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Maths > Modelling Assumptions > Flashcards

Modelling Assumptions Flashcards

1
Q

Light string

A

The mass is negligible

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2
Q

Particle

A

Dimensions of the object are negligible

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3
Q

Particle Assumption

A
  1. Mass of the object is concentrated at a single point
  2. Rotational forces and air resistance can be ignored
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4
Q

Rod

A

All dimensions but one are negligible, like a pole or a beam

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5
Q

Rod assumptions

A
  1. Mass is concentrated along a line
  2. No thickness
  3. Rigid (does not bend or buckle)
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6
Q

Lamina

A

Object with area but negligible thickness,like a sheet of paper

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7
Q

Lamina assumption

A

Mass is distributed across a flat surface

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8
Q

Uniform Body

A

Mass is distributed evenly

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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

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10
Q

Light Object

A

Mass of the object is small compared to other masses, like a string or a pulley

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11
Q

Light Object Assumptions

A
  1. Treat as having zero mass
  2. Tension the same at both ends of a light string
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12
Q

Inextensible string

A

A string that does not stretch under load

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13
Q

Inextensible string assumption

A

acceleration is the same in objects connected by a taut inextensible string

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14
Q

Smooth surface assumption

A

Assume that there is no friction between the surface and any object on it

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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

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16
Q

Wire

A

Rigid thin length of metal

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17
Q

Wire Assumption

A

Treated as one dimensional

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18
Q

Smooth and Light pulley

A

All pulleys you consider will be smooth and light

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19
Q

Smooth and Light pulley Assumptions

A
  1. Pulley has no mass
  2. Tension is the same on either side of the pulley
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20
Q

Peg

A

A support from which a body can be suspended or rested

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21
Q

Peg Assumptions

A
  1. Dimensionless and fixed
  2. Can be rough or smooth as specified in the question
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22
Q

Air resistance

A

resistance force experienced as an object moves through the air

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23
Q

Air Resistance Assumption

A

usually modelled as being negligible

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24
Q

Gravity

A

Force of attraction between all objects. Acceleration due to gravity is denoted by g

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25
Q

Gravity assumptions

A
  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
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26
Q

What does particle moving at a constant velocity mean?

A

forces parallel to the slope are balanced.

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27
Q

Thrust

A

Opposite to tension (happens when car brakes)

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28
Q

Limitations of Q (car)

A
  • 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.
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29
Q

Particle hanging (lightbulb)

A

Only has one tension (going up)

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30
Q

Velocity

A

Magnitude and direction
Displacement from starting point ÷ time

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31
Q

Uniform rod

A

Mass is in centre

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32
Q

Newton’s first law

A

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.

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33
Q

Newton’s second law

A

The acceleration of an object depends on the mass of the object and the amount of force applied

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34
Q

Newton’s third law

A

for every action (force) in nature there is an equal and opposite reaction.

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35
Q

Suggest one improvement that could be made in the model (pulleys)

A

Do not model ball B as a particle but give its dimensions so distance it falls changes

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36
Q

What makes acceleration in a pulley the same?

A

If the string is modelled as a light inextensible string

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37
Q

Identify one limitation of the model that will affect the accuracy of your answer (pulley)

A

Weight of string

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38
Q

Find the force on the pulley

A

Tension x2

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39
Q

The string is not light. How would this impact the equation?

A

The tensions would be different

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40
Q

A heavier block is placed on the slope with the same friction. Why does it remain at rest?

A

The friction will increase in the same proportion as the weight

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41
Q

Instantaneous rest

A

Differentiate to find subject
(Sub into equation and add for distance)

42
Q

Acceleration of velocity and time equation

A

Differentiate

43
Q

Finding position vector

A

Integrate and sub in point and 0

44
Q

Fulcrum

A

A pivot

45
Q

When loads are suspended on a rod/bar

A

The loads have no reaction force (normal reaction)

46
Q

Smooth support

A

No normal reaction

47
Q

Train moving on tracks (SUVAT). State an improvement to the model

A
  • A smooth change from acceleration to constant velocity
  • have the train accelerating at a variable rate
48
Q

Limiting equilibrium

A

Forces = 0

49
Q

Maximum value of mass on pulley

A

Moving in that direction

50
Q

Modelled as a particle

A

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
Q

Hinge reaction

A

Up and friction reaction

52
Q

Moments units

A

Distance must be in m

53
Q

Position vector

A

Integrate velocity

54
Q

Find displacement, velocity and acceleration

A

S-v-a
Differentiate

55
Q

(Kinematics)
Find the distance of P from O at the instant when P changes its direction of motion

A

When v=0 to find time
Substitute into s equation

56
Q

Find the value of t at the instant when P is moving in a direction perpendicular to i

A

i of v =0

57
Q

r relation to s

A

r = s

58
Q

Take up as positive (are acceleration and displacement pos or neg)?

