Newtonian Mechanics or Newtonian Physics – describe how things move.
Three L aws of Motion applied to all nearly all objects in the universe.
Has problems with the very largest (i.e. fastest = galaxies and expansion of the universe) and smallest objects (nuclear particles).
Newtonian mechanics is used to analyze how tiny, one celled organisms move, how humans move, and how planets and solar systems move.
Newton, b. 1642
Force, By Definition Force – a push or pull by one object onto another – always applied through contact between two objects and termed, “Reaction Force.” Force = Mass * Acceleration F = m a Force is a vector (magnitude & direction) and is measured in Newtons: 1 N = 1 kg m/s 2 N = m * a 1 N = 0.225 Lbs. or 1 Lb. = 4.448 N 150 Lbs. = 667 N 200 Lbs. = 890 N 250 Lbs = 1,112 N Never measure force in kg. Mass is measured in kg.
Vector Nature of Force – Magnitude and Direction
Force is a vector – The vector nature is seen in the direction of force relative to a bone.
Shear – force across an object
Compression – force into an object, squeezing the object
Tension – force away from the object, stretching the object
Patella-Femur compression 5,000 N in stair ascent Squat has shear (5,000 N) and compression (10,000 N) on spine Cruciate knee ligaments resist shear forces
Mass: scalar quantity measuring the amount of matter in an object
Barbell on Earth: Barbell mass is 4.5 kg. Barbell weighs 10 lbs = 44.5 N.
Barbell in Space: Barbell mass is 4.5 kg. Barbell weighs 0 lbs = 0.0 N.
Weight: the force from the interaction between the planet’s mass and the object’s mass
Person’s mass is 70 kg. What is:
Person’s weight = 70 kg * -9.81 m/s 2 = -883 N
Person’s mass on the moon = 70 kg
Person’s weight on the moon = 70 kg * -1.64 m/s = -115 N
Mass and weight are perfectly correlated thus it is easy to think they are equivalent. We will see how they are used differently in the physics used in biomechanics.
2) Ground Reaction Force (GRF) is… … the force applied to a person form the supporting ground or floor. … the force that produces human movement around the environment (i.e. the force that causes locomotion. … produced in response to the person’s weight plus any propulsive force generated by muscles. GRF propels runner GRF stops vaulter GRF propels jumper into the air GRF propels pogo-er into the air
GRFs in Walking Resultant GRF resolved into vertical & horizontal components. Vertical about 4 times larger than horizontal. Heel strike Vertical GRF Horizontal GRF Up Back Forward Late stance No force the instant before floor contact Large force at maximum knee flexion – direction is up and slightly backwards Large force at maximum push-off – direction is up and slightly forwards Vertical – stops downward motion then creates upward motion Horizontal – slows then accelerates the person -1000 -1000 1000 1000 1000 1000 Show Level-walking-3-speeds.cmo Early stance -1000 1000 1000
Vertical GRFs in Walking and Running Running has higher force for a shorter duration. Walking less “dynamic” than running – forces closer to bodyweight – walking is more similar to standing than to running Bodyweight = 850 N
Vertical GRFs in Lean and Obese People Everyone who walks normally has, more or less, this basic shape: early and late force peaks above bodyweight and a force minimum in midstance below bodyweight. Obese vs. lean individuals have more weight pushing down and greater GRF pushing up in response. Bodyweight = 850 N Lean
Vertical GRF in Jumping and Landing Vertical GRF in jumping propels (accelerates) by pushing person upward with large magnitude. Vertical GRF in landing stops (accelerates) by pushing person upward with large magnitude. Vertical GRF both produces and stops movement.
3) Muscle & 4) Joint Forces (done previously and more to come)
Internal force – a force entirely within an object that does not cause the object to move.
External – a force applied from outside the object (i.e. from the environment). Only external forces can move an object through the environment. Weight, GRFs, contact with other object (a linebacker tackles a running back).
Object – must be clearly defined (see below and next slide).
Pole vaulting: Object is the vaulter. External forces: weight pulls the vaulter down and the pole pulls the vaulter up. Weight lifting: Object is the dumb bell External forces: dumb bell’s weight pulls it down and the Hand reaction Force pushes the dumb bell up.
