Modelling Assumptions Flashcards
1
Q
Light string
A
The mass is negligible
2
Q
Particle
A
Dimensions of the object are negligible
3
Q
Particle Assumption
A
- Mass of the object is concentrated at a single point
- Rotational forces and air resistance can be ignored
4
Q
Rod
A
All dimensions but one are negligible, like a pole or a beam
5
Q
Rod assumptions
A
- Mass is concentrated along a line
- No thickness
- Rigid (does not bend or buckle)
6
Q
Lamina
A
Object with area but negligible thickness,like a sheet of paper
7
Q
Lamina assumption
A
Mass is distributed across a flat surface
8
Q
Uniform Body
A
Mass is distributed evenly
9
Q
Uniform Body assumption
A
Mass of the object is concentrated at a single point at the geometrical centre of the body - centre of mass
10
Q
Light Object
A
Mass of the object is small compared to other masses, like a string or a pulley
11
Q
Light Object Assumptions
A
- Treat as having zero mass
- Tension the same at both ends of a light string
12
Q
Inextensible string
A
A string that does not stretch under load
13
Q
Inextensible string assumption
A
acceleration is the same in objects connected by a taut inextensible string
14
Q
Smooth surface assumption
A
Assume that there is no friction between the surface and any object on it
15
Q
Rough Surface Assumption
A
Objects in contact with the surface experience a frictional force if they are moving or are acted on by a force
16
Q
Wire
A
Rigid thin length of metal
17
Q
Wire Assumption
A
Treated as one dimensional
18
Q
Smooth and Light pulley
A
All pulleys you consider will be smooth and light
19
Q
Smooth and Light pulley Assumptions
A
- Pulley has no mass
- Tension is the same on either side of the pulley
20
Q
Peg
A
A support from which a body can be suspended or rested
21
Q
Peg Assumptions
A
- Dimensionless and fixed
- Can be rough or smooth as specified in the question
22
Q
Air resistance
A
resistance force experienced as an object moves through the air
23
Q
Air Resistance Assumption
A
usually modelled as being negligible
24
Q
Gravity
A
Force of attraction between all objects. Acceleration due to gravity is denoted by g
25
Gravity assumptions
1. Assume that all objects with mas are attracted towards the Earth
2. Earth's gravity is uniform and acts vertically downwards
3. g is constant and is taken as 9.8m/s-2 unless otherwise stated in the question
26
What does particle moving at a constant velocity mean?
forces parallel to the slope are balanced.
27
Thrust
Opposite to tension (happens when car brakes)
28
Limitations of Q (car)
- The force due to air resistance will reduce as the car slows.
- If the skid causes the tyres to heat, the value of μ is also likely to vary.
29
Particle hanging (lightbulb)
Only has one tension (going up)
30
Velocity
Magnitude and direction
Displacement from starting point ÷ time
31
Uniform rod
Mass is in centre
32
Newton’s first law
every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force.
33
Newton’s second law
The acceleration of an object depends on the mass of the object and the amount of force applied
34
Newton’s third law
for every action (force) in nature there is an equal and opposite reaction.
35
Suggest one improvement that could be made in the model (pulleys)
Do not model ball B as a particle but give its dimensions so distance it falls changes
36
What makes acceleration in a pulley the same?
If the string is modelled as a light inextensible string
37
Identify one limitation of the model that will affect the accuracy of your answer (pulley)
Weight of string
38
Find the force on the pulley
Tension x2
39
The string is not light. How would this impact the equation?
The tensions would be different
40
A heavier block is placed on the slope with the same friction. Why does it remain at rest?
The friction will increase in the same proportion as the weight
41
Instantaneous rest
Differentiate to find subject
(Sub into equation and add for distance)
42
Acceleration of velocity and time equation
Differentiate
43
Finding position vector
Integrate and sub in point and 0
44
Fulcrum
A pivot
45
When loads are suspended on a rod/bar
The loads have no reaction force (normal reaction)
46
Smooth support
No normal reaction
47
Train moving on tracks (SUVAT). State an improvement to the model
- A smooth change from acceleration to constant velocity
- have the train accelerating at a variable rate
48
Limiting equilibrium
Forces = 0
49
Maximum value of mass on pulley
Moving in that direction
50
Modelled as a particle
we can ignore the effects of air resistance, the weight of the ball and any energy or path changes caused by the spin of the ball.
51
Hinge reaction
Up and friction reaction
52
Moments units
Distance must be in m
53
Position vector
Integrate velocity
54
Find displacement, velocity and acceleration
S-v-a
Differentiate
55
(Kinematics)
Find the distance of P from O at the instant when P changes its direction of motion
When v=0 to find time
Substitute into s equation
56
Find the value of t at the instant when P is moving in a direction perpendicular to i
i of v =0
57
r relation to s
r = s
58
Take up as positive (are acceleration and displacement pos or neg)?
