foundation of biomechanics Flashcards
Pythagoras theorem?
A^2 + B^2 = C^2
Formula for finding out angles and lengths in a right angled triangle?
SOH CAH TOA
How to label a triangle?
Hypotenuse will be the diagonal
Adjacent will be side next to angle which isn’t the hypotenuse
Opposite will be side opposite from angle you are looking at?
How can triangle formulas be used to find distance traveled by ball?
Draw right angle triangle, will be given angle and vertical velocity or horizontal velocity and just work it out using formula
Qualitative analysis is?
Description of movement
Requires experienced coach
Quantitative analysis?
Numerical evaluation based on data collected during motion
Allows assessment of aspects which can’t be observed eg. force
Removes subjectivity
What is kinesiology?
Scientific study of human movement
Mainly qualitative
What is biomechanics?
Considered to be more quantitive
Derived from mechanics, involves motion and effect of forces on living organisms
2 types of motion present in human movement or object propelled by a human?
Linear (translational) - motion along a straight or curved pathway in which all points on a body/object move the same distance in the same amount of time
Angular - motion about a given point so that different regions of the same body part/region do not move through the same distance in a given time.
What is kinematics?
Characteristics of motion from a spatial and temporal perspective
Without references to forces causing the motion
Variables of interest are therefore position, velocity and acceleration
What is kinetics?
Area of study that examines forces acting on a system (human body or an object)
The forces can be external (ground reaction force)
Internal (muscle and bones)
What’s a static system?
Systems that aren’t moving, or moving at a constant speed
So it’s in equilibrium
What’s a dynamic system?
Systems that are being accelerated
What’s sagittal plane?
Cut through the middle of pecs
What’s transverse plane?
Cut through belly button (rubber ring around you)
What’s frontal plane?
Cut across shoulders
What’s rectilinear translation?
Body travels in a straight path
What’s curvilinear translation?
Body travels in a curved path
What is the sampling frequency?
Number of pictures per second (frames/fields)
Units = Hz
What is digitisation?
Giving selected points numerical values allowing linear and angular displacements of joints and anatomical landmarks to be determined
This allows the calculation of velocities and accelerations
Effectively turns a qualitative video into a quantitative one
What is scaling?
Conversion of measured distance into real units
To work this out from screen to reality
Find out what 1mm is on the screen in metres by dividing in reality by mm on screen
Then multiply what your value is by the amount of mm if you asked a different length
Always make sure answer is in metres
Difference between distance and displacement?
Distance is the length of the path that it follows
Where as displacement is the length of a straight line joining its initial and final positions, taking note of the direction of this line
What is speed?
speed = distance / time
Scalar quantity
What is velocity?
How fast an object moves and in which direction
Velocity = displacement / time
So velocity = change in position / change in time
Vector quantity ( magnitude and direction)
Equation for the first central difference method?
Vx2 = (x3 - x1) / (t3 - t1)
Essentially velocity = (Final x position - starting x position) / (final time - initial time)
units of velocity is m/s or m.s^-1
Use values either side of the one your trying to find at a specific time point
With new values for velocity can do this again to find out acceleration
What is acceleration?
a = change in velocity / change in time
So basically = (final velocity - initial velocity) / (final time - initial time)
Units are m.s^-2
What is uniform acceleration?
Rate of change of velocity is constant
So acceleration is constant
Value of gravity?
9.81 m.s^-2
Equations for uniform acceleration?
u= initial velocity v = final velocity s = displacement of the object a = acceleration t = time
v = u + at v^2 = u^2 + 2as s = ut + 0.5at^2
Does mass influence motion in flight?
NO
If an object is moving upwards it’s acceleration is and if it’s moving downwards?
a = -g = -9.81 m.s^-2
Air resistance assumed to be negligible
a = g = 9.81 m.s^-2
Theory on motion of flight?
An object will take the same amount of time to reach max height to then reach floor again
Time up = time down
When an abject is in flight do we consider the vertical and horizontal components separately?
Yes
Equations apply to both
How to answer a question when you need to use horizontal and vertical velocity?
Work out flight time, using vertical component
Work out with acceleration, initial velocity and the final velocity being 0, but remember need to multiply the flight time by 2 to find full value
Now can work out the unknown you want
What is the resultant velocity composed of?
Vertical and horizontal velocity
Worked out with Pythagorus and SOH CAH TOA
What angle in theory gives optimum range in a projectile?
45 degrees
What does a greater vertical velocity component consist of?
Greater Height
Greater flight time
Greater range
What does a greater horizontal velocity consist of?
Same height
Same flight time
Greater range
What is inertia?
