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BMSc SB > Mechanics Unit 1 > Flashcards

Mechanics Unit 1 Flashcards

1
Q

there are 7 SI base units - which 3 do we need to know

A

metre (m) - measure of length
second (s) - measure of time
kilogram (kg) - measure of mass

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2
Q

there are 2 supplementary SI units - which 1 do we need to know

A

radian (rad) - measure of angle

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3
Q

what is 2 pie radians equal to

A

360 degrees

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4
Q

how can we convert radians into degrees

A

180/pie multiply by angle in radians

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5
Q

how can we convert degrees into radians

A

pie/180 multiply by angle in degrees

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6
Q

what is the definition of a scalar and vector quantity

A

scalar = quantity with magnitude only

vector = quantity with magnitude and direction

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7
Q

list some vector quantities

A 
displacement 
velocity 
angular displacement 
angular velocity 
force
momentum 
acceleration
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8
Q

what are the 2 ways to write location of a vector

A

Cartesian system - x, y and z axis

Polar co-ordinates - resultant vector and angle in degrees

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9
Q

equation for average velocity

A

change in displacement / time taken

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10
Q

on a displacement-time graph, how can the velocity be calculated

A

the gradient of the graph is the velocity

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11
Q

what is instantaneous velocity on a displacement-time graph

A

the gradient on the graph at a certain point

- can be found drawing a tangent to the curve to find slope and calculate a gradient

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12
Q

equation for acceleration

A

change in velocity / time taken

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13
Q

unit for velocity

A

m/s

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14
Q

unit for acceleration

A

m/s^2

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15
Q

what needs to be considered when calculating acceleration

A

acceleration due to gravity = 9.81m/s^2

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16
Q

what graph can be used to calculate acceleration

A

velocity-time graph

- the gradient is the acceleration

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17
Q

what do the letters u, v, a, s and t stand for

A

u = starting velocity (m/s)

v = final velocity (m/s)

a = acceleration (m/s^2)

s = displacement (m)

t = time taken (s)

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18
Q

what are the equations of linear motion

A

v = u + at

v^2 = u^2 + 2as

s= 1/2 (u + v)t

s = ut + 1/2at^2

s = vt - 1/2at^2

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19
Q

what is rotary motion

A

object rotating about a point on itself or about an external fixed point

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20
Q

what is angular velocity

A

angular displacement travelled per second

i.e. change in angular displacement / time taken

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21
Q

what is the unit for angular velocity

A

rad/s

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22
Q

what is instantaneous angular velocity

A

angular velocity at an instant time

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23
Q

what is angular acceleration and its units

A

rate of change of angular velocity

rad / s^2

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24
Q

equation of angular acceleration

A

change in angular velocity / time taken

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25
Q

unit of Force

A

Newton (N)

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26
Q

what is 1N equal to

A

1 kg m/s^2

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27
Q

what is the 2 effects of a force

A

change the body’s position

deform the body’s shape

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28
Q

what is rigid body mechanics

A

when it is assumed that the bodies are rigid under the force i.e. they do not deform

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29
Q

what is one way to measure force

A

calibrated spring balance

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30
Q

what is mass, its unit and how it is denoted in formulas

A

quantity of matter of which a body is composed

Kg

m

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31
Q

what is weight, its unit and how it is denoted in formulas

A

force of gravity acting on a body

Newton

W

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32
Q

convert mass into weight

A

weight = mass x gravity

gravity = 9.81 m/s^2

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33
Q

convert weight into mass

A

mass = weight/gravity

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34
Q

what is density

A

mass per unit volume

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35
Q

equation and unit of density

A

density = mass/volume

unit = kg/m^3

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36
Q

what is important to remember about the density of a material

A

density of a material remains constant

if the mass of a body varies then the volume of the body will change proportionately

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37
Q

what is the definition of gravity

A

acceleration due to gravitational attraction between two bodies

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38
Q

how is gravity denoted in formulas and what is its unit

A

g

m/s^2

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39
Q

what is centre of mass and what does its location depend on

A

point where all the mass of the body can be assumed to act

location depends on distribution of mass in the object

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40
Q

what is the centre of gravity

A

point where the weight of the body can be assumed to act

astronauts would not have a centre of gravity

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41
Q

true or false - centre of mass always lies within the body

A

false - when leaning forward, centre of mass shifts to outside the pelvis

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42
Q

what is the definition of friction and what is its unit

A

force arising between two surfaces when they rub together

Newton

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43
Q

what does the amount of friction depend on

A

roughness of the surfaces and magnitude of force pushing them together

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44
Q

what is the measurement of the maximum friction force between 2 surfaces

A

co-efficient of friction

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45
Q

what is the equation of co-efficient of friction

A

co-efficient of friction

= Friction force / forces acting normally to the surface

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46
Q

what are the 3 types of friction

A

static, sliding and rolling

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47
Q

when does static friction only exist

A

when motion is ABOUT to occur between 2 surfaces

  • static friction force present is just sufficient to oppose the applied force
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48
Q

when does sliding friction only exist

A

when sliding occurs between two surfaces

49
Q

what is the relationship between static and sliding friction

A

sliding friction is LESS than static friction

more force is required to start a body moving against a frictional force than to keep it moving

