Foundations of biomechanics mid term test notes 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
What is the sampling frequency?
Number of pictures per second (frames/fields)
Units = Hz
What is speed?
speed = distance / time
What is velocity?
Rate of change in position
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)
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
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 work out acceleration
What is acceleration?
Rarely constant in sports
Acceleration (a) is the rate of change of velocity
a = change in velocity / change in time
So basically = (final velocity - initial velocity) / (final time - initial time)
If finding at certain time calculate from the frames either side
Units are m.s^-2
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
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
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
Equation for force?
Force = mass x acceleration
What is Newtons law of gravitation?
Any 2 particles of ammeter attract one another with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them
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
Units for weight?
Newtons
Equation for momentum (P)?
Momentum (kh.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
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 = Force x time over which force was applied
Increase force
Increase time over which the force is applied
How to work out a final velocity if given net impulse, initial velocity and mass?
Use fact impulse = change in momentum = (mass x final velocity) - (mass x initial velocity)
Can then just rearrange
Given impulses and mass how do you work out how high someone has jumped?
Use v^2 = u^2 + 2as
To get s = (v^2-u^2)/2a = s
However can’t work out s as don’t know u
So use change in momentum = mass x (u -v) = impulse
Add all the impulses together to get a total net impulse
So (impulse / mass) = u
(as v will be 0)
Then input u into the original equation
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 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
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?
KE = 1/2 x mass x velocity^2
Equation gravitational energy and definition?
PE = mass x gravity x height
Equation for strain energy and definition?
SE = 1/2 . k . x^2
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
