ocr a level physical education a 7875 next previous module 2565 b1.2.1 ocr examinations a level...

Module 2565 B1.2.1

OCR A Level Physical Education A 7875

NextPrevious

OCR ExaminationsA Level Physical Education

A 7875

Module 2565 : Option B1part 2

Biomechanical Analysis of Human Movement

Module 2565 B1.2.2


NextPrevious

INDEX27 - LEVERS28 - CLASSIFICATION OF LEVERS29 - EFFICIENCY OF LEVERS30 - MOMENT OF FORCE - TORQUE - PRINCIPLE of

MOMENTS31 - CALCULATION OF EFFORT IN MUSCLE FORCE IN TRICEPS MUSCLE a worked example32 - PRINCIPAL AXES OF ROTATION - BODY PLANES &

AXES 33 - BODY PLANES FOR MOVEMENT34 - ANGULAR MOTION - TORQUE MOMENT OF FORCE / TORQUE / COUPLE35 - ANGULAR MOTION - ANALOGUES OF NEWTON’s

LAWS36 - ANGLE - ANGULAR DISPLACEMENT37 - ANGULAR VELOCITY38 - ANGULAR ACCELERATION39 - MOMENT OF INERTIA40 - MOMENT OF INERTIA41 - MOMENT OF INERTIA - The SPRINTER’S LEG42 - CONSERVATION OF ANGULAR MOMENTUM ANGULAR MOMENTUM CONSERVATION of ANGULAR MOMENTUM43 - CONSERVATION OF ANGULAR MOMENTUM -

EXAMPLES THE SPINNING SKATER / THE TUMBLING

GYMNAST44 - CONSERVATION OF ANGULAR MOMENTUM -

EXAMPLES DANCER - SPIN JUMP / THE SLALOM 45 - CONSERVATION OF ANGULAR MOMENTUM -

EXAMPLES THE LONG JUMPER - BEFORE TAKE-OFF

Index

3 - IMPULSE4 - IMPULSE - FOLLOW THROUGH5 - IMPULSE - FORCE TIME GRAPHS6 - IMPULSE - CALCULATION OF VELOCITY OF STRUCK BALL7 - WORK AND ENERGY - WORK8 - WORK AND ENERGY - ENERGY9 - APPLICATIONS OF WORK FORMULA

WORK FORMULA APPLIED TO THROWS10 - APPLICATIONS OF WORK FORMULA11 - APPLICATIONS OF WORK FORMULA

BOB SLEIGH START12 - POWER13 - PROJECTILES - PROJECTILES AND YOUR PPP14 - RELEASE15 - FLIGHT16 - FLIGHT - WEIGHT17 - FLIGHT - RELATIVE SIZE OF FORCES18 - FLIGHT - LARGE AIR RESISTANCE19 - FLIGHT - THE BERNOULLI EFFECT20 - FLIGHT AND LIFT - LIFT FORCES21 - SPIN - THE MAGNUS EFFECT22 - BOUNCING BALLS WITH SPIN23 - CENTRE OF MASS - WHERE IS THE CENTRE OF MASS?24 - BALANCE and TOPPLING25 - CENTRE OF MASS - GENERATION OF ROTATION

FORCE ACTING AT TAKE-OFF THROUGH CoM26 - CENTRE OF MASS - GENERATION OF ROTATION

FORCE ACTING AT TAKE-OFF NOT THROUGH CoM

Module 2565 B1.2.3


NextPrevious

IMPULSE

IMPULSE • another concept derived from Newton's second

law

• impulse = total change of momentum• = force x time• useful when large forces are applied for short

times

• examples of use of impulse :– fielder catching a hard cricket ball– bat, racquet, stick, golf club striking a ball– footballer kicking a ball

Impulse

Module 2565 B1.2.4


NextPrevious

IMPULSE

IMPULSE• = force x time

• when a bat strikes a ball, a large force is applied to the ball for a short time