If moving like a quadratic = s+ and a-
If moving down from a raised point = s- and a-
59
Finding speed from acceleration and time
a = Δv/Δt
60
is moving due north with speed 0.6 m s–1.
V only has j vector
61
Find the value of t when the boat is north-east of O.
V —> i = j
62
Parallel vectors
Have same length (magnitude) and same direction. Parallel vectors are multiples of each other e.g. i+2j-3k and 2i+4j-6k
63
Position vectors: AB=
OB-OA
64
RUVAT
r= ut + 0.5at^2
65
At constant velocity: s=
vt
66
Highest point on projectile
v =0
67
A particle is projected from a point on a horizontal plane with an initial velocity U at an angle x above horizontal moves freely under gravity until it hits the plane at point B
Find equation for time of flight?
(2Usinx)/g
68
A particle is projected from a point on a horizontal plane with an initial velocity U at an angle x above horizontal moves freely under gravity until it hits the plane at point B
Find the time to reach the greatest heigh?
(Usinx) / g
69
A particle is projected from a point on a horizontal plane with an initial velocity U at an angle x above horizontal moves freely under gravity until it hits the plane at point B
Find an equation for the range on horizontal plane?
(U^2sin2x)/g
70
A particle is projected from a point on a horizontal plane with an initial velocity U at an angle x above horizontal moves freely under gravity until it hits the plane at point B
Find an equation for the equation of trajectory?
71
Acceleration in velocity time graph
y=mx
v=mt
v=at
72
Speed regarding velocity
Magnitude of velocity
73
) the speed of the stone when it is 10.8 m above sea level, giving your answer to 2 significant figures.
Vertical: v^2=u^2+2as
Horizontal: u
Speed = magnitude of velocity = square root of v^2+u^2
74
Find the velocity of P at the instant before it collides with Q.
Find velocity of vertical and horizontal
- find magnitude to find speed
- use tan and velocities to find angle
- speed^-1 downwards at angle to the horizontal
75
Colliding particles in kinematics
Equate displacement from both equations
76
Suggest two refinements to the model that would make it more realistic. (Pulley)
- have the model consider air resistance
- have the model use an extensible string
77
Why will pushing the object make the acceleration less than pulling?
Pushing the object will increase friction since normal reaction is greater
78
Velocity time graph for pulley
Constant velocity
79
Why will someone standing the the ladder help it from slipping?
Pushing the object will increase friction since normal reaction is greater
80
If a particle comes to rest, then what is acceleration?
a= -9.8
81
Instantaneous rest
V=0
82
Finding maximum/minimum velocity
Differentiate v equation and set =0 to find t
Sub into original equation
83
If acceleration is 0
U and V is the same
84
Position vector
Displaced,ent + initial position vector
85
Constant acceleration
Use suvat
86
Why is the reaction perpendicular to the object/drum?
There is no friction so the reaction is perpendicular
87
When to use μR or F?
For limiting friction, use μR otherwise use F
88
What is the horizontal velocity when the ball is moving up?
The horizontal velocity stays constant
89
Weight
Don’t use g
90
Find the position vector of Q when Q is due West of P
equate the j vectors of Q and P
91
Show that at t=3,5m both particles are moving in the same direction
If both particles are moving in the same direction then velocity should be ratios of each other.
- Velocity if one particle = lambda velocity of other particle
92
Assumptions of uniform rod
uniform – mass is or acts at midpoint of plank; centre of mass is at middle of plank; weight acts at the middle of the plank, centre of gravity is at midpoint
rod - plank does not bend, remains straight, is inflexible, is rigid
93
How have you used the fact that the block is modelled as a particle
Masses concentrated at a point or weights act at a point
94
How have you used that fact that the block is modelled as a particle?
Masses concentrated at a point or weights act at a point
95
Brick Q is now projected with speed 0.5 down a line of greatest slope of the plane. Describe the motion.
Brick Q slides down at a a constant speed (there’s not resultant force down the plane so no acceleration)
96
P moves along the a Xia with displacement x=0.5t^2(t^2-2t+1).
Show that P will never move along the negative along the x axis
Complete the square to show x with never be negative
97
Speed from acceleration and time
V=at
98
The **direction of motion/moving** is north east
Find velocity and equate i and j vectors
99
Find the value of t when the object **is** north east of O
Find s or r and equate i and j vectors
100
parallel to vector I
J=0
101
Explain why the frictional force acting on the rod at A acts horizontally to the right
The horizontal component of T acts to the left and since the only other horizontal force is friction, it must act to the right oe
