Resources: Physics 101 for Performance Enhancement (Elite FTS)

Introduction to Biomechanics:

Lecture #1 W1

What is biomechanics?

The study of biological systems from a mechanical perspective.

Kinetics vs Kinematics

Kinetics: Describes the study of forces that cause motion (torque, gravity, friction, i.e. what intrinsically causes the movement)

Kinetics (forces) cause obseravle kinematics.

Kinematics: Describes the motion of objects/movement with respect to time (no reference of forces).

‘What the movement looks like?’ (Technique)

Linear & Angular Kinematics

Forms of Motion:

Linear Motion

When a body moves so that all parts of it travel exactly the same distance, direction and time. Linear motion can be along a straight OR curved path. 

E.G. Moving around an oval shaped track.

Linear Kinematics Summary

Speed = The rate of an object’s movement in space (scaler)

Velocity = The magnitude of directional speed (vector)

Acceleration = The change in velocity over time

Athletics – Sprinting: Stride Length & Stride Frequency

The speed at which the athlete covers the distance is a product of two factors.
1. The distance that is covered in each stride taken (Stride Length).
2. The number of strides taken in a given time (Stride Rate).

Thus a runner who has a 1.90 meter stride and takes three strides per second runs at a speed of 5.70 meters per second (m/s).

If this runner is able to increase their stride frequency to four strides per second while maintaining the same stride length as before, the runners speed will be markedly increased:
Original speed = 1.90 m x 3 strides/s = 5.70 m/s
New speed = 1.90 m x 4 strides/s = 7.60 m/s

However if the increase in stride frequency results in a decrease in stride length to 1.42 meters, the effort made to bring about this change is lost. This is known as a negative interaction.
Original speed = 1.90 m x 3 strides/s = 5.70 m/s
New speed = 1.42 m x 4 strides/s = 5.68 m/s

In other words the increased stride frequency would be matched by a decrease in stride length and the running speed would be unaltered. Therefore a runner must bring about an increase without negatively affecting the other factor. For example:
Original speed = 1.90 m x 3 strides/s = 5.70 m/s
New speed = 1.70 m x 4 strides/s = 6.80 m/s

If the runner wishes to increase their speed, this could be achieved by an increase in stride length or stride rate, or both these variables. Research has shown that at lower speeds it is more efficient for a runner to increase stride length than stride rate (accerlation). This changes as speed requirements are increased. In sprinting, results have shown that runners alter their velocity throughout the race.

These changes are called ‘split times’, and are simply a measure of the time elapsed for a displacement of the body. They are typically measured in 10 m increments for a 100 m race. Using these split times it is therefore possible to calculate the average velocities.

Do sprinters tend to increase speed by an increase in stride length stride rate, or both?

They can do both as shown in the graph below. Until a sprinter reaches a velocity of 8-10 m/s, increasing both SL and SF will result in an overall increase in SV. At higher speeds there is a trade-off between increasing SL and SF; negative interaction.

Angular Motion (Rotation)

When parts of a body in motion are constantly moving around an axis of rotation (rotation around a fixed axis).

E.G. Gymnastics swinging around a bar or golf swing.

E.G. Cirumducting the arm via the shoulder.

E.G. Sprinting: lower body = a linear direction but arms/shoulders are producing angular motion around the shoulder joint (axis of rotation).

1 rad = 57.3°

General Motion:

Combination of linear and angular (real life/sport)

Scalers & Vectors

Scalers: E.G. SPEED

Measuring magnitude (size) only. E.G. A distance of 3m, speed of 50km or mass of 100kg.

Vectors: E.G. VELOCITY

Measuring magnitude and direction.

E.G. A displacement (how far you’ve gone relative to where you’ve started) of 3m or -3m, a velocity of 10km/h.

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Projectile Motion I

Lecture 2 W2

What is a Projectile?

A projectile is any body projected into the air.

A projectile must have 2 of the following characterisitcs:

1. It is free falling and…
2. Subject only to gravity and air resistance

E.G. Once a soccer ball leaves your foot it becomes a projectile.

With heavier objects air resistance isn’t such a factor so it’s terminal velocity takes longer to reach

Optimum Projection Conditions: Is 45° when relative projection height is 0 m (release height = landing height)

Summary:

1. Optimum projection conditions depends on the relative projection height

2. When the landing is higher than the release the angle is greater than 45°

3. When the landing is lower than the release, the angle is less than 45°

4. The velocity of the release is the other key determinant of the range of the projectile

Mass, Weight & Gravity

Mass = The inertial property of an object that doesn’t change.

Weight = Dependent on Mass and Gravity. (Formula W = mg) (mass x gravity)

Acceleration on the moon is abotu 1/6 than on Earth

Gravitational acceleration – Always downwards (-ve)

Earth – 9.81 m/s2 

mass = 100 kg (mass = scaler because it just references the magnitude/size only)

weight = mg (weight = vector because it considers the vertical direction of gravity)

= 100 x (-9.81)

= -981 Newtons

Moon – 1.63 m/s2

mass = 100 kg

weight = mg

= 100 ´ (-1.63)

= -163 Newtons\

Free Falling

Free Fall:

Is defined as a motion where g is the only F acting upon a body. Objects in free fall are under the sole influence of g.

This explains how two free falling objects regardless of their shape or mass always land on the ground at the same time when released at the same time from the same height …

Under such conditions where g is the only F present, objects will fall at the same rate of a regardless of their shape or mass.

Falling with Air Resistance

Air resistance is the result of collisions of the object’s leading surface with air molecules. In real‐life projectile motion, air resistance reduces the horizontal displacement (range) by ~1.46%

The two most common factors that have a direct effect upon the amount of air resistance are the

1. Speed of the object

Increased speeds result in an increased amount of air resistance.

2. Cross-sectional area of the object.

Increased cross-sectional areas result in an increased amount of air resistance.