• follow through when striking a ball :– increases time of contact– therefore increases impulse– therefore increases final momentum (and hence the

speed) of struck ball

• the turn in the discus throw– increases the time over which force is applied– therefore increases the impulse– and increases the final momentum of the discus– hence increases the speed of release and the distance

thrown

Impulse

Module 2565 B1.2.5


NextPrevious

IMPULSE

FORCE TIME GRAPHS• the area under this graph is the impulse

• the graph below represents the force time graph for the force between foot and ground during a foot strike when sprinting

• the bigger the area – the bigger the impulse– and the greater the change of

momentum of the runner– the greater the acceleration

Impulse

Module 2565 B1.2.6


NextPrevious

IMPULSE

CALCULATION OF VELOCITY OF STRUCK BALL

• estimate the area under the force time graph• this is the impulse, I = Ft• and I = change of momentum of the ball, =

mv

• divide by the mass of the ball gives you the change in velocity of the ball, = v

• subtract incoming velocity (= - u) (remember to make it negative if ball travels towards the bat)

• final velocity v = v - (- u)

Impulse

Module 2565 B1.2.7


NextPrevious

WORK AND ENERGY

WORK• is the scientific form of mechanical energy• work = force x distance moved in direction of force• unit the joule J

• example :– work done on a cycle ergometer– work = force x distance moved– force = weight hung from wheel in Newtons (the

weight will be 10 N per kg mass)– distance = circumference of wheel x number of

revolutions of wheel– answer in joules

Work and Power

Module 2565 B1.2.8


NextPrevious

WORK AND ENERGY

ENERGY• work is the same thing as energy• work is the energy used for exerting forces (i.e.

mechanical energy)

• energy for physical activity comes from chemical fuel foods

• the chemical reaction which converts this energy into work is a complex biochemical / physiological process involving ATP, glucose, and oxygen

• kinetic energy (KE) is energy due to movement

Work and Power

Module 2565 B1.2.9


NextPrevious

APPLICATIONS OF WORK FORMULA

WORK FORMULA APPLIED TO THROWS• work = force x distance• this work is provided by energy converted from food

fuel in the body

• the throwing action converts this work into kinetic energy (KE = energy of movement) of the thrown object

• therefore to maximise this KE, the thrower must maximise :– the force applied to the implement throughout the

throw– by doing strength training– and the distance over which the force is applied– by learning the technique of the throw– and doing flexibility training

Work and Power

Module 2565 B1.2.10


NextPrevious


Work and Power

FORCE DISTANCE GRAPH• work = force x distance• the area under the force time graph is equal to the work

done by the force over the distance

• in the case of the thrower this work is converted into kinetic energy (KE)

• the formula for KE = 1 m v2 2

• this formula enables you to work out the release velocity of the thrown implement

Module 2565 B1.2.11


NextPrevious


BOB SLEIGH START• the work formula is relevant• because force is applied over a

distance

• the work done by the pushers is converted into kinetic energy of the sleigh + bobsleighmen

• work = force x distance

• therefore maximum possible force has to be exerted over the maximum possible distance during the shove

Work and Power

Module 2565 B1.2.12


NextPrevious

POWER

POWER• = rate of doing work

= rate of using energy= work done or energy used

time taken • unit the watt W

• power = force x speed (another definition)• a powerful sportsperson can apply force at

speed

• example : to find a person's power running upstairs– he exerts a force = weight of

person– through a distance = height

moved– work = weight (N) x height (m) (ans J)

= potential energy gained by person

– power = work (ans W) time taken to run upstairs

Work and Power

Module 2565 B1.2.13


NextPrevious

PROJECTILES

PROJECTILES• the motion of objects in flight

– human bodies– shot / discus / javelin /

hammer– soccer / rugby / cricket

tennis / golf balls

• is governed by the forces acting– weight– air resistance– Magnus effect– aerodynamic lift