In vaulting the left lower extremity moves upward as the hip flexes. The object is now the left lower extremity. What Forces are external to it?
In the dumb bell bench press, the arm moves up. The object is now the arm. What Forces are external to it?
Pole vaulting: Object is the left lower extremity. External forces: lower extremity weight (white arrow) pulls the lower extremity down and the hip flexor muscles pull the extremity. Muscle Force is EXTERNAL in this situation. Weight lifting: Object is the right arm External forces: arm weight pulls it down and shoulder muscles pull it up. Muscle Force is EXTERNAL in this situation.
Muscle Force is External to Forearm Muscle force from outside of forearm and reaching into the forearm. Muscle force accelerates the forearm in the upward direction. MUST CAREFULLY DEFINE THE OBJECT.
Force Resolution – Identifying Force Components Force Resolution : separation of a force into components: 1) Vertical and horizontal forces in environmental reference frame – used to analyze locomotion and other full body movements 2) Stabilizing and rotational forces in anatomic reference frame – used to analyze muscle forces on skeletal bones Biceps force Rotating component Stabilizing component Early stance -1000 1000 1000
Force Resolution in the Environment ` Environmental reference frame for general movement. 60 ° 20 ° 4,000 N at 60 to horizontal 4,000 N at 20 to the horizontal Force hor = 4,000 N cos 60 = 2,000 N Force hor = 4,000 N cos 20 = 3,759 N Force vert = 4,000 N sin 60 = 3,464 N Force vert = 4,000 N sin 20 = 1,368 N Long Jump – more horizontal than vertical High Jump – more vertical than horizontal
Anatomical Force Resolution ` Anatomical reference frame for muscle forces: = 30 ° Biceps force = 2,000 N Rotating Stabilizing Calculate stabilizing and rotating components not horizontal and vertical Stabilizing: Force = 2,000 cos 30 = 1,879 N Rotating: Force = 2,000 sin 30 = 1,000 N Rotating force < Stabilizing force because < 45
Newton’s Laws of Linear Motion The next ~30 slides explain Newton’s Laws of Motion. These laws describe the underlying causes of movement. Two of these laws (#1 & #3) are conceptual and do not require mathematics. Law #2 will have much mathematics and IS OUR PRIMARY FOCUS. Please note, we will discuss laws #1 and #3 first and then law#2.
Newton’s Laws of Linear Motion I. Law of Inertia – An object will remain stationary or move with constant velocity until an external force is applied to the object “ Constant velocity” – implies straight line (direction) and constant speed Inertia – measures on object’s resistance to motion. Inertia = mass (kg) Shot put has greater resistance – it is harder to accelerate. We can throw a softball farther. What would happen if we attempted to throw a shot put?
Perceiving the Law of Inertia The Elevator Test: stand in elevator with knees flexed about 20 and then press the UP button. Upward force from elevator What happens?
Perceiving the Law of Inertia The Seat Belt Test: what happens when you press on the brakes as you are driving or if you JAM on the brakes? Brakes slow the car Trunk accelerates forward relative to thighs and car. The more you JAM on the breaks, the greater the acceleration, the faster your trunk moves forward.
Law of Inertia and Inertial Forces Inertial forces – motion-dependent forces (but really acceleration-dependent forces) Forces due to the acceleration of an object: in lifting an object we accelerate the object. The object applies force on us equal to its weight PLUS the inertial force. The faster we lift (i.e. the greater the acceleration), the greater the inertial force and the total force. Thus lifting slowly reduces spinal force while lifting rapidly increases spinal forces. Inertial force is important because of the extra load it places on humans in rapid movements, not because it is the force that caused the movement. The person applies the movement force on the object and the object applies the reaction force (weight + inertial force) back onto the person.
Law of Inertia and Inertial Forces Inertial forces and Grocery Bags – the paper bags are full and the food in them is heavy. Lift the bags slowly and they are fine. Lift too fast (i.e. accelerate too rapidly) and they rip. Why? The heavy load and the high acceleration creates a large inertial force (f = m a) applied downward against the bags. We accelerate the bags and food up and the food resists with a downward force: the bag rips.