Conclusion: Under air resistance, more massive objects fall faster than less massive objects because they are acted upon by a larger force of gravity; for this reason, they accelerate to higher speeds until the air resistance force equals the gravity force.

Air resistance explains why two objects with similar shapes released at the same time from the same height would not land at the same time (but then if they have similar shapes wouldn’t they have similar CSA therefore be subject to similar air resistance therefore land at similar/same time?)

Terminal Velocity: As an object falls, it picks up speed. The increase in speed leads to an increase in the amount of air resistance. Eventually, the force of air resistance becomes large enough to balances the force of gravity. At this instant in time, the net force is 0 Newton; the object will stop accelerating. The object is said to have reached a terminal velocity.

Source.

Centre of Mass and Reach Height

Vector Resolution: Vy and Vx of a Projectile

x and y coordinates are independent

vy = vertical velocity / vx = horizontal velocity

vx (horizontal velocity) will always stay at a constant, an object only loses speed and falls because gravity is placing a downward pull through the y axis, not the x axis – thus the y axis changes velocity.

 

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Projectile Motion II

Lecture #3 W3

Concept

Vector Resolution

• A shot was released at an angle of 35° above the horizontal, with a velocity of 10 m/s.
• What are the horizontal and vertical release velocities?

Horizontal Axis Equation: vx = v∙cosθ

= 10 cos (35) = 8.19 m/s

Vertical Axis Equation: vy = v∙sinθ

= 10 sin (35) = 5.74 m/s

θ = angle

If you know the angle and release velocity you can calculate how high and far an object can travel, but it only works in the absence of air resistance so it’s very impractical because there is air resistance in real life (except space). So these equations are mainly only practical for tesing the theory of understanding in a exam/uni setting. 

Equations of Constant Acceleration

When a body experiences the same acceleration (e.g. free falling), there are certain inter-relationships among the kinematic variables (time, displacement, velocity & acceleration).

The 3 Equations of Constant Acceleration:

v = u + at (velocity = initial velocity + acceleration x time)

What is missing? ‘s’ so you cannot use this equation to find displacement

s = ut + (1/2) at² (displacement = initial velocity x time + (1/2) of acceleration x time squared.

Talkes about displacement (velocity x time) (1/2) at squared accounts for acceleration with displacement

What is missing? Final velocity is missing.

v² – u² = 2as (final velocity squared – acceleration = 2 x acceleration x time)

The difference between your final and initial velocity is related to acceleration

What is missing? There is not ‘time’ variable so you cannot find time using this.

u = initial velocity, v = final velocity, a = acceleration,  t = time, and s = displacement.

Why so many equations?

• There are only THREE basic equations. All other forms are derived from these three.
• We apply these equations only when acceleration (a) is constant, e.g. Projectile (vertical a = g = -9.81 m/s² , horizontal a = 0) (e.g. accelerating a car) not for something like a 100-m sprint on a track where a ≠ constant.
• When applied to projectile motion, we calculate the vertical and horizontal variables independently (because gravity only acts in the vertical direction).

Factors Affecting Projectile Trajectory – ASHR

1. Projection angle

2. Projection speed

3. Release height

4. Air resistance

Every exam has had these q’s and how they are relevent to sport remember them.

1. Projection Angle

For the same speed, projecting at different angles will lead to different vertical and horizontal distances.

2. Projection Speed

Does double the speed mean double the distance?

No, the relationship between speed and distance = ? 

3. Release Height

How does release height affect the optimal projection angle?

E.G. different release heights of a basketball shot.

4. Air Resistance

In real‐life projectile motion, air resistance reduces the horizontal displacement (range) by ~1.46%

When can we neglect air resistance?

In ‘space’ and in the exam we need to assume that there air resistance is negligable/not applicable otherwise the above equations do not work.

Important Concepts

1. Once you are in the air, there is nothing you (or a projectile) can do  o jump higher or travel further but you can change your reach height but manipulating your body.
2. If we neglect air resistance, the trajectory of a projectile is completely determined by its release conditions (height, angle and  speed) so you can predict the path (for the purpose of learning theory and applying it to uni/exam we will assume air resitance is not applicable)
3. The vertical velocity is constantly decreasing due to gravity,  whereas the horizontal velocity remains unchanged (no gravity  influence).

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Motion Capture – Conducting Video Analysis

Lecture #4 W4

Hz and FPS are the same thing 

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Forces (Newton’s Laws)

Lecture #5  W5

One Newton of force is defined as the force required to accelerate a 1 kg mass at a rate of 1 m/s2

Co‐Linear Forces Forces have the same line of action (e.g. partner rope pull)

What is a Force?

Reminder:

Kinetics – The branch of mechanics that studies the action of forces. (Hall ’95)

Dynamometry – The measurement of force.

FORCE = A force (F) is a push or pull which tends to change the motion of an object.

Examples of contact forces:

• Ground Reaction Forces (GRF)
• Joint Reaction Force (JRF)
• Friction
• Fluid resistance
• Inertial, muscle and elastic forces of tendons

Compresion Force, Tension Force, Shear Force, Torsion Force, Bending Force

Action vs Reactive Forces

Forces always come in pairs – known as “action-reaction force pairs.”

Forces always act in pairs and always act in opposite directions. When you push on an object, the object pushes back with an equal force  (until the action force is greater the reactive force can handle) Think of a pile of books on a table. The weight of the books exerts a downward force on the table. This is the action force. The table exerts an equal upward force on the books. This is the reaction force. Note that the two forces act on different objects. The action force acts on the table, and the reaction force acts on the books.