The resistance of a body to motion
What is mass?
The amount of matter makes up a body
Greater mass = greater inertia
Standard unit is kg
What is force?
The cause of motion
Alters, or tends to alter, a body’s state of rest or uniform motion
Unit = Newtons (N)
1 N accelerates a 1 kg mass by 1m.s^-2
What is a vector?
Provides magnitude and direction
What is Newtons law of gravitation?
F ∝ (m1 x m2 ) / d^2
F = force acting on each particle
m1 = mass of first object
m2 = mass of second object
d = distance between the mass centres
Features of weight?
Weight = Mass x gravity
Weight varies slightly depending on location (as distance to centre of earth varies)
Unit is newtons
What is Newton’s first law of motion?
Everybody continues in a state of rest, or uniform motion in a straight line, unless compelled to change that state by external forces exerted upon it
What is Newtons second law of motion?
Force = mass x acceleration
Newton’s 3rd law of motion?
For every force that is exerted by one body on another, there is an equal and opposite force exerted by the second body on the first
In a vertical Ground Reaction force graph for running, what’s is the small increase, and the highest point and scalings?
Peak impact force is the small increase in bell curve
Peak active force top of bell curve
0.3 seconds on x axis
Around 2500 N on y axis
Features of horizontal GRF for running?
Symmetrical goes negative then positive (sideways figure of 8)
Peak braking force is smallest value
Peak propulsive force is highest value
It’s the same for walking but obviously time increases
0.3 seconds on x axis
Around 400 N on y axis
Features of vertical GRF for walking?
“M” shaped
Time has increased
What does running with a forefoot stride potentially suggest? (promoted from being barefoot)
Reduce risk in injury as there isn’t the peak impact force (it’s not as prominent)
Factors that affect GRF?
Speed Mass Surface Type of running technique Footwear
Equation for momentum (P)?
Momentum (kg.m.s^-1) = mass (kg) x velocity (m.s^-1)
Vector quantity so has magnitude and direction
Total momentum of a system =?
Sum of the momenta of all the particle in the system
What is newtons law of inertia?
An object/system will remain at rest or un uniform motion in a straight line unless acted upon by an external force
Law of the conservation of momentum?
Doesn’t change unless an external force act upon it
2 types of collisions?
Elastic collisions - kinetic energy of the system is conserved - very uncommon
Inelastic collisions - kinetic energy is transferred to another form of energy
Total system momentum is conserved during collisions
So momentum before the collision = momentum after collision
How to work out the momentum of a system and then the final velocity of the system?
Work out Total momentum of system by summing all the individuals momentum’s taking into account direction
Then add all the masses and rearrange for the system velocity
Equation for force involving momentum and time?
Force (N) = (mass (kg) x change in velocity) / change in time
Force (N) = Change in momentum / Change in time
What does impulse equal, therefore how do we increase it?
Impulse (N . s) = Change in momentum
= Mass x (v-u)!!!!!!!!!!!!!!!!
= Force x time over which force was applied
Increase force
Increase time over which the force is applied
Describe horizontal force and impulse in running?
Initially there is a negative horizontal impulse and braking, then mid stance switches to a positive horizontal impulse which is propulsive
Impulse = area under the force-time curve if plotted
So total net impulse = positive + negative impulse (negative horizontal impulse is negative on graph)
If impulse = 0, then there is no change in impulse so the person is moving at a constant speed
Also if positive is larger then speeding up, if negative is larger then we are slowing down
Given impulses and mass how do you work out how high someone has jumped?
Find net impulse in N.s
Look at second half of jump so time is halved
Use Net impulse = mass x v
(as u will be 0)
Now know u so can input into Suvat to work out s
or if don’t need to use impulse can just imput the second half of the jump into s = ut + 0.5at^2
Equation for pressure?
Force(N) / Area (m^2)
Units = Pascals = N . m^-2
Equation for mechanical work?
Work(J) = Force (N) x Displacement (m)
1 joule = 1 Nm
What is positive work?
When the displacement is in the same in the same direction as the force of interest
What is negative work?
When the displacement is in the opposite direction of the force of interest
Joules value will be negative as well
What is the total system work?
= Sum of positive (normally work done by muscle) and negative work (normally work done by gravity)
Can be Simplified to:
W = d(f -mg)
w= total system work d = displacement f = force m = mass g = gravity
What’s the value for mechanical work if an object isn’t moving?
0
Why is work done not a very accurate measure?
It doesn’t consider time
Equation for power?
It’s the rate at which work is performed
Power = Work / time
Units = J.s^-1 = Watts (W)
Or
Power = Force x velocity
Equation for kinetic energy and definition?