Law of Inertia and Inertial Forces Inertial Forces important in lifting – total force can be separated into weight plus inertial force. While holding the barbell stationary, the inertial force is zero and total force equals barbell weight. Inertial Forces in Bench Press: barbell weight is 1,330 N. All force above 1,330 N is inertial force due to acceleration in lift, especially important at start of lift. Force = mg + ma (vertical) = weight + inertial force While holding, ma (vertical) =0 Inertial force in early lift during initial acceleration
Law of Inertia and Inertial Forces Lifting too rapidly, especially with bad technique creates large inertial load against your trunk extensor muscles and lumbar discs. The box may weigh 80 N (20 lbs.) but your trunk may weigh 400 N (100 lbs.) and the combined inertial force can be over 2,000 N (500 lbs.) in a fast lift.
Newton’s Laws of Linear Motion III. Law of Reaction – When one object applies a force on a second object, the second object applies an equal and opposite force onto the first object “ equal and opposite” – equal magnitude and opposite direction Basis for force platform measurements and Ground Reaction Forces
Force Plate in Balance and Locomotion Platform measures the reaction forces to the forces applied by the person. After release, the person must step and apply force onto floor (force plate) to maintain support. Person with ACL injury, surgery, and brace walks over force plate to analyze gait.
Walking direction Vertical force Mediolateral force Anteroposterior force Platform measures the reaction forces to the forces applied by the person in 3 dimensions Force Platforms and the Law of Reaction To walk, we push down and back on the floor and the floor pushes up and forward on us. The external GRF causes locomotion.
Newton’s Laws of Motion II. Law of Acceleration – a force will accelerate an object in the direction of the force, at a rate inversely proportional to the mass of the object Force = mass x acceleration or F = m a The basis for all biomechanics – forces cause motion Force – a pushing or pulling effect on an object This force is an EXTERNAL force
Law of Acceleration & and the Impulse-Momentum Relationship Law of Acceleration describes change in momentum of the object, a change in the quantity of motion. F = m a Positive acceleration – increase quantity of motion Negative acceleration – decrease quantity of motion Momentum is the Quantity of Motion or Mass in Motion Momentum = mass * velocity in kg*m / s
Momentum = Mass * Velocity Momentum depends on the mass of the object and its velocity. Momentum does not equal Mass (see Mr. Elephant)
Law of Acceleration restated: F = m * a F = m * (vf – vi) / time F * time = m * (vf – vi) - Impulse-Momentum equation Interpretation: impulse changes momentum – force applied for a period of time can either increase or decrease the velocity of an object. Law of Acceleration & and the Impulse-Momentum Relationship
Impulse Changes Momentum When impulse and momentum are in opposite directions, impulse will reduce momentum, as in tackling. When impulse and momentum are in the same directions, impulse will increase momentum, as in javelin. http://www.youtube.com/watch?v=PMtrMhGDFtU
Impulse Changes Momentum Human activities are quick, short duration movements. Since time potion of impulse is low than force portion is high. Muscle forces are high. Quick actions to increase momentum Quick actions to decrease momentum
Force and Time in Impulse and Athletic Skill Novice athletes – beginners – tend to exert force over shorter periods of time. Beginning golfers swing with only the upper body. This motion is a quicker, jerkier motion, that does not produce the highest impulse. Skilled athletes exert force over longer times. They build up more force using more muscle groups. Skilled golfers use lower extremities more. This motion is smooth, lengthy, and it produces high impulse – the golf club moves faster and more accurately.
