Mechanics Unit 1 Flashcards Preview

BMSc SB > Mechanics Unit 1 > Flashcards

Flashcards in Mechanics Unit 1 Deck (119):
1

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

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

2

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

radian (rad) - measure of angle

3

what is 2 pie radians equal to

360 degrees

4

how can we convert radians into degrees

180/pie multiply by angle in radians

5

how can we convert degrees into radians

pie/180 multiply by angle in degrees

6

what is the definition of a scalar and vector quantity

scalar = quantity with magnitude only

vector = quantity with magnitude and direction

7

list some vector quantities

displacement
velocity
angular displacement
angular velocity
force
momentum
acceleration

8

what are the 2 ways to write location of a vector

Cartesian system - x, y and z axis

Polar co-ordinates - resultant vector and angle in degrees

9

equation for average velocity

change in displacement / time taken

10

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

the gradient of the graph is the velocity

11

what is instantaneous velocity on a displacement-time graph

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

12

equation for acceleration

change in velocity / time taken

13

unit for velocity

m/s

14

unit for acceleration

m/s^2

15

what needs to be considered when calculating acceleration

acceleration due to gravity = 9.81m/s^2

16

what graph can be used to calculate acceleration

velocity-time graph
- the gradient is the acceleration

17

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

u = starting velocity (m/s)

v = final velocity (m/s)

a = acceleration (m/s^2)

s = displacement (m)

t = time taken (s)

18

what are the equations of linear motion

v = u + at

v^2 = u^2 + 2as

s= 1/2 (u + v)t

s = ut + 1/2at^2

s = vt - 1/2at^2

19

what is rotary motion

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

20

what is angular velocity

angular displacement travelled per second

i.e. change in angular displacement / time taken

21

what is the unit for angular velocity

rad/s

22

what is instantaneous angular velocity

angular velocity at an instant time

23

what is angular acceleration and its units

rate of change of angular velocity

rad / s^2

24

equation of angular acceleration

change in angular velocity / time taken

25

unit of Force

Newton (N)

26

what is 1N equal to

1 kg m/s^2

27

what is the 2 effects of a force

change the body's position

deform the body's shape

28

what is rigid body mechanics

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

29

what is one way to measure force

calibrated spring balance

30

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

quantity of matter of which a body is composed

Kg

m

31

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

force of gravity acting on a body

Newton

W

32

convert mass into weight

weight = mass x gravity

gravity = 9.81 m/s^2

33

convert weight into mass

mass = weight/gravity

34

what is density

mass per unit volume

35

equation and unit of density

density = mass/volume


unit = kg/m^3

36

what is important to remember about the density of a material

density of a material remains constant

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

37

what is the definition of gravity

acceleration due to gravitational attraction between two bodies

38

how is gravity denoted in formulas and what is its unit

g

m/s^2

39

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

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

location depends on distribution of mass in the object

40

what is the centre of gravity

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

(astronauts would not have a centre of gravity)

41

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

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

42

what is the definition of friction and what is its unit

force arising between two surfaces when they rub together

Newton

43

what does the amount of friction depend on

roughness of the surfaces and magnitude of force pushing them together

44

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

co-efficient of friction

45

what is the equation of co-efficient of friction

co-efficient of friction

= Friction force / forces acting normally to the surface

46

what are the 3 types of friction

static, sliding and rolling

47

when does static friction only exist

when motion is ABOUT to occur between 2 surfaces

- static friction force present is just sufficient to oppose the applied force

48

when does sliding friction only exist

when sliding occurs between two surfaces

49

what is the relationship between static and sliding friction

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

what is the equation for calculating maximum force

Fmax = Weight x friction co-effecient

51

what is unit for maximum force

Newton

52

what is definition of pressure

force exerted per unit area on a surface

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

53

equation and unit for pressure

pressure = force / area

unit = Pascal (Pa)

[area should be in metres squared]