A

If moving like a quadratic = s+ and a-
If moving down from a raised point = s- and a-

59
Q

Finding speed from acceleration and time

A

a = Δv/Δt

60
Q

is moving due north with speed 0.6 m s–1.

A

V only has j vector

61
Q

Find the value of t when the boat is north-east of O.

A

V —> i = j

62
Q

Parallel vectors

A

Have same length (magnitude) and same direction. Parallel vectors are multiples of each other e.g. i+2j-3k and 2i+4j-6k

63
Q

Position vectors: AB=

A

OB-OA

64
Q

RUVAT

A

r= ut + 0.5at^2

65
Q

At constant velocity: s=

A

vt

66
Q

Highest point on projectile

A

v =0

67
Q

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?

A

(2Usinx)/g

68
Q

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?

A

(Usinx) / g

69
Q

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?

A

(U^2sin2x)/g

70
Q

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?

A
71
Q

Acceleration in velocity time graph

A

y=mx
v=mt
v=at

72
Q

Speed regarding velocity

A

Magnitude of velocity

73
Q

) the speed of the stone when it is 10.8 m above sea level, giving your answer to 2 significant figures.

A

Vertical: v^2=u^2+2as
Horizontal: u
Speed = magnitude of velocity = square root of v^2+u^2

74
Q

Find the velocity of P at the instant before it collides with Q.

A

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
Q

Colliding particles in kinematics

A

Equate displacement from both equations

76
Q

Suggest two refinements to the model that would make it more realistic. (Pulley)

A
  • have the model consider air resistance
  • have the model use an extensible string
77
Q

Why will pushing the object make the acceleration less than pulling?

A

Pushing the object will increase friction since normal reaction is greater

78
Q

Velocity time graph for pulley

A

Constant velocity

79
Q

Why will someone standing the the ladder help it from slipping?

A

Pushing the object will increase friction since normal reaction is greater

80
Q

If a particle comes to rest, then what is acceleration?

A

a= -9.8

81
Q

Instantaneous rest

A

V=0

82
Q

Finding maximum/minimum velocity

A

Differentiate v equation and set =0 to find t
Sub into original equation

83
Q

If acceleration is 0

A

U and V is the same

84
Q

Position vector

A

Displaced,ent + initial position vector

85
Q

Constant acceleration

A

Use suvat

86
Q

Why is the reaction perpendicular to the object/drum?

A

There is no friction so the reaction is perpendicular

87
Q

When to use μR or F?

A

For limiting friction, use μR otherwise use F

88
Q

What is the horizontal velocity when the ball is moving up?

A

The horizontal velocity stays constant

89
Q

Weight

A

Don’t use g

90
Q

Find the position vector of Q when Q is due West of P

A

equate the j vectors of Q and P

91
Q

Show that at t=3,5m both particles are moving in the same direction

A

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
Q

Assumptions of uniform rod

A

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
Q

How have you used the fact that the block is modelled as a particle

A

Masses concentrated at a point or weights act at a point

94
Q

How have you used that fact that the block is modelled as a particle?

A

Masses concentrated at a point or weights act at a point

95
Q

Brick Q is now projected with speed 0.5 down a line of greatest slope of the plane. Describe the motion.

A

Brick Q slides down at a a constant speed (there’s not resultant force down the plane so no acceleration)

96
Q

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

A

Complete the square to show x with never be negative

97
Q

Speed from acceleration and time

A

V=at

98
Q

The direction of motion/moving is north east

A

Find velocity and equate i and j vectors

99
Q

Find the value of t when the object is north east of O

A

Find s or r and equate i and j vectors

100
Q

parallel to vector I

A

J=0

101
Q

Explain why the frictional force acting on the rod at A acts horizontally to the right

A

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

Maths (5 decks)

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