Action forces are applied via an object or body into the ground or an object

• Reactive forces are acted upon you.
• Produced as a response to a action force pushing or pulling into it (e.g. the ground providing reactive forces into the body during a sprint)

Pushing Forces: Sprint start, rugby tackle

Forces acting from the ground to the sprinter

Pulling Forces: Judo/BJJ takedowns

Law of Gravitation

All bodies are attracted to one another with a force proportional to the product of their masses and inversely proportional to the distance between them

Newton’s Laws of Motion (Classical Mechanics)

1. Law of Inertia
2. Law of Acceleration
3. Law of Reaction

Newton’s First Law – Law of Inertia

A body remains at rest or at a constant velocity, unless acted on by a external force.

If there are no forces acting on a body you will remain at rest.

AKA BODIES AT REST TEND TO STAY AT REST 

A net force implies an imbalanced force acting on the body – not even force applied to both sides of a body

Newton’s Second Law – Law of Acceleration / F = M x A 

A force applied to a body causes an acceleration of that body of a magnitude proportional to the force, in the direction of the force, and inversely proportional to the body’s mass.

Force applied to mass = acceleration

What appens if we apply the same amount of force to double the mass – it halves

If I want to maximize the

Newton’s Third Law – Law of Reaction 

For every action, there is an equal and opposite reaction.

Some think well if there is one action and the equal and opposite reaction is same coming back why is there any movement at all? Why does newton’s 3^rd law work to create movement instead of the forces being 0 and nothing moves?

1. It’s because of the difference in masses.
2. The action and reaction are acting on different objects which is why one object sees a visible movement

To be clear it’s one object acting on another, i.e. reaction action forces.

Why does your weight decrease when you squat down or go down in an elevator?

RF (reaction force) and weight at rest = 0kg

Weight going downwards
Force going upwards

Going up in a squat/elevator 
F = m x a (a = positive, it’s going with gravtiy so the mass increases as you go up)

Going down in a squat/elevator
Acceleration is negative becuase the reaction force is acting a negative force against gravity (which remember IS negative, -9.81) therefore you will be lighter as you go down.

m x -9.81 (gravity)

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Forces & Impulse

Lecture #6 W6

Impulse = F x T

Free Body Diagram

A sketch that shows a defined system in isolation with all of the forces acting on the system (kinetics).

EXAM: Have to be able to draw and label-free diagram and the forces acting on it.

The length of the arrow indicates that one force is larger than the other

∑ = summation.

We are interested in the summation ∑/resultant of forces.

What are the forces acting on the barbell vs the athlete?

Free Body Diagram (Player)

Understanding all the forces acting on the player 

Reaction force = upwards from the ground.

Do weighing scales really measures “weight”?

The summation of forces is 0 on a weight scale because…

• The action force is what your pushing down on the weight scale.
• The reaction is what the scale is pushing back on you.
  • Hence the summation of forces = 0 .
• Your mass is always fixed by gravity in newtons.

Acceleration upwards, you weigh more

When does upward acceleration occur? Two scenarios.

1. When the lift is starting to go up.
2. On the way down when the lift is slowing down to stop…

• There are only two forces, the weight W = mg and the reaction force FN.
• For the lift to accelerate upwards, the upward force must be greater than the downward force.

• ΣF = ma = -mg + FN
• Rearrange to get:

FN = mg + ma

FN = (50kg x 9.81) + (50 x 1)

= 540.5N

• The net force is going upwards means your weight is negative (the FN is upwards).
• 2nd scenario: When you are slowing down to stop you are getting heavier. As the lift is coming down it deaccelerates – there must be an upwards force to slow down the elevator.

Acceleration downwards, you weigh less

When does downward acceleration occur? Two scenarios.

1. Lift is starting to go down.
2. On the way up when lift is slowing down to stop.

• There are only two forces, the weight W = mg and the reaction force FN.
• For the lift to accelerate downwards, the downward force must be greater than the upward force.

• ΣF = -ma = -mg + FN
• Rearrange to get:

FN = mg – ma

Newton’s Second Law – Law of Acceleration

Definition 1: A force applied to a body causes an acceleration of that body of a magnitude proportional to the force, in the direction of the force, and inversely proportional to the body’s mass.

Doubling the mass halves the acceleration. E.G. Putting on double your bodies mass in body fat can halve your ability to accelerate a weight or accelerate your own body in space (sprint).

If you jump upwards on an escalator what happens?

You land on the same step because you have the forward momentum from the escalator and you were both going at the same acceleration together when you jumped.

Impulse-Momentum

The rate of change of momentum of a body of constant mass is proportional to the force causing it, and in the direction of the force.

• Momentum is the quantity of motion that an object possessesis and is relient only on mass and velocity.
• (M = linear momentum / m = mass) 

The object with the higher mass has more momentum.

Conservation of Momentum Principle: In the absence of external forces, the total momentum of a system remains constant

Linear momentum = Mass x Velocity (M = m x v)

Change in momentum = Final momentum – Initial momentum. F = ma = (mv – mu)/t

Impulse = Force x Time

The accumulated effect of force exerted on an object for a period of time

Impulse also known as the change in momentum

Ft = mv – mu

Strategies in Sport & Movement

Generating impulse (force application) (maximise force in the optimum amount of time) e.g. batting, throwing

Receiving impulse (force absorption) (minimise force by increase time of absorption) e.g. landing, receiving

Walking vs. Running

Look at the peaks to distinguish running from walking.

We know the right diagram is a rearfoot strike because there is an initial peak.

Forefoot Striking vs Rearfoot Striking Kinetics

 

Jumping & Landing

• Initial Dip: There is an initial dip because there is a negative acceleration on the squat descent downwards which is a moment you’ll be temporarily lighter.
• Negative flight time: The reason it’s negative during flight time and not 0 is because 0 is your mass when your standing on it. So it minuses from your mass.

Interpreting the diagram:

1. a-f = Jump impulse
2. g = Air time
3. h = Landing impulse

Landing impulse is different because you can consciously improve your landing by taking more time in the air. The longer time in the air means you flatten out the landing impulse (I think I heard that correctly?)