54

what is static equilibrium in force analysis

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

what is Newton's III Law

To every action there is an equal and opposite reaction

56

what is the equation for Force

Force = mass x acceleration

57

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

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

Law of inertia

58

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

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

a body's inertia is represented by its mass

59

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

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

Law of acceleration

60

what is equation for acceleration

acceleration = force / mass

[rearranged from force = mass x acceleration]

61

what is forward dynamics

finding the acceleration due to known forces acting on the body

62

what is backwards dynamics

working out forces when motion is known

63

what is dynamic equilibrium

when sum of forces does not equal zero

[left with resultant unbalanced force]

64

what is the equation for inclined plane

mgsin(theta)

where m = mass, g = gravity

65

what is the equation for perpendicular plane

mgcos(theta)

66

what is momentum

body's resistance to change its motion and its velocity

67

equation for momentum and units

momentum = mass x velocity

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

68

how does Newton's II law applied to momentum

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

69

what does Conservation of momentum mean

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

70

what is the equation for rate of change of motion

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

71

what is Newton's I law in relation to momentum

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

72

what is a moment of a force

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

73

what is the equation and units of a moment

moment = force x radius

units = Newton metres (Nm)

74

what is rotational equilibrium

when the sum of all moments equals zero

75

what are the 3 components of a lever system

rigid bar
fulcrum
effort and resistance force

76

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

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

77

what is the equation to calculate mechanical advantage

effort distance / resistance distance

MA = df / dr

78

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

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

79

why are muscles at mechanical disadvantage

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

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

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

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

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

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

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

what is the equation for the tangential linear velocity

tangenital linear velocity = radius x angular velocity

84

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

tangential acceleration = radius x angular acceleration

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

85

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

anti-clockwise = positive
clockwise = negative

86

when is tangential acceleration = 0

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

87

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

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

centripetal acceleration i.e. towards the centre

88

what is moment of inertia and what is it dependant on

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

body's mass and how the mass is distributed

89

how do you calculate the moment of a rotating object

M = I x alpha

where I = moment of inertia
alpha = angular acceleration

90

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

I = m x r^2

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

unit = kg m^2

91

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

the bigger the radius, the bigger the moment of inertia

92

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

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

the principle of conservation of momentum

93

what is equation for angular momentum, and the units

angular momentum = moment of inertia x angular velocity

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

94

what are the 2 assumptions of bio-mechnical models

1. the body segments are rigid.
2. the joints are frictionless.

95

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

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

what is Anthropometry and what parameters are needed to calculate it

to calculate the human body's size and form

length, mass, centre of mass and radius of gyration

97

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

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

98

equation to calculate work done and units

work done = force x distance

w = Fs

unit = Joules

99

what is the equivalent unit of Joules

1 kg m^2 s^-2

100

what is 'work'

occurs when a force moves a body

101

what is 'power'

rate at which energy is expended or work is done

102

equation of power and unit

power = work done / time taken

p = w/t

unit = watt (W)

103

what is the equivalent of 1 watt

1 J s^-1

104

what is energy and its unit

the capacity to do work

unit = Joules (J)

105

what is the equation for linear kinetic energy

KE = 1/2 x mass x velocity^2

KE = 1/2mv^2

106

what is the equation for rotary kinetic energy

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

107

what is the definition of kinetic energy and potential energy

KE = energy possessed by a body due to its motion

PE = energy possessed by a body because of its position

108

what is the equation for PE

PE = mass x gravity x height
OR = weight x height

109

what is the 1st law of thermodynamics

Conservation of Energy
- energy cannot be created or destroyed
- energy can be changed from one form to another.

110

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

PE = KE

111

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

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

what is the relationship between acceleration due to gravity and mass

acceleration due to gravity is independent of mass

113

what are the aerodynamic forces

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

114

what is laminar flow

when air flows in a smooth regular manner

115

what is turbulent flow

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

116

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

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

why are golf balls dimpled

to cause less drag

118

what is the magnus effect

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

multiplication factors

kilo = k = 10 ^ 3
mega = M = 10 ^ 6
G = 10 ^ 9

centi = c = 10 ^ -2
milli = m = 10 ^ -3
micro = 10 ^ -6