Vertical Impulse in Running Vertical impulse is the area under the Force-Time curve (gray area) = total effect of the applied force. Measured in Newton*seconds (Ns) In this example, impulse from vertical GRF = 300 Ns during the stance phase of running with half occurring during flexion and half during extension phases. At heel strike (the start of stance phase), person’s momentum was downward. Upward force from ground reduces this momentum until the person stops at midstance (hip, knee flexion & ankle dorsiflexion all stop at vertical line). Additional impulse after midstance propels the person upward, increasing momentum. 150 Ns 150 Ns -1.5 m/s 0.0 m/s +1.5 m/s Vertical velocity Heel Strike Mid-stance Toe Off
Horizontal Impulse in Running Braking impulse reduces horizontal momentum (i.e. velocity) – impulse & momentum in opposite directions. Propelling impulse increases horizontal momentum (i.e. velocity) – impulse & momentum in same direction. Is this person speeding up or slowing down? Negative force is backwards Positive force is forwards
Horizontal Impulse in Running Runner’s mass = 70 kg Initial velocity (vi) = 4.00 m/s Braking imp. = -18 Ns Propelling imp = 20 Ns What is runner’s velocity at midstance and at toe off? Calculations on next slide Imp= -18 Ns Imp = 20 Ns Heel Strike Midstance Toe off 4.00 m/s ? m/s ? m/s Horizontal velocity
Horizontal Impulse in Running Braking imp. = -18 Ns -18 Ns = 70 kg (vf – 4.00 m/s) -18 Ns / 70 kg + 4.00 = vf 3.75 m/s = vf at midstance Imp= -18 Ns Imp = 20 Ns Heel Strike Midstance Toe off 4.00 m/s ? m/s ? m/s Horizontal velocity Propelling imp = 20 Ns 20 Ns = 70 kg (vf – 3.75 m/s) 20 Ns / 70 kg + 3.75 = vf 4.04 m/s = vf at toe off
Impulse – Momentum Relationship Shows the underlying physics demonstrating how forces cause objects to move and how forces cause objects to stop moving. Impulse represents the total effect of a force applied over time. In human movement, time intervals are typically short and forces are typically high. Momentum represents the quantity of motion and is a function of the mass and the velocity of the moving object.
Law of Acceleration and Inverse Dynamics Inverse Dynamics – an analysis that calculates unknown forces inside the human body. Forces in joints, muscles, bones, ligaments, etc Direct measurement is best but not many people volunteer to have force transducers surgically implanted into their bodies. Weird, huh?
Achilles tendon forces along with GRFs during walking with buckle and fiber optics. Achilles force looks just like ankle torque during walking.
Swing Stance Ant/Post GRF Vertical GRF Slow Fast
Inverse Dynamics Analysis Inverse Dynamics – combines position and acceleration data from video motion analysis and force data from force platforms or other force sensors to calculate internal forces. Most commonly used in locomotion but also in rowing, cycling and other activities.
Inverse Dynamics Analysis Inverse Dynamics uses two basic physics tools: a Free Body Diagram (FBD) and Equations of motion . Free Body Diagram – a diagram showing an object and all the forces applied to the object at a single instant in time. FBDs of a person standing - all drawings are equivalent: mg = weight Fv = vertical floor reaction force mg Fv mg Fv mg Fv Fv mg
Inverse Dynamics Analysis FBD of a running person: mg Fv mg Fh Wind resistance FBD of the leg of a running person: Knee Vert. & Hor. Joint Reaction Forces – Thigh pushing on Leg Ankle Vert. & Hor. Joint Reaction Forces - Foot Pushing on Leg Vert. & Hor. GRF Segment CoM about 43% from proximal end The person is one object and it has one weight
Inverse Dynamics Analysis Equation of motion – the physics equation that describes the free body diagram. The equation that shows the forces (kinetics) and their effects on the mass (the acceleration or kinematics). The particular equation of motion is simply a re-working of the law of Acceleration, F = ma. mg Fv Equation of motion for the standing person: F v = ma v (sum of the vertical forces = mass x vertical acceleration) mass = 70kg, a v = 0 (standing person has mass but no accel.) -mg + Fv = 0 (equation of motion for a standing person) Fv = mg (the floor applies an upward force equal to the person’s weight during standing) Fv = 70kg (9.81m/s 2 ) = 687 N
Inverse Dynamics Analysis mg FBD of a the leg of the running person: Knee Vert. & Hor. Joint Reaction Forces Ankle Vert. & Hor. Joint Reaction Forces Segment CoM about 43% from proximal end Inverse Dynamic Analysis to calculate the force under a standing person? Why bother? Buy a bathroom scale for that. Ahhh, but we do need this analysis to identify unknown forces applied to our joints or ligaments or generated by our muscles. Need data describing characteristics of each body segment (location inn space, mass, location of the center of mass in the segment - See next slide).