50
Q

what is the equation for calculating maximum force

A

Fmax = Weight x friction co-effecient

51
Q

what is unit for maximum force

A

Newton

52
Q

what is definition of pressure

A

force exerted per unit area on a surface

[i.e. as size of area increases, pressure decreases]

53
Q

equation and unit for pressure

A

pressure = force / area

unit = Pascal (Pa)

[area should be in metres squared]

54
Q

what is static equilibrium in force analysis

A

no resultant force, all the forces are perfectly balanced

no change in state of motion

NO ACCELERATION i.e. can be in constant linear/angular velocity

55
Q

what is Newton’s III Law

A

To every action there is an equal and opposite reaction

56
Q

what is the equation for Force

A

Force = mass x acceleration

57
Q

what is Newton’s I law and what is it called

A

Every body remains at rest or moving at constant velocity unless it is acted upon by a resultant force

Law of inertia

58
Q

what is inertia and what is it represented by in the body

A

a body has a certain reluctance to accelerate which is its inertia

a body’s inertia is represented by its mass

59
Q

what what is Newton’s II law and what is it called

A

The acceleration of a body is proportional to the applied force and inversely proportional to its mass

Law of acceleration

60
Q

what is equation for acceleration

A

acceleration = force / mass

[rearranged from force = mass x acceleration]

61
Q

what is forward dynamics

A

finding the acceleration due to known forces acting on the body

62
Q

what is backwards dynamics

A

working out forces when motion is known

63
Q

what is dynamic equilibrium

A

when sum of forces does not equal zero

[left with resultant unbalanced force]

64
Q

what is the equation for inclined plane

A

mgsin(theta)

where m = mass, g = gravity

65
Q

what is the equation for perpendicular plane

A

mgcos(theta)

66
Q

what is momentum

A

body’s resistance to change its motion and its velocity

67
Q

equation for momentum and units

A

momentum = mass x velocity

unit = kg m/s or N s (newton second)

68
Q

how does Newton’s II law applied to momentum

A

the rate of change of linear momentum is proportional to the applied force

69
Q

what does Conservation of momentum mean

A

total momentum before collision is equal to total momentum after collision.

70
Q

what is the equation for rate of change of motion

A

Force = mass(final velocity - initial velocity) / time

71
Q

what is Newton’s I law in relation to momentum

A

a body will continue to move with constant momentum unless an external force acts to change that momentum

72
Q

what is a moment of a force

A

is the tendency of a force to produce a rotation about an axis

73
Q

what is the equation and units of a moment

A

moment = force x radius

units = Newton metres (Nm)

74
Q

what is rotational equilibrium

A

when the sum of all moments equals zero

75
Q

what are the 3 components of a lever system

A

rigid bar
fulcrum
effort and resistance force

76
Q

in the human body, what parts are the rigid bar, effort force and the resistance force

A

rigid bar - limb
effort force - muscles contracting
resistance force - external force e.g. gravity

77
Q

what is the equation to calculate mechanical advantage

A

effort distance / resistance distance

MA = df / dr

78
Q

in the human body lever system, what are muscles normally at

A

mechanical disadvantage

i..e forces produced by the muscles are greater than the forces resisting them

79
Q

why are muscles at mechanical disadvantage

A

the muscles insertion point tend to be closer to the fulcrum than the resistance force
i.e. have a smaller effort arm

also speed of movement
i.e. closer muscle is attached, smaller the contraction needed to make a larger movement and the quicker the movement

80
Q

what is a first class lever system and an example of it

A

when the fulcrum is located between the effort and the resistance

e.g. crowbar

system can be in either mechanical advantage or disadvantage depending on the length of the effort arm

81
Q

what is a second class lever system and an example of it

A

when the resistance is located between the effort and the fulcrum
e.g. wheelbarrow

system is at mechanical advantage as effort arm is always longer than resistance arm.

82
Q

what is a third class lever system and an example of it

A

when the effort is located between the fulcrum and the resistance

e.g. fishing rods, human body lever system

system is at mechanical disadvantage as effort arm is always shorter than resistance arm.

83
Q

what is the equation for the tangential linear velocity

A

tangenital linear velocity = radius x angular velocity

84
Q

what is the equation for tangential acceleration and what does it represent

A

tangential acceleration = radius x angular acceleration

represents the linear acceleration directed at a tangent to the circle formed by the motion.