Stiff Landing vs Soft Landing

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Pressure & Friction

Lecture 7 W7

Pressure

Pressure = Force/Area

When the area is smaller the pressure is larger (given the masses and forces are the same) because the force is distributed of a smaller area.

Reducing Pressure

To break a fall you want to increase the contact area (assuming you cannot reduce the force).

Friction

• Friction is a force that acts parallel to two surfaces in contact and opposite to the direction of either impending or actual motion.
• Friction can cause energy of motion to be lost in the form of heat.
• There are two types of friction; sliding and rolling

Why does more weight on ice cause someone to travel faster?

Heavier  = higher pressure on the ice causing a localised melting of ice and reduced friction 

Chalk & Friction

The use of chalk helps increase friction to help grip the bar more effectively.

Coefficient of Friction

The magnitude of a frictional force may be calculated by the formula:

f =μR

f = frictional force

μ = coefficient of friction (used to describe the relationship of how two surfaces interact)

R = normal (90-degree to surface) reaction force between the object and the surface it contacts.

• Lecture: The coefficient of friction (m) is a unitless number indicating the relative ease of sliding between two surfaces in contact.
  • In general, 0 (smooth) < μ < 1 (rough)
  • Steel and Ice: m @ 0.03
  • Concrete and rubber: m @ 1.0 (high frictional force)
• Internet: The coefficient of friction is a number between 0 and 1 that reflects the amount of interaction between the two surfaces in contact, with a higher number indicating a greater amount of interaction and thus a greater resistance to motion.

Static versus Kinetic Friction

The coefficient of friction (μ) differs depending on whether the two bodies in contact are:

• motion-less (static), or
• in motion (kinetic)

With static friction the more force you apply the higher the friction .. when it starts to move we enter dynamic friction.

Once entered into the dynamic friction no matter how fast or slow you move the object the dynamic friction is the same.

f = frictional force

μ = coefficient of friction

R = normal reaction force

Practice Problems

In the World’s Strongest Man competition, athletes need to drag an anchor and chain which weight 300 kg.

Given the coefficients of friction μs (static friction) = 0.78  and μk (kinetic friction) = 0.54, (0.78×300?) (fxR

1. How much force (N) must be applied to start the anchor and chain in motion? (Ans = 2296 N)
   • We want frictional force so the formula: 300 is the mass not the reactional force. You have to get 300 x 9.81 gravity = 0.78
   • 0.78 (fs) x 300kg = 234kg of force applied to pull it .. but we need N and 300kg is the mass NOT reactional force .. so 300 x 9.81 (gravity) = 2943N x 0.78 (fs) = 2296
2. Once the anchor and chain is in motion, how much friction is acting on it moving at 1 m/s? (Ans = 1589 N)
   • Now we use the dyamic coefficient because its in motion: 0.54 (300×9.81) f= coefficent x R
   • 0.54 x 2943 (300 x 9.81) = 1589N
3. How much force must be applied to maintain dragging at 1 m/s? (Ans = 1589 N)
   • No calcuation needed – once the body is in motion the dynamic coefficient friction is fixed. Once entered into the dynamic friction no matter how fast or slow you move the object the dynamic friction is the same.

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Work, Power & Energy

Deakin

Work: The product of force applied against resistance

Power: The amount of mechanical work performed in a given time (the rate of doing work)

Positive power indicates concentric muscle activity

Negative power indicates eccentric muscle activity

Mechanical Energy: The capacity to do mechanical work

Kinetic Energy: Energy due to the motion of an object. Affected by the mass and velocity of the object

Potential Energy: The capacity to do work based upon its position

Two forms of potential energy:

• Gravitational potential energy: Energy due to the position (height) of a body or object
• Strain energy: Energy due to deformation of an object. Strain energy is also stored in tendons e.g. AT during hopping and running

Conservation of Mechanical Energy

When gravity is the only external force acting upon a system, mechanical energy of the body remains constant

Mechanical Work and Energy Expenditure

• The mechanical efficiency of the human machine rarely exceeds 25%
• The energy required to perform work is higher due to this inefficiency

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Torque & Levers

Lecture #7 W7

Force and Torque

• Force (F) produces translation (force has to act through the centre of the object)
• Role of Muscle: A muscle controls or creates a movement through the development of torque. The force is generated in the muscle along the line of action of the force and applied to a bone, which causes a rotation about the joint (axis).

When summation of forces = 0 the object is at rest or in continuous motion 

• Torque (T), also known as Moment, produces rotation (the force acts off center)

T = F × d

d = Moment Arm

The perpendicular distance between the axis of rotation and line of force.

When the summation of torque = 0 the object is equilibrium 

Yellow dot represents centre of the force through the object

Muscular Torque

• The rotary effect created by an applied force
• It is the angular equivalent of linear force
• The cause of angular motion
• Muscles produce torque on joints, resulting in movements (e.g. elbow flexion)
• Resultant Torque: The sum of all torques produced by the muscles around a joint

 

When you extend and flex your knee torque is in play because the line of force acts through the muscle belly, but it is off centre from the joint which is why it = torque

Hamstring to quadriceps (H:Q) ratio

Reciprocal muscle group ratio is an indicator of joint balance (or imbalance).

The H:Q ratio is commonly used in the clinical management to predict hamstrings injuries.

What ratio is good?

• It depends …
• Commonly accepted that H:Q ratio of  60% or greater is desirable in  rehabilitation (Ghena et al., 1991; Orchard et al., 1997)

Measuring your joint torque

• An isokinetic dynamometer measures joint torque, which is a good reflection of the force produced by muscles.
  • Constant angular velocity (e.g. 60º/s)
  • Various joints (e.g. knee, hip, shoulder)
  • Both directions (e.g. flexion/extension)

Peak torque (unit = Nm) is usually measured

• e.g. knee extension torque = 200 Nm

To calculate H:Q ratio, we will measure your

• Peak knee extension torque
• Peak knee flexion torque

Sit-up exercise

To overcome the downward rotating torque that is acting to push you back to the ground (Tdown) due to the upper body weight, your muscles (abdominal muscles and hip flexors) must work to produce an upward rotating torque (Tup).

