it in half resolve forces to middle line see OneNote 'connected particles' pg

Question 33

key points with projectiles

Answer 33

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

Question 34

describe how to solve problems with projectiles

Answer 34

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

Question 35

what are the formulae for Ux & Uy?

Answer 35

Ux = Ucosα Uy = Usinα α is the angle of projection

Question 36

when does a projectile reach its point of greatest height?

Answer 36

when Uy = 0

Question 37

for deriving projectile motion formulae, what is assigned to each letter of SUVAT?

Answer 37

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

Question 38

derive time of flight formula

Question 39

derive time to reach greatest height formula

Question 40

derive range on horizontal plane formula

Question 41

derive equation of trajectory

Question 42

in kinematics, acceleration is

Answer 42

not constant

Question 43

describe how to get from s to v to a when acceleration is variable

Answer 43

differentiate

Question 44

describe how to get from a to v to s when acceleration is variable

Answer 44

integrate

Question 45

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?

Answer 45

r = r0 + vt this is distance = speed x time for vectors its displacement from its initial position at time t is: vt

Question 46

what formulae can be used with vector questions involving constant acceleration?

Answer 46

v = u + at r = ut + 1/2at^2 r is displacement be careful of where r is being measured from

Question 47

solve projectile problems involving vectors

Question 48

describe how to differentiate vectors

Answer 48

differentiate each function of time separately

Question 49

what is dot notation?

Answer 49

short-hand for differentiation with respect to time 1 dot = first derivative 2 dots = 2nd derivative

Question 50

describe how to integrate vectors

Answer 50

integrate normally with +c make +c a column vector with i & j components: (p q)

Question 51

what is true if the rope is not light?

Answer 51

tension is not constant tension is different either side of the pulley

Question 52

how do you find the resultant force acting at a point?

Answer 52

Pythagoras with component forces

Question 53

if a particle is 'attached to' or 'placed on' a suspended/resting rod

Answer 53

it has no reaction force

Question 54

what is the effect on the initial velocity is air resistance is considered in the model & why?

Answer 54

initial velocity is greater because air resistance slows the ball down so much be overcome

Question 55

what is the effect of changing a force from pushing down on a block on a rough plane to lifting it upwards at an angle?

Answer 55

greater reaction force so greater friction so decreased acceleration

Question 56

what improvements can be made to projectile models of particles moving freely under gravity?

Answer 56

use a more accurate value of g consider air resistance consider the effect of wind consider the dimensions of the ball consider the size of the ball consider the spin of the ball

Question 57

why is reaction force perpendicular?

Answer 57

because surface is smooth

Question 58

when asked for velocity,

Answer 58

give speed & angle to horizontal

Question 59

if Q does not specify the object is in limiting equilibrium, what is the friction?

Answer 59

Fr ≤ μR

Question 60

how to explain the direction friction acts in

Answer 60

describe other horizontal components e.g. friction acts right because the horizontal component of RB acts left & the only other horizontal force is friction, which must act right for the rod to be in equilibrium & to prevent the rod from sliding