Biomechanics A level PE

Question 1

Linear motion definitions

Answer 1

Direct force- the force applied through the centre of mass
Centre of mass- point at which weight appears to act, body is balanced in all directions
Linear motion- movement of a body in either a straight line or curve where all parts move the same distance, same direction same time.
Distance- total length of the path covered (m)
Displacement- shortest straight line route from A to B (m)
Speed- rate of change in distance - eg distance/time (m/s)
Velocity - rate of change of displacement eg displacement/time (m/s)
Acceleration -rate of change of velocity
= (final velocity - initial velocity)/time (m/s/s)
Deceleration is negative acceleration or slowing down

Question 2

Linear motion time/distance graphs

Answer 2

Gradient- steepness of slope change in y/change in x
4 types of Distance time graphs they never go down because distance travelled can’t decrease
flat = rest
Straight = constant speed
up curve = acceleration Half a u
downwards curve = deceleration 1st half an n
HINTS don’t forget the units-
- use the triangle to help calculate

Question 3

Linear motion speed/time graphs

Answer 3

speed time graphs distance covered is area under graph
flat = constant speed
up curve = acceleration Half a u (gradient)
down curve = deceleration 2nd half an n
Always remain above the x axis

Question 4

Velocity time graphs

Answer 4

Above and below the x axis to show changes in direction

velocity time graphs can show change in direction as well as well as changes in motion
flat = content velocity
up curve = increase in velocity
down curve = decrease in velocity
below the x axis shows change in direction

Question 5

Angular motion definitions

Answer 5

Angular motion- movement of a body or part of a body in a circular path about an axis of rotation
axis of rotation- imaginary line that runs through the centre of mass about which rotation occurs
Eccentric force- A force applied outside the centre of mass which results in angular motion
Torque- Measure of the turning force applied to the body
Moment of inertia- resistance of a body to change it’s state of angular motion (kgm2)
Radian- measurement used in angular motion 57.3 degrees
Angular velocity rate of change of displacement (Displacement/time) (rad/s)
Angular momentum- quantity of angular motion of a body MI x angular velocity (kgm2rad/s)

Question 6

Moment of inertia (MI)

Answer 6

Measured in kg/m2
Mass of the body x distribution of mass from axis of rotation
Therefore the greater the mass of the body the greater the moment of inertia. Practically this means that sports requiring a lot of rotation, spins and twists are typically performed by athletes with lower body mass.
EG gymnasts, divers etc are smaller
Distribution of mass from the axis of rotation means that the further away the higher the MI therefore tucked shapes are performed more quickly than open shapes when somersaulting around the transverse axis.
Direct correlation between MI and angular velocity , high MI means velocity is slower, low MI is quicker.
EG skater spinning brings arms in to speed up and takes them away from the axis to slow down

Question 7

Angular momentum

Answer 7

AM =MI x AV
measured in kgm2rad/sec
If you are asked to calculate don’t forget the units!
Angular momentum is always generated by an eccentric force (outside the centre of mass), the greater the force the greater the AM.
Once angular momentum has been generated it remains constant unless acted on by an external eccentric force.
This is Newtons first law of motion but the angular analogue version.
A rotating body will continue to turn about it’s axis of rotation unless acted upon by an eccentric force or external torque
This is known as conservation of momentum

Question 8

Conservation of angular momentum practical examples

Answer 8

When answering a question on this include
axis of rotation and phases of motion.
1. Generation of angular momentum take off phase applying an eccentric force outside of the centre of mass
2. Distribution of mass straight after take off is usually away from the axis of rotation allowing control of the movement. High MI- low AV
3. Distribution of mass brought closer to the axis of rotation to enable spin and rotation to complete the moves. Low MI- high AV
4. Distribution of mass in initial landing phase moves away from axis of rotation again in order to slow rotation/twisting and enable safe controlled landings at a lower velocity. High MI- low AV.
5. External torque applied in landing removes the angular momentum stopping the rotation.
The angular momentum remains the same throughout until the external force is applied.