Sit-up exercise modifications

You can make a sit-up harder by:

1) Increasing the moment arm (d)

• e.g. hands by chest < by ears < above head

2) Increasing resistance (R)

• e.g. weighted sit-up

3) Increasing both d and R

Levers

Machine: An apparatus/system that uses the combined action of several parts in order to apply mechanical force

Musculoskeletal Analogy: The human body is composed of machines and is a machine itself

Each machine is used to fulfil one or both of the following functions:

• Transmit a force
• Modify the magnitude of a force

In the human body this is achieved through levers

A lever is a rigid bar-like body that rotates around an Axis (fulcrum – what a lever sits on)

Applied force (effort) to the lever must be off axis to produce torque

Force (F) applied to a lever moves a Resistance (R).

Anatomical Levers

In the human body…

• Bone = rigid bar/lever
• Joint = axis/fulcrum
• Muscles = apply force torque
• Weight/Momentum of the Segment, Reaction Force, External Resistance (if present) = resistance torque

Two types of torque in a lever system:

1. Force (Effort) Torque: Force that attempts to rotate the lever in one direction about the fulcrum
2. Resistance Torque: Force that attempts to rotate the lever in the opposite direction

Equations:

Force Torque = Force (F) x Force Arm (FA)

Resistance Torque = Resistance (R) x Resistance Arm (RA)

(F)(FA) = (R)(RA)

Mechanical Advantage:

The relationship between the applied effort force and the resistance force. MA = F/R = FA/RA

• If the fulcrum is in the middle there is no mechanical advantage (Class 1 – spine relative to head and posterior neck muscles)
• If the fulcrum is further away from the applied effort force (increased force arm) then the applied force has the mechanical advantage (Class 2 – calf raise/wheelbarrow)
• If the fulcrum is closer to the applied effort force (reduced force arm), the resistance force has the advantage (Class 3 – bicep curl)

Three classes of lever

There are 3 classes of lever, depending on the relative arrangement of the applied force (F), resistance (R), and axis of rotation.

First class lever

• Rare in human body.
• See-saw
• Example: Head and neck muscles
  • Axis: atlantooccipital joint
  • Resistance: weight of the head
  • Force: posterior muscles attached to the skull

 

What if you lean your head forward? Increase the moment arm and load on the axis of rotation (load on the spine)

Second Class Lever 

• Also rare in human body.
• ‘Wheelbarrow’ – advantageous efficient lever
• Example: Calf raise / Heel raise
  • Axis: metatarsophalangeal joint
  • Resistance: weight of the body
  • Force: calf muscles  (gastrocnemius and soleus) via  Achilles tendon

Why is calf raise so “easy”?

• Second class lever is very efficient.
• Recall T = F × d
• With a longer moment arm (df > dr),  we can apply a smaller force F to lift  a heavier weight R. (why is it a longer moment arm)

H

Third Class Lever

Most human muscles work like a 3rd class lever.

Showing the longer the moment arm the more mechanical advantage. I don’t understand why they’re measuring from those positions though. Where is the line of force?

 

The force is acting very near to the axis but the resistance is far away from the joint which means there is a much larger torque placed on the joint therefore a longer moment arm.

Musculoskeletal Mechanics: Moment Arm

• The moment arm is affected by the distance of the muscle insertion from the axis of rotation
• In most joints the muscle moment arm depends on the joint angle
• The resistance moment arm also depends on limb orientation
• The insertion point of a muscle tendon is genetically determined
  • Strength does not depend only on muscle strength
  • Strength is partly genetically determined

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Practice Problem: Exam Q + Be Able To Label Diagram 

How much force (F) must be produced by the biceps brachii, attaching at 90° to the forearm at 2.5 cm (df = 2.5 cm) from the axis of rotation at the elbow joint, to hold a weight of 8-kg (resistance R) in the hand  at a distance of 32 cm (dr = 32 cm) from the elbow joint? Neglect the weight of the forearm and hand.

Have to state summation of T = 0

Always calculate in metres (e.g. 0.025)

 

 

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Centre of Mass, Stability & Equilibrium

Lecture #8 W8

Centre of mass (gravity)

Centre of mass (CM) = average location of all masses in a system AKA the body’s mass is evenly distributed.

Stability: the resistance to both linear and angular acceleration, or the resistance to a disruption of equilibrium

Centre of mass position

• CM is not fixed to any part of the body.
• CM does not have to be within the material of the body.
  • E.G. A donut the CM is in the hole
  • Wheel asana the centre of mass lies just underneath middle of spine.
• CM position varies with age, sex and other factors.
• CM skews towards the heavier side of object
• At rest CM is around the naval assuming anatomical position
• High junp: the fosbury flop provides a mechanical advantage by arching the spine leaving the CM below the middle of the spine below the crossbar meaning you dont need to jump as high as the other high jump techniques like the scissor.
  • If your CM is outside your body

Example in sports – Jumping

 

Methods to locate CM

There are four commonly used methods to locate the CM position of an object:

1. Balance Method
2. Suspension Method
   1. Shows where the object CM is as it’s hanging in a suspended position via triangulation of 3 points
3. Reaction Board Method
   1. When the body is in equilibrium, the summation of torque and forces = 0.
4. Segmentation Method
   • Identify from a photo where the CM is based on the average location of the masses.