• and the direction of motion

PROJECTILES AND YOUR PPP• you should include an analysis

of any relevant projectile motion in your chosen sports in your PPP

• include analysis of– release conditions– forces likely to be acting– spin– flight pattern or path

Projectile Motion

Module 2565 B1.2.14


NextPrevious

RELEASE

Projectile Motion

DI STAN CETR AVELLED BY

PR OJ ECTI LE

angle ofrelease

height ofrelease

speed ofrelease

Module 2565 B1.2.15


NextPrevious

FLIGHT

Projectile Motion

FOR CES ACTI NG

w eight airresistance

aerodynam iclift

M agnuseff ect

Module 2565 B1.2.16


NextPrevious

FLIGHTWEIGHT• weight will always act on a body in flight• the amount to which weight is a predominant force acting

governs the shape of the flight path• if weight were the only force acting then the shape of the flight

path would be a parabola• some flight paths are similar to this

– shot / hammer– human body in jumps / tumbles / dives

Projectile Motion

Module 2565 B1.2.17


NextPrevious

FLIGHT

RELATIVE SIZE OF FORCES• the faster the projectile travels the

greater will be air resistance

• aerodynamic lift applies to– thrown objects with a wing shape

profile– javelin / discus / rugby ball /

American football / frisbee

• the Magnus effect applies to spinning balls

• if the shapes of the flight path differ from a parabola then some combination of these forces must be relatively large compared with the weight

Projectile Motion

Module 2565 B1.2.18


NextPrevious

FLIGHTLARGE AIR RESISTANCE• example :

– badminton shuttle struck hard

– the air resistance is very large compared with the weight

– the resultant force is very close to the air resistance

Projectile Motion

• the shuttle would slow down rapidly over the first part of the flight

• later in the flight of a badminton shuttle :– now the air resistance is much

less– and comparable with the weight

• This pattern of the resultant force changing markedly during the flight

• predicts a markedly asymmetric path

Module 2565 B1.2.19


NextPrevious

FLIGHT - THE BERNOULLI EFFECT

BERNOULLI EFFECT • is the effect that enables

aerofoils to fly

• caused by reduction in pressure on a surface across which a fluid moves

• the greater the speed, the bigger the pressure difference, the greater the force

• this effect is used in sport :– inverted wings on racing

cars– create down-force– which then increases

friction for cornering

• as layers of air flow past the wing

• the layers under the wing flow further and faster than those over the top of the wing

Projectile Motion

• this causes reduced pressure under the wing

• and hence a downward force

Module 2565 B1.2.20


NextPrevious

FLIGHT AND LIFT

LIFT FORCES• these forces are caused by bulk

displacement of fluid and are similar to air resistance

• a wing shaped object moves through the air– discus– ski jumper

Projectile Motion

• as it moves forward and falls through the air, it pushes aside the air

• creating a higher pressure underneath the object

• and a lower pressure over the top of the object

• and creates a lift force

• this force is similar to the force which enables a stone to skip over the surface of water

Module 2565 B1.2.21


NextPrevious

SPIN

THE MAGNUS EFFECT• this is the Bernoulli effect applied

to spinning (swerving) balls• the spin takes more layers of air

the long way round the ball• this means that the air travels

faster round this part of the ball

Projectile Motion

• therefore there is a reduction in pressure on this side of the ball

• this causes the Magnus effect force as shown

• the direction of swerve of spinning ball is therefore in the same sense as the direction of spin

• back spin - soar• top spin - dip• side spin - slice and hook• soccer free-kicks - swerving

Module 2565 B1.2.22


NextPrevious

BOUNCING BALLS WITH SPIN

BOUNCING BALLS• as a ball bounces there is friction

between the lowest point of the ball and the ground

• if the ball is spinning, this friction can be increased or reduced

• a ball with back spin will have increased backwards friction with the ground which will cause the ball to bounce backwards form its normal path

Projectile Motion

• a ball with top spin will have friction driving forwards on the ball - making the ball travel forward of its normal path

Module 2565 B1.2.23


NextPrevious

CENTRE OF MASS

CENTRE of MASS (CoM)• this is the single point in a body which represents all

the spread out mass of a body

WHERE IS THE CENTRE OF MASS?