Question 9

Fluid mechanics definitions

Answer 9

Air resistance- force opposing the direction of motion of a body through air
Drag - force opposing the direction of motion of a body through water
Streamlining- smooth air flow around an aerodynamic shape
Aerofoil- streamlined shape with curved upper surface and flat lower surface
Projectile- object or body launched into the air
Projectile motion- curved flight path followed by a body under the force of gravity
Free body diagram- sketch showing all of the forces acting through the centre of mass
Parallelogram of forces- diagram showing the size and position of the resultant force

Question 10

Magnitude of air resistance and drag (factors affecting)

Answer 10

1. Velocity- greater velocity = greater AR/drag
2. Frontal cross sectional area greater CSA = greater AR/drag
3. Streamlining, the more streamlined the lower the drag/AR
4. Surface characteristics the smoother the surface the lower the AR/drag

Question 11

Practical examples air resistance/drag

Answer 11

Cyclists aim to minimise air resistance by

1. bringing the handlebars in to reduce the CSA area
2. Aerodynamic riding position, high seat, shoulders forward
3. Streamlining on helmet, aerodynmamic shape and smooth glossy surface
4. Tight fitting lycra suits & shaved skin to maximise the smooth surface.

Question 12

Effect of altitude and temperature on AR/drag

Answer 12

As air temperature increases so does density and therefore air resistance
As altitude increases so does density and therefore air resistance
Both of these help improve performance, more world records produced altitude

Question 13

Projectiles

Answer 13

Flight path shown on simples graphs of height (y) and distance covered (x)
Factors affecting horizontal distance are:
1. Speed of release
2. height of release
3. Angle of release
4. Lift and/or spin (Bernoulli & Magnus)

Question 14

Projectiles gaining horizontal distance

Answer 14

1. Speed of release- the higher the speed of release the greater the distance covered.
2. Height of release, the higher the height the further the horizontal distance covered.
3. The optimal angle of the release depends on the height of release
   At ground level it is 45 degrees
   If the height of release is lower than the landing then the angle needs to be increased eg hitting a bunker shot in golf
   Above ground level the optimal angle reduces to below 45 degrees eg optimal release angle of a shot is around 35 degrees depending on height of performer.

Question 15

Flight paths

Answer 15

True flight path of a projectile is a parabola- a uniform curve. If weight is the dominant force then this will occur. Eg a shot put,
If air resistance is the dominant force- eg the weight is low a non parabolic flight path occurs
Eg shuttlecock
The Bernoulli effect which creates lift will decrease the weight force creating a non parabolic flight path
Eg when throwing discus

Question 16

Bernoulli effect (lift)

Answer 16

Lift will increase the time spent in the air and therefore overall distance.
An aerofoil shape has a smooth upper curve and straight underneath.
As it passes through the air the air travels more quickly as it comes down the back of the curve on the top surface
As velocity increases pressure decreases.
This means that the air pressure is higher below the object than above it.
This forms a pressure gradient with air moving from high pressure (below) to low pressure (above)
The air moving upwards creates lift.
Best examples- discus and ski jumping.
If the aerofoil is inverted then instead of lift upwards there is an increased downwards force.

Question 17

Drawing free body diagrams and parallelograms of forces

Answer 17

Tips
1. Draw your lines through the centre of mass
2. Air resistance always acts in the opposite direction to direction of motion- they make a straight line!
3. Weight always acts straight down. Lift will decrease weight force as it acts in the opposite direction
4. Parallelogram of forces diagrams. Measure the same distance down from your AR arrow as the length of your weight arrow. Use a dotted line and connect them to make a parallelogram. Draw a full line to the point of your parallelogram to show the resultant force.
Remember you can work out weather it is a parabolic or non- parabolic flight path from a parallelogram of forces diagram. If the RF is closer to the weight arrow it is parabolic, closer to the AR arrow it is non- parabolic.

Question 18

Magnus forces (spin)

Answer 18

The Magnus force can make an object deviate from it’s flight path. It is a rotating force called spin and there are 4 types usually applied to a ball.