1, 2. Balance and Suspension Methods

3. Reaction Board Method

Modified “Reaction Board” Method

4. Segmentation Method

Stability & Balance 

Stability = the resistance to disruption of equilibrium

Property of an object or characteristic expressed

Equilibrium: The state of a system that is not changing its speed or direction

Balance = ability to control equilibrium and maintain CM within the base of support (BOS). Once CM falls outside BOS then you lose balance. 

What is “base of support”?

Base of Support (BOS) = Area enclosed by the outermost edges of the body in contact with the supporting surface

4 Factors influencing balance

There are four factors influencing the stability of a system. The more “unstable”, the harder to “balance”.

1. Body Mass
   • Higher the more stable
2. Friction
   1. More friction = more stable
3. Size of the Base of Support (BOS)
4. Position of the Centre of Mass (CM)

4. Centre of mass position

CM horizontal position

Increase stability by horizontally positioning the CM near the edge of the BOS on the side of the external force.

Blue arrow = incoming horizontal force, if you shift your weight to the direction the force is coming you can maintain balance and your CM. E.G. Leaning forward into a tackle or leaning the pad to catch a punch or kick.

CM vertical position

Increase stability by vertically positioning the CM as low as possible.

 

Red block = person standing the torque will be the highest and CM is highest

Lowering CM makes you more stable 

Disruption of stability

In sport, it is sometimes desirable to disrupt one’s stability as quickly as possible in order to move. E.G. Simply going from a stationary postion to jumping into a pool.

 

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Moment of Inertia & Angular Momentum

Lecture #9 W10

Newton’s Law’s In Angular Kinetics Context

1. A rotating body will maintain a state of constant rotational motion unless acted on by an external torque

2. The rate of change of angular momentum of a body is proportional to the torque causing it and the change takes place in the direction in which the torque acts

3. For every torque that is exerted by one body on another there is an equal and opposite torque by the second body on the first

Moment of Inertia

The resistance of a body to changes in motion is termed inertia. (Taking the slack out of the bar reduces the inertia (resistance to motion) causing the weight to need less force to move it.

• In linear motion, inertia of a body is measured by its mass
• The more massive a body the greater its inertia
• It is also dependant upon how the mass is distributed wit respect to the axis of rotation.
• If mass is concentrated close to its axis then it is easier to alter the angular motion than if the mass is farther from the axis.

The inertia for a single particle of mass is: I = mr2

The moment of inertia for an entire body is: I = Ʃmr2

“Moment of Inertia” (I) is the inertial property for rotating bodies, representing the resistance to angular acceleration.

• How hard it is to rotate an object?
• The larger the Moment of Inertia, the harder to rotate.

Why can’t you throw a shot put as a far as a tennis ball? Explain the biomechanical concept behind this (Hint: Angular Momentum).
The increased mass of the shot putt creates more moment of inertia and requires much greater force to be able to produce the same rotational velocity as the tennis ball.

“Moment of Inertia” depends on two factors:

• Moment of  intertia IS SOMETHING ROTATING BODIES have.
• MOI describes what is preventing something from rotating – how hard is it to rotate an object.
• The larger the MOI the harder it is to rotate an object.
• If you add an object/weight to the distal end of an object it is harder to rotate.

Axes of Rotation in the Human Body

There are 3 principal axes of rotation in our body:

Axis of rotations are linked to planes of movement. The axis is what goes through the plane. The person is rotating around the metal rod.

Rotation in anteroposterior axis = cartwheel

Rotation in longitudinal axis = jumps with turns, e.g. skateboarding OR = spinning, e.g. figure skating 

Rotation in transverse axis = somersaults, e.g. gymnastics, trampolining, diving

Radius of Gyration

Radius of Gyration (k) = the summary of all ‘r’s (radiuses)

I = the summation of mass

The radius is the distance from the axis

Example in Sports: Sprinting

The layout is the hardest because it has the longest momen of inertia and longest moment arm.

The opposite is true for the tuck where it has the shortest radius of inertia and shortest moment arm.

Can you explain why good sprinters “draw up” their heels when they run?

Top = Running fast / Bottom = jogging

• Flexing the knee back to the but reduces the summation radius of gyration which can be seen in the top – the red lines are shorter in the last 2 diagrams with more knee flexion
• Anything that can rotate you can apply this concept of the radius of gyration and moment of inertia

Angular Momentum

Angular momentum (H) is the quantity of angular motion that a body possess.

If a body has no angular velocity, it has no “Angular Momentum” – Not moving = 0 angular velocity

• Angular momentum is the product of moment of inertia and angular velocity
• The factor that most affects angular momentum during sports performance is k (distribution of that mass with respect to the axis of rotation)

Calculate Angular Momentum

Factors Affecting H

• The body’s mass (m)
• The distribution of that mass with respect to the axis of rotation (k)
• Angular velocity of the body (w)

Conservation of Angular Momentum

When airborne, angular momentum is conserved as there are no forces acting upon the system

The magnitude and direction of angular momentum vector for an airborne performer is established at the instant of take‐off

Transfer of Angular Momentum

• Angular momentum of the whole body is conserved unless acted upon by an external torque
• Angular momentum of body parts or axes can be changed by the action of internal torques (e.g. cat rotating it’s body so it lands on it’s feet)

What if the diver does not generate enough “angular momentum” during the takeoff phase?

• They will likely land flat on their back or stomach.
• You must jump sufficiently off centre to cause that angular velocity to create a somersault
• *Once in the air you cannot change the angular momentum, but you can change the moment of inertia* 
• When the arms are spread the moment of inertia is large because radius of gyration is long, therefore the angular velocity is slow.

Compared to…

• When you bring the arms in, the moment of inertia is smaller, because the radius of gyration is shorter, thus angular velocity increases.

While the angular momentum (H = I w) is constant in the air, we can change the moment of inertia (I).

