Foundations of biomechanics mid term test notes

Question 1

Pythagoras theorem?

Answer 1

A^2 + B^2 = C^2

Question 2

Formula for finding out angles and lengths in a right angled triangle?

Answer 2

SOH CAH TOA

Question 3

How to label a triangle?

Answer 3

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?

Question 4

How can triangle formulas be used to find distance traveled by ball?

Answer 4

Draw right angle triangle, will be given angle and vertical velocity or horizontal velocity and just work it out using formula

Question 5

What is the sampling frequency?

Answer 5

Number of pictures per second (frames/fields)

Units = Hz

Question 6

What is speed?

Answer 6

speed = distance / time

Question 7

What is velocity?

Answer 7

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)

Question 8

Difference between distance and displacement?

Answer 8

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

Question 9

Equation for the first central difference method?

Answer 9

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

Question 10

What is acceleration?

Answer 10

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

Question 11

Value of gravity?

Answer 11

9.81 m.s^-2

Question 12

Equations for uniform acceleration?

Answer 12

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

Question 13

If an object is moving upwards it’s acceleration is and if it’s moving downwards?

Answer 13

a = -g = -9.81 m.s^-2

Air resistance assumed to be negligible

a = g = 9.81 m.s^-2

Question 14

Theory on motion of flight?

Answer 14

An object will take the same amount of time to reach max height to then reach floor again

Time up = time down

Question 15

How to answer a question when you need to use horizontal and vertical velocity?

Answer 15

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

Question 16

What is the resultant velocity composed of?

Answer 16

Vertical and horizontal velocity

Worked out with Pythagorus and SOH CAH TOA

Question 17

Equation for force?

Answer 17

Force = mass x acceleration

Question 18

What is Newtons law of gravitation?

Answer 18

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

Question 19

Units for weight?

Answer 19

Newtons

Question 20

Equation for momentum (P)?

Answer 20

Momentum (kh.m.s^-1) = mass (kg) x velocity (m.s^-1)

Vector quantity so has magnitude and direction

Question 21

Total momentum of a system =?

Answer 21

Sum of the momenta of all the particle in the system

Question 22

How to work out the momentum of a system and then the final velocity of the system?

Answer 22

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

Question 23

Equation for force involving momentum and time?

Answer 23

Force (N) = (mass (kg) x change in velocity) / change in time

Force (N) = Change in momentum / Change in time

Question 24

What does impulse equal, therefore how do we increase it?

Answer 24

Impulse (N . s) = Change in momentum = Force x time over which force was applied

Increase force

Increase time over which the force is applied

Question 25

How to work out a final velocity if given net impulse, initial velocity and mass?

Answer 25

Use fact impulse = change in momentum = (mass x final velocity) - (mass x initial velocity)

Can then just rearrange

Question 26

Given impulses and mass how do you work out how high someone has jumped?

Answer 26

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

Question 27

Equation for pressure?

Answer 27

Force(N) / Area (m^2)

Units = Pascals = N . m^-2

Question 28

Equation for mechanical work?

Answer 28

Work(J) = Force (N) x Displacement (m)

1 joule = 1 Nm

Question 29

What is the total system work?

Answer 29

= 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

Question 30

Equation for power?

Answer 30

It’s the rate at which work is performed

Power = Work / time

Units = J.s^-1 = Watts (W)

Or

Power = Force x velocity

Question 31

Equation for kinetic energy and definition?

Answer 31

KE = 1/2 x mass x velocity^2

Question 32

Equation gravitational energy and definition?

Answer 32

PE = mass x gravity x height

Question 33

Equation for strain energy and definition?

Answer 33

SE = 1/2 . k . x^2

k = stiffness (N/m)

x = displacement (m)

Question 34

A way to find total mechanical energy?

Answer 34

= KE + PE +SE

Question 35

At the apex of a projectiles flight the potential energy will be?

Answer 35

All of the total energy of the system