Kinematic chain of the lower extremity and individual body segments: Kinematic chain The objects or masses in this analysis are each of the individual body segments.
3. Goal – calculate unknown ankle joint forces. Start with distal segment – the foot and analyze ankle, then knee, then hip joints. External forces applied to a segment include segment weight, force from contact with ground, and joint reaction force from contacting body segment (i.e. the leg). 2. 1. GRF v GRF h GRFv GRFh Ankle v Ankle h
Inverse Dynamics Analysis Subject walking up the ramp. Video to produce position and acceleration data. Force plate to measure the known external forces. See analysis on next few slides and on board. White line is force plate. Curves are vertical and ant-post GRFs.
Data used in the I.D. analysis in next few slides: Masses and moment of inertias: Subject: 70 kg Foot: 1.7 kg, 0.0023 kgm 2 Leg: 3.44 kg, 0.0044 kgm 2 Accelerations: Foot vertical: 2.47 m/s 2 Foot horizontal: 4.70 m/s 2 Foot rotational: -52.5 rad/s 2 Leg vertical: 1.30 m/s 2 Leg horizontal: 9.23 m/s 2 Leg rotational: -10.3 rad/s 2
Av – large & down: the body weight plus inertial force of accelerating body mass upward push down on the foot. The upward GRF is larger than the downward ankle reaction force – THUS THE FOOT AND PERSON MOVE UPWARD. Ankle Joint Forces Vertical Ankle Joint Reaction Force (JRF) Av: Fv = ma v GRFv – mg + Av = ma v 975 – (1.07) (9.81) + Av = (1.07) (2.47) Av = -961 N Foot Ankle Vertical Direction: -961 N Av mg Note: Weight applied at the center of mass GRFv = 975 N
Ah – small and backward: the foot pushes the body forward & the body pushes back on the foot at the ankle. The forward GRF is larger than the backward ankle reaction force – THUS THE FOOT AND PERSON MOVE FORWARD. Ankle Joint Forces Horizontal Ankle Joint Reaction Force (JRF) Ah: Fh = ma h GRFh + Ah = ma h 162 + Ah = (1.07) (4.7) Ah = -157 N GRFh = 162 N Foot Ankle Horizontal Direction: -157 N Ah
Goal: calculate unknown knee joint forces. 4. Net force at of leg onto foot is reversed for foot onto leg. Leg pushed down and back on foot and foot pushes up and forward on leg. This is the Law of Reaction – one object pushes a second and the second push back on the first. Ankle v Ankle h Knee v Knee h Leg mg
Kv – large & down: the body weight plus inertial force of accelerating body mass upward push down on the knee The upward ankle force is larger than the downward knee force – THUS THE LEG AND PERSON MOVE UPWARD. Knee Joint Forces Vertical Knee Joint Reaction Force (JRF) Kv: Fv = ma v Av – mg + Kv = ma v 961 – (3.44) (9.81) + Kv = (3.44) (1.30) Kv = -922 N Av = 961 N Leg Knee Ankle Note: Ankle JRFs reversed onto leg (the law of reaction) Vertical Direction: Kv mg -922 N
Kh – small and backward: the leg pushes the body forward & the body pushes back on the leg at the knee. The forward ankle force is larger than the backward knee force – THUS THE LEG AND PERSON MOVE FORWARD. Knee Joint Forces Horizontal Knee Joint Reaction Force (JRF) Kh: Fh = ma h Ay + Kh = ma h 157 + Kh = (3.44) (9.23) Kh = -125 N Ah = 157N Leg Knee Ankle Horizontal Direction: Note: Ankle JRFs reversed onto leg (the law of reaction) Kh -125 N
Joint Reaction Forces from Inverse Dynamics Forces calculated through the stance phase. The position and acceleration of the body segments are derived from each video frame. The ground reaction forces are applied to the foot and the analysis calculates the ankle JRF. The procedure is repeated for leg and knee and then thigh and hip.