E.g. Figure skaters bring their arms close to the chest when performing axel jumps (rotation about the longitudinal axis) because you’ve changed the resistance to angular rotation (which I assume means by placing your arms closer to your CM you’ve reduced the resistance to angular rotation to help you spin more – AKA increase the angular velocity) 

So, why do figure skaters bring their arms in?

Since angular momentum is conserved in the air,

H = Iω = constant

Reducing moment of inertia (I) will lead to an increase in angular velocity (ω), i.e. rotates faster.

If H is constant than you are changing I by reducing the radius of gyration so the omega of angular velocity must be higher.

Example in Sports: Long Jump

During the takeoff phase of long jumping, “unwanted” angular momentum is generated.

Why is it unwanted? 

Wont be tested on this.

The GR force is behind the CM so it causes a forward rotation and enough angular momentum to propel you forward.

Example in Sports: Long Jump

Why do long jumpers adopt a hitch-kick technique (bicycle with legs, windmill the arms) in the flight phase?

• Angular momentum of the jumper is conserved in the air (because there is no external torque).
• Forward rotation of the arms and legs will result in backward rotation of the torso (Action = Reaction).
• Backward Rotation of the torso? By putting your arms and legs forward (forward roation)  it means that something must go backwards – if your arms go forwards your torso will go backwards. For every action there is an equal opposite reaction.

The kinetic chain involves a sequence of events where there is a transfer of angular momentum from one body part to another

Why does a person fall forward when hitting a hurdle gate instead of falling backward because of the off center reaction force causing the person to fall forward?

Angular Impulse

• Equal to the change in angular momentum
• Also equal to the product of torque and the time interval over which it acts

Angular Impulse‐Momentum Relationship

Angular momentum can be changed by:

• Increased time in which torque is applied
• Increased torque over constrained time period
• Increasing both time and force

Centripetal Force

• = A force that makes a body follow a curved path.
• Centripetal force acts on all rotating bodies and is always directed towards the centre of rotation
• Prevents a body from leaving its circular path while rotating around a fixed axis
• The radial component of acceleration is produced from centripetal force
• E.G. Cycling around a curve.

 

 

 

 

 

 

 

 

 

Equations summary

Practice Problems

A 60-kg diver initially rotates at an angular velocity of 4 rad/s in the straight position, where radius of gyration is 0.5 m. How fast will he be rotating when he is in a tucked position, where radius of gyration is 0.25m?

Answer: 16 rad/s

m = 60kg (convert to newtons?) 588.6

AV / r = 4 rad/s

Intial k = 0.5m

Tucked k = 0.25m

Omega = solve

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Fluid Mechanics

W11 L10

The branch of mechanics about the forces that fluids exert on  objects in them or moving through them

Fluid Mechanics

• “A fluid is any substance that tends to flow or continuously deform when acted on by a shear force.” (p. 470, Hall, 2014)
• OR a fluid is a substance that flows due to deformation when subjected to a shear stress (Deakin)
• All Liquids are Fluids, but not all Fluids are Liquids (e.g. air is a fluid but not a liquid).
• Air is also classified as a fluid. It’s just less dense compared to water.

Hydrodynamics

Motion of an object or body through a fluid where there is virtually no density change

Aerodynamics:

Motion of an object or body through air at any speed

Fluid Resistance

• As an object passes through a fluid medium, energy transfers from that object to the fluid (fluid resistance)
• Fluid resistance increases when an objects speed increases by the square of the change in speed

Relative Motion

The motion of one medium relative to another

Velocity of A with respect to B:
vA -> B = (A m/s) – (B m/s)
where -> +ve and <- ‐ve

Fluid Properties

Different fluids have varying characteristics that affect the resistive forces that they apply to objects that move through them. Primarily these include:

Viscosity: The rate of deformation of the fluid when a shear stress is applied

Density or Fluid specific weight: The mass per unit of volume.
Convention symbol is the Greek letter rho (ρ).
Common unit is kg/m3.

Can you float?

Do you float in these four conditions?

1. Hold a deep breath
2. While holding a deep breath,  tense up all your muscles.
3. Hold a normal breath
4. Exhale fully

How much does exhaling all the air our and inhaling all the air in affect your buoyancy?

Exhaling: Cause you to sink by creating a negative buoyancy force

Inhaling: Cause you to rise by creating a positive buoyancy force

• Your lungs displace approximately six pounds of water – when fully inflated. Assuming your are neutrally buoyant – at mid-breath.
• When you slowly and fully exhale – you will apply a negative force that will peak out at 3 pounds.
• Let’s imagine that you exhale over a count of say 8 seconds. The application of force over time must and will cause you to sink – assuming you are not counteracting the change in the water column with your trim, hands or feet.
• Likewise – slowly and fully inhaling will create a positive buoyant force – causing a brief rise in the water column.

Free Body Diagram of a Swimmer

Buoyant Force

A body placed in water will experience a buoyant force that pushes it upwards.

• A fluid force that acts vertically upwards about the body’s centre of volume
• Magnitude based on Archimedes Principle where the buoyant force is equal to the displaced fluid volume and the fluid specific weight

• Buoyancy is one of the few forces that lifts upwards and fights gravity
• Buoyancy also acts in the air

Buoyant force (Fb) = Weight of an equal volume of fluid displaced by the body (Archimedes’ Principle).

Specific Gravity

To float in water, the weight of body (W) must be less than or equal to, the weight of water displaced (Fb).

If specific gravity is ≤1 the body will float. *The specifc gravity of water is 1.

If the materials specific gravity value is less than the fluid, the material will float in the fluid. The values for air = 0.0012.

What floats and what doesn’t? Specific gravity value:

• Fat: ~ 0.7-0.9 Floats
• Muscle: ~ 1.06 Sinks
• Bone: ~1.5-2.0 Sinks

Specific gravity of human body is ~1.06, thus people tend to sink. 

