Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

Maths > Modelling Assumptions > Flashcards

Modelling Assumptions Flashcards

1
Q

Light string

A

The mass is negligible

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Particle

A

Dimensions of the object are negligible

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
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
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

Rod

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Rod assumptions

A
  1. Mass is concentrated along a line
  2. No thickness
  3. Rigid (does not bend or buckle)
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

Lamina

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

Lamina assumption

A

Mass is distributed across a flat surface

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Uniform Body

A

Mass is distributed evenly

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Light Object

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Light Object Assumptions

A
  1. Treat as having zero mass
  2. Tension the same at both ends of a light string
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Inextensible string

A

A string that does not stretch under load

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

Inextensible string assumption

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

Smooth surface assumption

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

Wire

A

Rigid thin length of metal

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

Wire Assumption

A

Treated as one dimensional

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

Smooth and Light pulley

A

All pulleys you consider will be smooth and light

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

Smooth and Light pulley Assumptions

A
  1. Pulley has no mass
  2. Tension is the same on either side of the pulley
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

Peg

A

A support from which a body can be suspended or rested

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

Peg Assumptions

A
  1. Dimensionless and fixed
  2. Can be rough or smooth as specified in the question
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

Air resistance

A

resistance force experienced as an object moves through the air

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

Air Resistance Assumption

A

usually modelled as being negligible

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

Gravity

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
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
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

What does particle moving at a constant velocity mean?

A

forces parallel to the slope are balanced.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
27
Q

Thrust

A

Opposite to tension (happens when car brakes)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
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.
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
29
Q

Particle hanging (lightbulb)

A

Only has one tension (going up)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
30
Q

Velocity

A

Magnitude and direction
Displacement from starting point ÷ time

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
31
Q

Uniform rod

A

Mass is in centre

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
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.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
34
Q

Newton’s third law

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
36
Q

What makes acceleration in a pulley the same?

A

If the string is modelled as a light inextensible string

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
37
Q

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

A

Weight of string

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
38
Q

Find the force on the pulley

A

Tension x2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
39
Q

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

A

The tensions would be different

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
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)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2025 Bold Learning Solutions. Terms and Conditions