• position of centre of mass depends on shape of body

• this is how the high jumper can have his CoM pass under the bar

• but he could still clear the bar

Centre of Mass

• the weight acts at the CoM since gravity acts on mass to produce weight

Module 2565 B1.2.24


NextPrevious

BALANCE and TOPPLING

BALANCE• to keep on balance the CoM must

be over the base of support

TOPPLING• the CoM must be over the base of

support if a person is to be on balance

• toppling would be caused by the weight acting at the CoM creating a moment about the near edge of the base of support

• this can be used by divers or gymnasts to initiate a controlled spinning (twisting) fall and lead into somersaults or twists

Centre of Mass

Module 2565 B1.2.25


NextPrevious

CENTRE OF MASS - GENERATION OF ROTATION

Centre of Mass

FORCE ACTING AT TAKE-OFF THROUGH CoM

• the line of action of a force on a jumper before take-off determines whether or not he rotates in the air after take off

• if a force acts directly through the centre of mass of an object, then linear acceleration will occur (Newton's second law), no turning or rotating

• example : – basketballer : force acts through CoM

therefore jumper does not rotate in air

Module 2565 B1.2.26


NextPrevious

CENTRE OF MASS - GENERATION OF ROTATION

FORCE ACTING AT TAKE-OFF NOT THROUGH CoM

• a force which acts eccentrically to the centre of mass of a body will cause the body to begin to rotate (will initiate angular acceleration)

• this is because the force will have a moment about the CoM and will cause turning

• example : – high jumper : force acts to one side

of CoM therefore jumper turns in air

Centre of Mass

Module 2565 B1.2.27


NextPrevious

LEVERS

LEVERS • levers have an pivot (fulcrum),

effort and load

Body Levers

J O I NTS ASLEVER S

eff ort inm uscle

load is forceapplied

pivot atjoint

class 1E-P-L

class 3L-E-P

class 2E-L-P

• and are a means of applying forces at a distance from the source of the force

Module 2565 B1.2.28


NextPrevious

CLASSIFICATION OF LEVERS

Body Levers

CLASSIFICATION OF LEVERS

• class 1 lever : pivot between effort and load• see-saw lever found rarely in the body• example : triceps / elbow

• class 2 lever : load between pivot and effort• wheelbarrow lever, load bigger than effort• example : calf muscle / ankle

• class 3 lever : effort between pivot and load• mechanical disadvantage, effort bigger than

load, most common system found in body• example : quads / knee and biceps / elbow

Module 2565 B1.2.29


NextPrevious

EFFICIENCY OF LEVERS

Body Levers

EFFI C I ENCY OFLEVER S

angle betw eeneffort and lever

arm

length oflever arm

distance betw eeneffort andfulcrum

Module 2565 B1.2.30


NextPrevious

MOMENT OF FORCE - TORQUE

MOMENT of a FORCE (TORQUE) PRINCIPLE of MOMENTS

• this law applies when a lever is balanced

• (When the arms of the lever are not accelerating)

• moments tend to turn a lever arm :– clockwise (CW) – or anticlockwise (ACW)

• anticlockwise moment = clockwise

moment

Moment of Force

• moment = force x distance from pivot to line of action of force

• unit newton metre Nm• example :

– moment = F x d– d measured at right angles to

F

Module 2565 B1.2.31


NextPrevious

CALCULATION OF EFFORT IN MUSCLE

FORCE IN TRICEPS MUSCLE a worked example

Moment of Force

• load (weight in hand is 20 kg) = 20 x 10 (each kg weighs 10 N) = 200 N

• distance of load to pivot (hand to elbow joint) = 0.3 m• anticlockwise moment (of load) = 200 x 0.3