85
Q

when summing the moments around the fulcrum, which way is positive and which way is negative

A 
anti-clockwise = positive
clockwise = negative
86
Q

when is tangential acceleration = 0

A

uniform angular motion (i.e. when the body rotates with a constant angular velocity).

87
Q

equation for radial acceleration, the second equation for radial acceleration and what is it also called

A

radial acceleration = radius x angular velocity^2
OR
radial acceleration = velocity^2 / radius

centripetal acceleration i.e. towards the centre

88
Q

what is moment of inertia and what is it dependant on

A

a quantity expressing a body’s tendency to resist angular
acceleration

body’s mass and how the mass is distributed

89
Q

how do you calculate the moment of a rotating object

A

M = I x alpha

where I = moment of inertia
alpha = angular acceleration

90
Q

what is the equation to calculate moment of inertia and what is the unit

A

I = m x r^2

r = radius of gyration
[can also be noted as k]

unit = kg m^2

91
Q

what is a way to roughly guess who has the biggest moment of inertia

A

the bigger the radius, the bigger the moment of inertia

92
Q

what is angular momentum and what principle also applies to angular momentum

A

incorporates a body’s resistance to change its rotatory motion (inertia) and its angular velocity

the principle of conservation of momentum

93
Q

what is equation for angular momentum, and the units

A

angular momentum = moment of inertia x angular velocity

L = I x omega 
Unit = kg m^2 rad s^-1
94
Q

what are the 2 assumptions of bio-mechnical models

A
  1. the body segments are rigid.

2. the joints are frictionless.

95
Q

given that it is assumed that body segments are rigid, what else is assumed

A
  1. the position of the centre of mass remains fixed relative to the segment.
  2. the moment of inertia of each segment remains constant.
  3. the length of each segment remains constant.
96
Q

what is Anthropometry and what parameters are needed to calculate it

A

to calculate the human body’s size and form

length, mass, centre of mass and radius of gyration

97
Q

why would the radius of gyration be larger at the proximal end than the distal end

A

because more mass is distributed further from the proximal end than the distal end

98
Q

equation to calculate work done and units

A

work done = force x distance

w = Fs

unit = Joules

99
Q

what is the equivalent unit of Joules

A

1 kg m^2 s^-2

100
Q

what is ‘work’

A

occurs when a force moves a body

101
Q

what is ‘power’

A

rate at which energy is expended or work is done

102
Q

equation of power and unit

A

power = work done / time taken

p = w/t

unit = watt (W)

103
Q

what is the equivalent of 1 watt

A

1 J s^-1

104
Q

what is energy and its unit

A

the capacity to do work

unit = Joules (J)

105
Q

what is the equation for linear kinetic energy

A

KE = 1/2 x mass x velocity^2

KE = 1/2mv^2

106
Q

what is the equation for rotary kinetic energy

A

KE = 1/2 x moment of inertia x angular velocity ^2

107
Q

what is the definition of kinetic energy and potential energy

A

KE = energy possessed by a body due to its motion

PE = energy possessed by a body because of its position

108
Q

what is the equation for PE

A 
PE = mass x gravity x height 
OR = weight x height
109
Q

what is the 1st law of thermodynamics

A

Conservation of Energy

  • energy cannot be created or destroyed
  • energy can be changed from one form to another.
110
Q

what does conservation of energy mean in terms of KE and PE

A

PE = KE

111
Q

if 2 objects were dropped from the same height, one at 10kg mass and one at 20kg mass, which would hit the ground first?

A

would hit the ground simultaneously
PE = KE therefore mgh = 1/2 mv^2

rearrange v = square root of 2 x gravity x height

therefore, velocity is independent of mass

112
Q

what is the relationship between acceleration due to gravity and mass

A

acceleration due to gravity is independent of mass

113
Q

what are the aerodynamic forces

A 
relative velocity 
type of flow - laminar or turbulent 
drag
lift
magnus effect
114
Q

what is laminar flow

A

when air flows in a smooth regular manner

115
Q

what is turbulent flow

A

when the regular smooth flow breaks down and the path that air particles take are random and unordered

116
Q

what can be used to predict whether an object will have laminar or turbulent flow

A

Reynolds Number

RE = {air density x diameter x velocity} divided by air viscosity

RE < 2000 = flow will be laminar

RE > 3000 = flow will be turbulent

117
Q

why are golf balls dimpled

A

to cause less drag

118
Q

what is the magnus effect

A

occurs when projectiles spin

  • one side of the ball, A, will have a higher flow velocity than the other side of the ball, B.
  • means pressure on side A is less than that of side B

think of the banana shot in football free kicks.

119
Q

multiplication factors

A 
kilo = k = 10 ^ 3 
mega = M = 10 ^ 6
G = 10 ^ 9
centi = c = 10 ^ -2
milli = m = 10 ^ -3
micro = 10 ^ -6

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