1. Top spin, force applied to the top of the ball ( above centre of mass) creating downward spin around the transverse axis and this shortens the flight path
2. Back spin, force applied to the bottom of the ball (below CoM) creating upwards spin around the transverse axis and this lengthens the flight path
3. Hook, force applied to the right of the centre of mass creating anticlockwise spin around the longtitudental axis and causing swerve to the left.
4. Slice, force applied to the left of the centre of mass creating clockwise spin around the longtitudental axis and causing swerve to the right.

Question 19

Effects of Magnus forces

Answer 19

Magnus forces create pressure gradients on opposite sides of the spinning object (ball). The surface rotating towards the oncoming air decreases the velocity of the air flow creating a high pressure zone. The opposite surface is spinning in the same direction as the air flow and therefore it increases forming a low pressure zone.
The resulting pressure gradient causes dip/lift or swerve depending on the direction.

Question 20

Practical examples for Magnus forces

Answer 20

1. Topspin on a tennis ball enables the player to hit the ball harder over the next whilst still landing it inside the baseline as the dip shortens the parabola of the flight path.
2. Backspin is often used in the drop shot in tennis as it decelerates the ball and makes the ball bounce at a steep angle as the friction of the court acts against the direction of the ball. In basketball it extends the flight path and deadens the ball if it touches the ring.
3. Hook and slice both affect the flight of the ball enabling football players to go ‘around’ a wall or making a tennis ball deviate from its path to land further away from an opponent. It is used in golf to enable the player to avoid obstacles such as trees.

Question 21

Newtons Laws of Motion

Answer 21

1st Law of motion also called the law of Inertia- a body will remain stationary or moving at a constant velocity unless acted on by a force.

2nd Law of Motion- a net force acting on a body will cause a change in acceleration or deceleration of a body
F = m x a
It can also cause a change in direction of the body (swerving)

3rd Law of motion- For every action there is a reaction which are equal and opposite

Question 22

Newtons laws in practice

Answer 22

1st Law
A player must exert a force on a stationary rugby ball in order to kick it through the posts for a conversion.
A skier must exert a force through their ski in order to change direction.

2nd Law
A cricketer hits the oncoming ball with his bat causing it to change direction the size of the force is
A skier pushes out of the start gate causing acceleration
A cyclist presses the brake pedal applying a force to the wheel and causing deceleration.

3rd Law
A trampolinist pushes down on the bed (action) the bed pushes back against the performer (reaction) causing them to gain height.
A skier pulls back against the start Gate (a) the start gate pushes forward against the skier (r) causing forward momentum out of the gate
Within the body the origin and insertion of muscles pull in opposite directions. The action pulling on the origin and causing a reaction at the insertion pulling the origin towards the insertion thus moving the limb

Question 23

Formulae for calculations

Answer 23

1. Velocity (m/s) = displacement(m) / time (s)
2. Momentum (kgm/s) = mass (kg) x velocity (m/s)
3. Force (N) = mass(kg) x acceleration (m/s/s)
4. Acceleration (m/s/s) = Final velocity (m/s) - Initial velocity (m/s) / time (s)

Question 24

Force

Answer 24

Is a push or a pull
Is measured in Newtons
Causes changes is speed (velocity) and direction of objects as well as changing it’s shape
Has both a value and a direction ( is a vector)
Had a point of action through which the force acts
Can be internal or external, within or outside of the body
Net force is the sum of all forces acting, if the opposite forces are equal they can cancel each other out giving a net force of 0

Question 25

External forces

Answer 25

Vertical
Weight (N) = mass (kg) x gravity (m/s/s)
Gravity (approx 10N per kg of mass)
Reaction ( measured in Newtons)

Horizontal
Friction opposes motion of surfaces which are in contact
Air resistance - opposes motion through the air

eg a cyclist will have
a force acting downwards of the combined weight of themselves and the bike
the reaction force acting upwards
the backwards force of the tyre against the ground being driven by the cyclist
the reaction force of the ground pushing forward on the cycle wheel
the friction force between the tyres and the surface
the air resistance of themselves moving forward