= 60 Nm• distance of effort from pivot (triceps muscle insertion to elbow

joint) = 0.02 m• clockwise moment (of effort) = effort x 0.02• ACW moment = CW moment• 60 Nm = effort x 0.02• therefore effort = 60

0.02 • effort = force in triceps muscle = 3000 N

Module 2565 B1.2.32


NextPrevious

PRINCIPAL AXES OF ROTATION

BODY PLANES & AXES • plane - an imaginary flat surface through the body

• axis of rotation- an imaginary line about which the body rotates or spins, at right angles to the plane

• vertical / longitudinal axis (V)- whole body movements - twisting /

turning, spinning skater / discus / hammer / ski turns

Principal Axes of Rotation

• frontal axis (F)- whole body movements include somersaults, pole vault take off, sprinting

• sagittal / transverse axis (S) - whole body movements include cartwheel

Module 2565 B1.2.33


NextPrevious

BODY PLANES FOR MOVEMENT

Principal Axes of Rotation

PLANES :• frontal - divides body into front and back sections :

abduction, adduction, lateral flexion• - whole body movements include cartwheel

• sagittal - divides the body into left and right sections : flexion, extension, dorsiflexion plantarflexion

• - whole body movements include somersaults, pole vault take off, sprinting

• transverse - divides the body into upper and lower sections : medial / lateral rotation,

supination, pronation • - whole body movements - twisting /

turning, spinning skater / discus / hammer / ski turns

• as a student you will have to identify the major planes and axes in physical activity

Module 2565 B1.2.34


NextPrevious

ANGULAR MOTION - TORQUE

MOMENT OF FORCETORQUECOUPLE• these are all terms which describe

the turning effect produced by a force

• when it acts eccentrically (to one side of) to an axis of rotation

• moment = F x d

Angular Motion

• such a moment would cause rotation / turning

Module 2565 B1.2.35


NextPrevious

ANGULAR MOTIONANALOGUES OF NEWTON’s LAWS

NEWTON’s 1ST LAW• rate of spinning will remain the same provided

no torque acts• strictly - angular momentum remains the same

(is conserved)• see later for explanation of angular momentum

NEWTON’s 2ND LAW• if a torque acts on a spinning system then this

will change the angular velocity of the system• the rate of spinning will speed up or slow

down

NEWTON’s 3RD LAW• if a torque acts from one body onto another• then the first experiences an equal and

opposite torque in the opposite direction

Angular Motion

Module 2565 B1.2.36


NextPrevious

ANGLE - ANGULAR DISPLACEMENT

ANGLE (ANGULAR DISPLACEMENT)• to be scientifically correct angle should not be

measured in degrees, but in RADIANS (r)

• angle = arc length = l radius of arc

r

Angular Motion - Measurements

• 360 degrees = 2 x radians = 6.28 radians– 180o = r = 3.14 r– 90o = 1/2 r = 1.57 r– 30o = 1/6 r = 0.52 r

• and so on (see maths text book for more)

Module 2565 B1.2.37


NextPrevious

ANGULAR VELOCITY

ANGULAR VELOCITY• = angle turned through per second = angle turned through =

time taken t

= Greek letter omega


• this is rate of spin, most easily understood as revolutions per second (revs per sec)

• revs per sec would have to be converted to the unit radians per second (rs-1) for calculations

• 1 rev per second = 2 x = 6.28 rs-1

• rates of spin apply to :– tumbling gymnasts– trampolinists (piked straight and tucked

somersaults) – discus and hammer throwers– spinning skaters– skiers turning and twisting between slalom gates

Module 2565 B1.2.38


NextPrevious

ANGULAR ACCELERATION

ANGULAR ACCELERATION• rate of change of angular velocity

• angular acceleration = change of angular

velocity time taken

• A =2 - 1 t

• note similarity of formula with linear motion

• used when rates of spin increase or decrease

• example :– hammer thrower


Module 2565 B1.2.39


NextPrevious

MOMENT OF INERTIA

MOMENT OF INERTIA (MI)• the equivalent of mass for rotating systems• rotational inertia

