Mechanics Unit 1 Flashcards
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
there are 2 supplementary SI units - which 1 do we need to know
radian (rad) - measure of angle
what is 2 pie radians equal to
360 degrees
how can we convert radians into degrees
180/pie multiply by angle in radians
how can we convert degrees into radians
pie/180 multiply by angle in degrees
what is the definition of a scalar and vector quantity
scalar = quantity with magnitude only
vector = quantity with magnitude and direction
list some vector quantities
displacement velocity angular displacement angular velocity force momentum acceleration
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
equation for average velocity
change in displacement / time taken
on a displacement-time graph, how can the velocity be calculated
the gradient of the graph is the velocity
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
equation for acceleration
change in velocity / time taken
unit for velocity
m/s
unit for acceleration
m/s^2
what needs to be considered when calculating acceleration
acceleration due to gravity = 9.81m/s^2
what graph can be used to calculate acceleration
velocity-time graph
- the gradient is the acceleration
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)
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
what is rotary motion
object rotating about a point on itself or about an external fixed point
what is angular velocity
angular displacement travelled per second
i.e. change in angular displacement / time taken
what is the unit for angular velocity
rad/s
what is instantaneous angular velocity
angular velocity at an instant time
what is angular acceleration and its units
rate of change of angular velocity
rad / s^2
equation of angular acceleration
change in angular velocity / time taken
unit of Force
Newton (N)
what is 1N equal to
1 kg m/s^2
what is the 2 effects of a force
change the body’s position
deform the body’s shape
what is rigid body mechanics
when it is assumed that the bodies are rigid under the force i.e. they do not deform
what is one way to measure force
calibrated spring balance
what is mass, its unit and how it is denoted in formulas
quantity of matter of which a body is composed
Kg
m
what is weight, its unit and how it is denoted in formulas
force of gravity acting on a body
Newton
W
convert mass into weight
weight = mass x gravity
gravity = 9.81 m/s^2
convert weight into mass
mass = weight/gravity
what is density
mass per unit volume
equation and unit of density
density = mass/volume
unit = kg/m^3
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
what is the definition of gravity
acceleration due to gravitational attraction between two bodies
how is gravity denoted in formulas and what is its unit
g
m/s^2
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
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
true or false - centre of mass always lies within the body
false - when leaning forward, centre of mass shifts to outside the pelvis
what is the definition of friction and what is its unit
force arising between two surfaces when they rub together
Newton
what does the amount of friction depend on
roughness of the surfaces and magnitude of force pushing them together
what is the measurement of the maximum friction force between 2 surfaces
co-efficient of friction
what is the equation of co-efficient of friction
co-efficient of friction
= Friction force / forces acting normally to the surface
what are the 3 types of friction
static, sliding and rolling
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
when does sliding friction only exist
when sliding occurs between two surfaces
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
what is the equation for calculating maximum force
Fmax = Weight x friction co-effecient
what is unit for maximum force
Newton
what is definition of pressure
force exerted per unit area on a surface
[i.e. as size of area increases, pressure decreases]
equation and unit for pressure
pressure = force / area
unit = Pascal (Pa)
[area should be in metres squared]
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
what is Newton’s III Law
To every action there is an equal and opposite reaction
what is the equation for Force
Force = mass x acceleration
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
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
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
what is equation for acceleration
acceleration = force / mass
[rearranged from force = mass x acceleration]
what is forward dynamics
finding the acceleration due to known forces acting on the body
what is backwards dynamics
working out forces when motion is known
what is dynamic equilibrium
when sum of forces does not equal zero
[left with resultant unbalanced force]
what is the equation for inclined plane
mgsin(theta)
where m = mass, g = gravity
what is the equation for perpendicular plane
mgcos(theta)
what is momentum
body’s resistance to change its motion and its velocity
equation for momentum and units
momentum = mass x velocity
unit = kg m/s or N s (newton second)
how does Newton’s II law applied to momentum
the rate of change of linear momentum is proportional to the applied force
what does Conservation of momentum mean
total momentum before collision is equal to total momentum after collision.
what is the equation for rate of change of motion
Force = mass(final velocity - initial velocity) / time
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
what is a moment of a force
is the tendency of a force to produce a rotation about an axis
what is the equation and units of a moment
moment = force x radius
units = Newton metres (Nm)
what is rotational equilibrium
when the sum of all moments equals zero
what are the 3 components of a lever system
rigid bar
fulcrum
effort and resistance force
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
what is the equation to calculate mechanical advantage
effort distance / resistance distance
MA = df / dr
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
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
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
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.
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.
what is the equation for the tangential linear velocity
tangenital linear velocity = radius x angular velocity
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.
when summing the moments around the fulcrum, which way is positive and which way is negative
anti-clockwise = positive clockwise = negative
when is tangential acceleration = 0
uniform angular motion (i.e. when the body rotates with a constant angular velocity).
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
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
how do you calculate the moment of a rotating object
M = I x alpha
where I = moment of inertia
alpha = angular acceleration
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
what is a way to roughly guess who has the biggest moment of inertia
the bigger the radius, the bigger the moment of inertia
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
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
what are the 2 assumptions of bio-mechnical models
- the body segments are rigid.
2. the joints are frictionless.
given that it is assumed that body segments are rigid, what else is assumed
- the position of the centre of mass remains fixed relative to the segment.
- the moment of inertia of each segment remains constant.
- the length of each segment remains constant.
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
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
equation to calculate work done and units
work done = force x distance
w = Fs
unit = Joules
what is the equivalent unit of Joules
1 kg m^2 s^-2
what is ‘work’
occurs when a force moves a body
what is ‘power’
rate at which energy is expended or work is done
equation of power and unit
power = work done / time taken
p = w/t
unit = watt (W)
what is the equivalent of 1 watt
1 J s^-1
what is energy and its unit
the capacity to do work
unit = Joules (J)
what is the equation for linear kinetic energy
KE = 1/2 x mass x velocity^2
KE = 1/2mv^2
what is the equation for rotary kinetic energy
KE = 1/2 x moment of inertia x angular velocity ^2
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
what is the equation for PE
PE = mass x gravity x height OR = weight x height
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.
what does conservation of energy mean in terms of KE and PE
PE = KE
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
what is the relationship between acceleration due to gravity and mass
acceleration due to gravity is independent of mass
what are the aerodynamic forces
relative velocity type of flow - laminar or turbulent drag lift magnus effect
what is laminar flow
when air flows in a smooth regular manner
what is turbulent flow
when the regular smooth flow breaks down and the path that air particles take are random and unordered
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
why are golf balls dimpled
to cause less drag
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.
multiplication factors
kilo = k = 10 ^ 3 mega = M = 10 ^ 6 G = 10 ^ 9
centi = c = 10 ^ -2 milli = m = 10 ^ -3 micro = 10 ^ -6