Newton’s Laws of Motion - Summary Three laws describing linear kinetics (We will also learn the analogous laws for angular kinetics.) Second law, the law of acceleration, is the basis for most Biomechanics All laws apply to all biomechanical situations, but each situation may best be analyzed with a subset of the laws
Vsevolod Meyerhold’s Biomechanical Theater in Russia, 1922
Energy, Work, and Power An alternative analysis to the dynamic analysis of F=ma for understanding the mechanics of physical systems Provides insight into motion in terms of a combination of kinematics (position & velocity) and kinetics (force) Provides insight into muscle mechanics in terms of contraction types, roles of muscles, sources of movement
Energy Energy has many forms – chemical, nuclear, electrical, mechanical, and more Energy is often transformed from one form to another: Electricity is used to spin CDs (the spinning CD has mechanical energy); Chemical energy in ATP is used to produce the, “power stroke” and slide actin over myosin Energy is a scalar variable that reflects the “energetic state” of the object – we measure how much or how little energy an object has at one point in time.
Energy, Conceptually Speaking…. The biomechanical concept of energy is exactly like the English concept: if someone is energetic biomechanically, that person is active, rambunctious, full of life, so to speak. If someone has low energy biomechanically, that person is tired, slow, lazy, lethargic, so to speak. We can assess human movement by assessing the energy in a person or a body segment and how that energy increases or decreases: Concentric contractions increase energy in our bodies and in objects we manipulate – they raise our position and/or increase our velocity or an object’s position and velocity – the high jump has concentric contractions to lift us and give us vertical velocity. Eccentric contractions decrease energy in our bodies and in objects we manipulate – they lower our position and/or decrease our velocity or an object’s position and velocity – landing from a jump has eccentric contractions to carefully lower ourselves after hitting the floor, lowering our position.
Energy, Biomechanically Speaking…. Mechanical energy is the capacity to do work – if a person has energy the person can do work: the javelin thrower runs up the runway and has developed high energy – she now can do much work on the javelin and throw it far. The capacity to do work means the thrower does work on the javelin – this work increases the energy of the javelin and it flies…flies…flies…
Energy, Technically Speaking…. Mechanical energy is the capacity to do work and work is the product of force and displacement Work = Force * Displacement Therefore, mechanical energy is the capacity to move objects Energy = Zero or positive value (a scalar), Joules = J 1 J is very small – move fingers a few centimeters? 133 J lifts 150 lb (666 N) person up one step (20 cm). It takes 1,330 J of energy for this person to ascend 10 steps. (We will return to Work-Energy relation in a few slides)
Forms of Mechanical Energy Two basic forms of mechanical energy: Potential energy – energy due to position above the floor or ground – the gymnast has high P.E. Kinetic energy – energy due to person’s mass and velocity – sprinters have high K.E.
Potential Energy (or Gravitational Potential Energy) Potential Energy = energy of position = energy associated with the weight (mg) of an object and its height (h) above the floor. P.E. = mgh in Joules Runner’s body has some P.E.: P.E. = 50 kg (9.81 m/s 2 ) (1 m) = 490 J Vaulter has more P.E. P.E. = 80 kg (9.81 m/s 2 ) (3 m) = 2,354 J Velocity does not matter, only vertical position. 1 m 3 m
Potential Energy and Work How does Potential Energy have the capacity to do work? Roller coasters exploit P.E. by lifting people to great heights, increasing their P.E., then letting the P.E. work on the people to create large and frightening velocity.
Potential Energy and Work Elite bowlers use large hyperextension at shoulder to lift ball and add energy to it. This P.E. can then be converted to greater ball velocity at release. Elite divers leap high to increase P.E. before final bending of the springboard. Higher P.E. produces greater bending and a larger springing action to propel the diver higher into the air. http://www.youtube.com/watch?v=sjf6pLmNYkI
Linear Kinetic Energy Kinetic Energy = energy of motion = energy associated with the mass and velocity of an object Linear K.E. = ½ mv 2 in Joules Jumper’s body has Linear K.E. at touchdown onto board: K.E. = ½ (65 kg) (7.4 m/s) 2 = 1,780 J Related to linear momentum = mv – if an object has momentum, it has kinetic energy
Kinetic Energy and Work How does Kinetic Energy have the capacity to do work? Large K.E. in the rolling bowling ball scatters the pins. The large kinetic energy in the swinging bat propels the ball over the outfield wall. In both cases, athlete did work on the implement (bowling ball or bat) and the implement did work on the next object (pins or baseball).