Energy resulting from motion
KE = 1/2 x mass x velocity^2
Equation gravitational energy and definition?
The energy an object posses because of it’s position in a gravitational field. We will usually think of this as an objects height from the ground
PE = mass x gravity x height
Equation for strain energy and definition?
Stored potential energy in a object which is deformed by a force
SE = 1/2 . k . x^2
(using “.” for multiplication)
k = stiffness (N/m)
x = displacement (m)
A way to find total mechanical energy?
= KE + PE +SE
At the apex of a projectiles flight the potential energy will be?
All of the total energy of the system
2 types of friction?
Sliding
Rolling
What’s force applied (P), friction force (F) and reaction force (R)?
P = the force pushing F = force resisting (limiting friction is the highest value it can take in the circumstance) R = perpendicular to contact surface (normally straight up)
Equation for friction force is equal to?
The reaction force (R) multiplied by a constant (u)
F = uR
F/R = u
Does mass and surface area affect friction?
NO
What does the constant (u) equal when you have been given an angle in which something starts to slide?
u = tan(x)
Equation for friction force in sliding friction?
Fs (friction force) = coefficient of sliding friction (us) x R (reaction force)
Coefficient of sliding friction < coefficient of limiting friction
What does Fy/Fz equal?
u
Equation for the coefficient of restitution?
Giving you e = square root of (height bounced /height dropped)
Other factors that can increase e?
Temperature
What increases force of attraction?
Smaller distance between objects
Larger masses
What’s the line of gravity?
Is the vertical line through the point at which the object would balance
What’s the centre of gravity (means the centre of mass as well)?
Where the 2 lines of gravity (horizontal and vertical) meet
= the point about which gravitational force is balance
it is the point through which the resultant force acts
3 ways to determine the centre of gravity?
Balance method
Suspension
Reaction board
5 ways to asses sports performance?
Direct observation
Video observation
Video analysis to obtain kinematic data
Force analysis to obtain kinetic data with a force plate
Pressure analysis to obtain kinetic data with a pressure plate
How to answer a large study question?
Introduction:
What is the question you are trying to answer?
Why would it be beneficial to investigate this?
Population:
How many participants would you use?
How would you determine the inclusion/exclusion criteria?
Equipment:
What equipment would be required?
Can you add extra information such as make/model and recording frequency?
Experimental setup
Testing procedures: What would happen? Conditions? Repeat trials? Order?
Data collected: What type (kinematic or kinetic)? Which variables would be of interest?
Implications:
What does the data tell you?
How does it relate to the question you were trying yo answer
How to draw a Standing vertical jump impulse and answer the question about working it out?
y axis goes up to 3.5 seconds
x axis goes up to 2500 N
In comparison to BW line, straight line for a bit, small down, big bump little bump, straight down to touch x axis, big gap, massive straight up, down through BW line then up to bw line and wiggle
Take up is on left side of gap on axis, landing is on right side
Peak take off force is top of hump before drop down and peak landing force is top off hump on right side
Negative take-off impulse is area of the dip at the beginning, and positive is the area above the BW line on the next bit
Have force time history printed onto gridded paper from the force plate
Calculate what one mm^2 is in N.s (0.5 N.s)
Net impulse = 100 squares in negative (-50 N.s) + 600 squares (300 N.s) = 250 N.s
Impulse = mass x final velocity
250 = 100v v = 2.5
2.5 = 9.81t t = 0.255
s = (0 x 0.255) + (0.5 x 9.81 x 0.255^2) = 0.32 m
Different foot arches on a pressure plate?
High Arch:
Only visible is toes and ball of foot
Medium Arch:
Just a normal foot toes are visible
Low arch:
Broader foot can only see big toe
Software used in digitising?
MaxTRAQ
Software used when we measured a punch?
Codamotion software
Describe steps in a friction experiment looking at turning?
Use the AMTI Force platform to obtain vertical and anterior-posterior force time histories at 500Hz during turning
From the anterior-posterior need the values of:
Peak Braking force
Time of peak braking force
Then from vertical:
Vertical force at time of peak braking force (N)
The put into the equation:
Coefficient of friction = Fy/Fz = Peak braking force / Vertical force at the time of peak braking
Describe steps in working out friction between a shoe and a surface?
Place shoe on a surface and slowly raise until find a point in which shoes starts to slide, find just before this point and measure the angle with a goniometer
Then use the equation u = tan(x)
When walking instead of walking what does it do to the scaling force?
Halves it roughly
How do you get mass in vertical jump and what do you call grid?
Create scaling factor
Calculate mass from body weight line (/9.81)