But 1.06 is measured with minimla air in the lungs. Taking a deep breath adds more air decreasing specific gravity to <1.0 making floating easier. Keeping air in the lungs reduces specific gravity which is a good reason to relax in a swimming pool or take controlled breaths in to maintain bouyency,

Is it good to naturally float flat?

If you have a low leg position (left) there is much more drag force experienced, which is dependent on surface area. When there is more surface area in contact with the water there is more resistance, AKA more drag.

Station 2: Can you float flat?

• Assume W = Fb , can everyone float horizontally in water?
• ONLY IF BOTH W and Fb (buoyant force) act along the same vertical line.

Centre of Buoyancy

• The place where the buoyant force concentrates in the body on object
• It is higher on the human body than the centre of gravity due to our lungs

When floating in water the two forces cause rotation where the legs drop down and the chest lifts upwards

Centre of Mass vs. Centre of Buoyancy

• COB = how much space a body occupies. 
• W acts through one’s centre of mass (CM).
• Fb acts through the centre of buoyancy (CM of the equal volume of water being displaced by the body).

• The orange dot = the centre of buoyancy where the buoyant force acts through, therefore creating torque.
• COB will always be upwards (superior) to the CM. The amount of air in the lungs shifts the COB upwards. The more air the more the COB shifts forward.
• What are the implications of torque? Torque will keep your body horizontal due to the buoyant force and weight acting off center.

Torque

The body will rotate until W and Fb are vertically aligned which is the point where no more torque is present.

• One in 6 females can float horizontal (Whiting, 1965)
• No man out of 291 could do so (Whiting, 1963)
• Higher proportion of fat for females helps keep them buoyant.
• This helps explains why male and female times are similar in Olympics because their extra natural bouyency helps make up for the gap in athletic differences.

Gliding

Streamlined body reduces drag force during swimming.

Pressure

The force exerted by a fluid (hydrostatic pressure) or force per unit area applied in an object. It is applied perpendicular (right angle) to the surfaces in contact. P = F/A

Snowshoes prevent the person from sinking because their weight is spread over a larger area. This reduces the pressure on the snows surface.

Atmospheric Pressure

• Atmospheric pressure decreases with altitude
• At higher altitude, the density and temperature of the air are lower
• The number of collisions between molecules are less, resulting in lower pressure

What is Drag?

• Drag, or drag force, is the resistance encountered by a body moving in a fluid medium.
• OR The retarding force from the pressure of the fluid on an object (Deakin)
• In this example, the kayak is moving leftwards, and experiences a (rightward) drag force from the water.

The components of total drag are:

1. Viscous (surface, friction) drag
2. Pressure (form/inertial) drag
3. Wave drag

Formula for Drag

Do not worry about the equations! More important to understand the concepts.

Concepts to remember:

• That drag force is proportionate to velocity squared when K is a constant. Fd = k v2
• Larger surface area = larger drag force. If your legs are down it increases surface area and increases drag force.
• The larger the velocity the bigger the drag force. Higher velocity doesn’t counteract drag force.

Relative Velocity

When moving in a fluid medium (e.g. air), a body has relative motion to the fluid.

Example – Cycling Round Trip

Components of Drag

The following wont be tested.

1. Form drag
2. Skin friction drag
3. Wave drag

1. Form Drag

• Caused by the shape of an object.
• Also known as profile or pressure drag.
• The more streamlined the object, the lesser the form drag.

2. Skin Friction Drag

Also known as surface or viscous drag.

• Friction between the surface of an object and the fluid medium.
• The smoother the skin surface, the lesser the skin friction.
  • Super suits in swimming. Banned by FINA since 2010.

3. Wave Drag

• Occurs at the air-water interface/boundary between two different fluids like when air and water meet.
• Bodies that are totally submerged do not experience wave drag.
• Swimming underwater removes wave drag which is why you can go faster under water.

4. Propulsive Drag

Occurs when the drag force is in the same direction as the motion of the object/body

People wear suits or shave their hair of their body to reduce drag and friction and enhance tangential forces (a force that acts on a moving body in the direction of a tangent to the curved path of the body). 

Why golf balls have dimple holes?

Dimples on a golf ball create a thin turbulent boundary layer of air that clings to the ball’s surface. This allows the smoothly flowing air to follow the ball’s surface a little farther around the back side of the ball, thereby decreasing the size of the wake.

See Deakin Lecture 20 for Laminar Flow, Turbulent Flow, Boundary Layer.

Summary:

• Patterns of drag changes with relative velocity (laminar, turbulent flow, boundary layer, boundary layer separation)
• In sport viscous (surface, friction) and pressure (form, shape) are the two most common components of total drag

Sport application – Cycling

They compared control non-aerodynamic gear to aerodynamic gear and this was how much faster the aerodynamic gear was to the non.

Drafting during a road race, where riders ride in a single file or in a peloton.

Lift Force

Bernoullis Principle: When regions of relatively low and high pressure regions are created on the opposite side of an object, the result is a lift force directed perpendicular to the object

When there is a drag force, there is a lift force perpendicular to drag force IF your object has an ‘angle of attack’. A body in water also has an angle of attack to create a lift force.

Is Drag always bad?

• We know that drag is a resistance encountered by a body moving through a fluid. So it slows down the body, but
• In water sports, we actually use drag to propel ourselves forward.
• So drag slows us down but at the same time propels us forward… How is this possible??

How it works

• Drag acting on the boat slows the boat down.
• But notice that drag acting on the paddle blade is the same direction where we want the boat to go (forward). If you’re pulling the paddle towards you the drag force is acting forward which is moving the boat forward.

Summary:

• A lift force acts from the high pressure region to the low pressure region
  The lift force is affected by the relative velocity, fluid density, object shape, and the angle of attack
  Spin can also be used to create a lift force in a direction to suit the intended performance. This is known as the Magnus Effect

 

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