Three Primary Work Scenarios in Human Movement 1) Muscles do work on the skeleton – concentrically they increase its height or velocity and eccentrically they decrease its height or velocity. 2) Skeleton does work on external objects – increasing or decreasing their height or velocity 3) The ground or floor does work on our skeleton – GRFs increase or decrease our energy
Work – Changing Energy Work represents the change in energy of an object Work occurs when energy changes Work occurs when objects are raised or lowered (change in P.E.) or when their velocity changes (change in K.E.) Work = Total Energy = (mgh + ½ mv 2 ) in = Joules Work – Energy Theorem: Force * Distance = (mgh + ½ mv 2 )
Work – Changing Energy in Jumping Work = Total Energy = (mgh + ½ mv 2 ) work = final energy – initial energy = (P.E. f – P.E. i ) + (K.E. f – K.E. i ) = (mgh f – mgh i ) + (½ mv 2 f – ½ mv 2 i ) = (61*9.81*1.4 – 61*9.81*1.1) + (0.5*61*3.02 2 – 0) = (838 J – 658 J) + (278 J – 0 J) = 180 J + 278 J = 458 J Energy was increased through the concentric contractions of muscles. Muscles did positive work on the skeletal system. Jumper’s mass = 61 kg CM height = 1.1 m at start & 1.4 m at take off
Initial floor contact Work – Changing Energy in Landing Final position Jumper’s mass = 61 kg CM height = 1.4 m at start & 1.1 m at end Work = Total Energy = (mgh + ½ mv 2 ) work = final energy – initial energy = (P.E. f – P.E. i ) + (K.E. f – K.E. i ) = (mgh f – mgh i ) + (½ mv 2 f – ½ mv 2 i ) = (61*9.81*1.1 - 61*9.81*1.4) + (0 - 0.5*61*3.02 2 ) = (658 J – 838 J) + (0 J - 278 J) = -180 J - 278 J = -458 J Energy was decreased through the eccentric contractions of muscles. Muscles did negative work on the skeletal system.
Work and Cyclic Movements Work = Total Energy = (mgh + ½ mv 2 ) work = final energy – initial energy = (P.E. f – P.E. i ) + (K.E. f – K.E. i ) Final position and velocity = initial position and velocity – Energy does not change, no net work was done. Cyclic activity has no net work and no change in energy. Humans perform equal amounts of positive and negative work through our 24 hour, cyclic lifestyles – we balance concentric and eccentric contractions (mostly).
Power – Rate of Work (or Rate of Changing Energy) Power represents the rate at which work is being done. Work occurs when energy changes and it occurs at various rates – i.e. fast or slow, high or low The power used in lifting depends on how fast or slowly the lift occurred. Strength training emphasizes high force at low speeds – has low power. Power training emphasizes moderate forces at moderate speeds – has high power.
Power – Rate of Work (or Rate of Changing Energy) P = Work / time = Force * displ. / time = Force * velocity in Watts (W)
Power During Lifting 0.20 m 40 N Work = Force * displacement = 0.20 m (40N) = 8 Nm = 8 J of work Lift in 0.5 s: P = Work/time = 16 W Lift in 1.0 s: P = Work / time = 8 W Lift in 2.0 s: P = Work / time = 4 W (We are not emphasizing power in this section)
Skeletal-Muscle Models & Force Resolution Skeletal-muscle models used to calculate individual muscle forces in different movements and the effects of illness and injury on these forces. Glitsch & Bauman, 1998 Pandy & Shelburne, 1998
Muscle Forces From Muscle Model Glitsch & Bauman, 1998 Vas. RF.
Measured Achilles Tendon Forces and Ankle Net Torque
Ankle torque curve similar to achilles tendon force curves. Gastroc EMG shows this muscle active in mid-late stance.