• objects rotating with large MI require large moments of forces / torque to change their angular velocity

• objects with small MI require small moments of force / torque to change their angular velocity or

• MI depends on the spread of mass away from the axis of spin, hence body shape

• the more spread out the mass, the bigger the MI

• unit kilogramme metre squared kgm2

Angular Motion - Moment of Inertia

Module 2565 B1.2.40


NextPrevious

MOMENT OF INERTIAMOMENT OF INERTIA (MI)• MI = Mr2

• MI depends on the spread of mass away from the axis of spin, hence body shape

• the more spread out the mass, the bigger the MI

• bodies with arms held out wide have large MI• the further the mass is away from the axis of

rotation increases the MI dramatically


• sportspeople use this to control all spinning or turning movements• pikes and tucks are good examples of use of MI, both reduce MI• in the diagram, I is the MI for the left most pin man, and I has a

value of about 1 kgm2 for an average person

Module 2565 B1.2.41


NextPrevious

MOMENT OF INERTIA

The SPRINTER’S LEG• when the leg is straight, the leg

has high MI about hip as axis• therefore requires large force /

torque in groin muscle to swing leg


• on the other hand when fully bent the leg has low MI

• therefore requires low force / torque in groin muscle to swing leg

• so a sprinter tends to bring the leg through as bent as possible (heel as close to backside as possible)

• this is easier and faster the more bent the leg

Module 2565 B1.2.42


NextPrevious

CONSERVATION OF ANGULAR MOMENTUM

ANGULAR MOMENTUM (H)• angular momentum = moment of inertia x angular

velocity = rotational inertia x rate of spin• H = I x

CONSERVATION of ANGULAR MOMENTUM• this is a law of the universe which says that angular momentum of a

spinning body remains the same (provided no external forces act)• a body which is spinning / twisting / tumbling will keep its value of H

once the movement has started

• therefore if MI (I) changes by changing body shape• then must also change to keep angular momentum (H) the same• if MI (I) increases (body spread out more) then must decrease (rate

of spin gets less)

Conservation of Angular Momentum

• strictly, this is only exactly true if the body has no contact with its surroundings, as for example a high diver doing piked or tucked somersaults in the air

• but it is almost true for the spinning skater !

Module 2565 B1.2.43


NextPrevious

CONSERVATION OF ANGULAR MOMENTUM - EXAMPLES

THE SPINNING SKATER• arms wide - MI large - spin slowly• arms narrow - MI small - spin

quickly


THE TUMBLING GYMNAST• body position open - MI large -

spin slowly• body position tucked - MI small -

spin quickly

Module 2565 B1.2.44


NextPrevious


DANCER - SPIN JUMP• the movement is initiated with arms

held wide - highest possible MI• once she has taken off, angular

momentum is conserved• flight shape has arms tucked across

chest - lowest possible MI• therefore highest possible rate of

spin


THE SLALOM SKIER• slalom skier crouches on approach

to gate therefore with large turning MI

• as he / she passes the gate he / she stands straight up (reducing MI)

• so turns rapidly past the gate, then crouches again (increasing MI)

• to resume slow turn between gates

Module 2565 B1.2.45


NextPrevious


THE LONG JUMPER

BEFORE TAKE-OFF• the jumper has an upward reaction

force acting on his / her take-off foot• which acts eccentrically to the CoM• and therefore causes clockwise

rotation of the jumper’s body after take-off


AFTER TAKE-OFF• the jumper would rotate forwards

and land on his / her face• unless he / she could minimise the

rate of rotation

• this is done by making the MI as big as possible

• as in the hang or sail technique

ocr a level physical education a 7875 next previous module 2565 b1.2.1 ocr examinations a level...

Documents