Can estimate Achilles tendon force from net torque: Torque/Achilles lever arm:
98 Nm / 0.05 m = 1960 N. Measured forces peak value ~2200 N. Estimate is reasonable.
Measurement and Prediction of Forces Inside the Human Body Sonomicrometery to measure muscle fiber lengths, forces transducer to measure tendon force. Biewener et al on many birds and other animals.
Measurement and Prediction of Forces Inside the Human Body Demonstrate isometric or even shortening contraction of muscle fibers during muscle eccentric contraction.
Inverse Dynamics Analysis We will do the analysis on the front board.
Large knee flexion creates large patella-femoral compressive forces: 4000 N stair descent, kicking 7000 N, parallel squat 14,900 N. How much in Bodyweights? Compression under the Patella
PCL and ACL Resist Knee Shear Forces ACL prevents anterior tibial displacement relative to the femur, PCL prevents posterior tibial displacement. Normal ligament function is to resist joint shear forces.
Horizontal Force & Velocity in Throwing Vertical impulse is the area under the Force-Time curve. Velocity starts at 0.0 m/s. As impulse builds or increases over time the ball velocity & momentum increase. During middle phase, force and therefore impulse are low and ball velocity & momentum are almost constant. During final phase and due to rapid internal shoulder rotation, force & impulse are high and ball velocity & momentum increase rapidly.
Energy & Work on a Trampoline Person has high energy at instant of contact with trampoline – mostly K.E. due to falling velocity & some P.E. Person’s energy does work on the trampoline and pushes it down, stretching the trampoline spring – person loses K.E. & P.E. Then trampoline’s stretch does work on person – person gains K.E. & P.E. and flies into air.
Inability of Gravity to Change Energy or Do Work Total Energy = P.E. + K.E. = mgh + ½ mv 2 Changes while on the trampoline but constant during flight phases As person rises through air, K.E. is converted to P.E. As person falls, P.E. is converted to K.E. Person leaves trampoline and then hits trampoline a few moments later with the same total energy.
3) Line of action of a force – In which direction is the force relative to the body segments?
- does the force create a flexor or extensor torque?
- does the force create compression or shear at a joint?
4) Rate of force application – is the force applied slowly or rapidly? – impact forces in running are applied very rapidly, lifting forces are applied relatively slowly
6) Frequency – how often is the force applied? GRFs are applied at 1 Hz (once a second) in walking and at 2-4 Hz in running. Seat vibrations occur at 60 Hz in truck driving (Ohhh, their aching backs!)
Biomechanical Issues About Forces
Ahhh, the Law of Reaction is Important in the Shot Put As you applied a large force onto the shot put, it applies an equally large force back on you. No wonder it would destroy our shoulder if we tried to throw the put. As we just learned, the inertial load is much lower in softball vs. shot put. Thus the reaction force in softball is low and not injurious.
Two Processes Used to Better Understand the Effects of Forces Force Composition : Combination of two or more forces into resultant or total force: e.g. calculate total muscle force from component muscles e.g. calculate the joint compressive force from many muscles
Force Composition for Shoulder Muscles What is total rotating force from both muscles (F resultant which is perpendicular to the arm)? Fmc = Clavicular portion of pectoralis major = 2,000 N at β = 40 ° Fms = Sternal portion of pectoralis major = 2,500 N at θ = 20 ° Fres. = 2,000 N = 2,500 N
Force Composition for Shoulder Muscles Fmc = Clavicular portion of pectoralis major = 2,000 N at β = 40 ° Perpendicular force (to arm): Cos 40 ° = Perp. Force / 2,000 N Perp. Force from Fm,c = 0.766 * 2,000 N = 1,532 N Perp. Force = 2,000 N
Force Composition for Shoulder Muscles Fms = Sternal portion of pectoralis major = 2,500 N at θ = 2 0 ° Perpendicular force (to arm): Cos 2 0 ° = Perp. Force / 2,000 N Perp. Force from Fm.s = 0.940 * 2,000 N = 1,879 N Total Perpendicular Resultant Force = 1,532 N + 1,879 N = 3, 411N From 4,500 N of total muscle force (the sum of the two components) Perp. Force θ = 2,500 N
Composition of Muscle Forces to Joint Loads Resultant joint forces during walking and running from muscle forces and musculo-skeletal model