# F5T25-THERMODYNAMIC EMPOWERED THE FUTURE GENERATIONS

Loading in 2 Seconds... Mechanical Energy, Work and Power. D. Gordon E. Robertson, PhD, FCSB Biomechanics Laboratory, School of Human Kinetics, University of Ottawa, Ottawa, Canada. Energy. Ability to do work Measured in joules (J)Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.D. Gordon E. Robertson, PhD, FCSB Biomechanics Laboratory, School of Human Kinetics, University of Ottawa, Ottawa, Canada Biomechanics Lab, U. of Ottawa Ability to do work Measured in joules (J) One joule is the work done when a one newton force moves an object through one metre 1 Calorie = 1000 cals = 4.186 kJ Can take many forms Measured in joules (J) One joule is the work done when a one newton force moves an object through one metre 1 Calorie = 1000 cals = 4.186 kJ Can take many forms Biomechanics Lab, U. of Ottawa Mass (E = mc2) Solar or Light (solar panels, photovoltaic battery) Electricity (electron flux, magnetic induction) Chemical (fossil fuels, ATP, food) Thermal or Heat Mechanical energy Solar or Light (solar panels, photovoltaic battery) Electricity (electron flux, magnetic induction) Chemical (fossil fuels, ATP, food) Thermal or Heat Mechanical energy Biomechanics Lab, U. of Ottawa Translational Kinetic = ½ m v2 v2 = vx2 + vy2 (+ vz2) this is usually the largest type in biomechanics Rotational Kinetic = ½ Iw2 this is usually the smallest type in biomechanics Gravitational Potential = m g y Elastic Potential = ½ k (x12 – x22) Assumed to be zero for rigid bodies v2 = vx2 + vy2 (+ vz2) this is usually the largest type in biomechanics Rotational Kinetic = ½ Iw2 this is usually the largest type in biomechanics this is usually the smallest type in biomechanics Gravitational Potential = m g y Elastic Potential = ½ k (x12 – x22) Assumed to be zero for rigid bodies Biomechanics Lab, U. of Ottawa Zeroth law When two quantities are in thermal balance to a third they are in thermal balance with each other. I.e., they have the same temperature. First Law (Law of Conservation of Energy) Energy is conserved (remains constant) within a “closed system.” Energy cannot be created or destroyed. Second Law (Law of Entropy) When energy is transformed from one form to another there is always a loss of usable energy. All processes increase the entropy of the universe. Third Law Absolute zero (absence of all atomic motion) cannot be achieved. When two quantities are in thermal balance to a third they are in thermal balance with each other. I.e., they have the same temperature. First Law (Law of Conservation of Energy) Energy is conserved (remains constant) within a “closed system.” Energy cannot be created or destroyed. Second Law (Law of Entropy) Energy cannot be created or destroyed. When energy is transformed from one form to another there is always a loss of usable energy. All processes increase the entropy of the universe. Third Law All processes increase the entropy of the universe. Absolute zero (absence of all atomic motion) cannot be achieved. Biomechanics Lab, U. of Ottawa If the resultant force acting on a body is a conservative force then the body’s total mechanical energy will be conserved. Resultant force will be conservative if all external forces are conservative. A force is conservative if it does no work around a closed path (motion cycle). Resultant force will be conservative if all external forces are conservative. A force is conservative if it does no work around a closed path (motion cycle). Biomechanics Lab, U. of Ottawa gravity Gravitational forces Biomechanics Lab, U. of Ottawa frictionless surface Gravitational forces Normal force of a frictionless surface Normal force of a frictionless surface Biomechanics Lab, U. of Ottawa elastic collision Gravitational forces Normal force of a frictionless surface Elastic collisions Normal force of a frictionless surface Elastic collisions Biomechanics Lab, U. of Ottawa pendulum Gravitational forces Normal force of a frictionless surface Elastic collisions Pendulum Normal force of a frictionless surface Elastic collisions Pendulum Biomechanics Lab, U. of Ottawa ideal spring Gravitational forces Normal force of a frictionless surface Elastic collisions Pendulum Ideal spring Normal force of a frictionless surface Elastic collisions Pendulum Ideal spring Biomechanics Lab, U. of Ottawa force load lever fulcrum Gravitational forces Normal force of a frictionless surface Elastic collisions Pendulum Ideal spring Lever system Normal force of a frictionless surface Elastic collisions Pendulum Ideal spring Lever system Biomechanics Lab, U. of Ottawa Simple machines: Pulleys Block & tackle Gears Cams Winch … Block & tackle Gears Cams Winch … Biomechanics Lab, U. of Ottawa Dry friction Air (fluid) resistance Viscous forces Plastic collisions Real pendulums Real springs Air (fluid) resistance Viscous forces Plastic collisions Real pendulums Real springs Biomechanics Lab, U. of Ottawa Treadmill Ergometry External work = m g t v sin q where, m = mass, g = 9.81, t = time, v = treadmill velocity, and q = treadmill’s angle of incline where, m = mass, g = 9.81, t = time, v = treadmill velocity, and q = treadmill’s angle of incline Biomechanics Lab, U. of Ottawa Cycle Ergometry External work = 6 n L g where, n = number of pedal revolutions, L = load in kiloponds and g = 9.81 Note, each pedal cycle is 6 metres motion of flywheel where, n = number of pedal revolutions, L = load in kiloponds and g = 9.81 Note, each pedal cycle is 6 metres motion of flywheel Biomechanics Lab, U. of Ottawa Gjessing Rowing Ergometry External work = n L g where, n = number of flywheel cycles, L = workload in kiloponds and g = 9.81 where, n = number of flywheel cycles, L = workload in kiloponds and g = 9.81 Biomechanics Lab, U. of Ottawa Point Mass Method Simplest, least accurate, ignores rotational energy Mechanical Energy = E = m g y + ½ m v2 External work = Efinal – Einitial Biomechanics Lab, U. of Ottawa Single Rigid Body Method Simple, usually planar, includes rotational energy Mechanical Energy = E= mgy + ½mv2 + ½Iw2 External Work = Efinal– Einitial Carriage load Biomechanics Lab, U. of Ottawa Multiple Rigid Body Method Difficult, usually planar, more accurate, accuracy increases with number of segments External Work = Efinal– Einitial E = sum of segmental total energies (kinetic plus potential energies) Biomechanics Lab, U. of Ottawa Inverse Dynamics Method Most difficult, usually planar, requires force platforms External Work = S ( S Mj wj Dt ) Sum over all joint moments and over duration of movement Biomechanics Lab, U. of Ottawa Absolute Power Method similar to previous method Total Mechanical Work = S ( S |Mj wj| Dt ) Sum over all joint moments and over duration of movement Notice positive and negative moment powers do not cancel (absolute values) Internal Work = Total mechanical work – External work Biomechanics Lab, U. of Ottawa Oxygen Uptake Difficult, accurate, expensive, invasive Physiological Work = c (VO2) Where, c is the energy released by metabolizing O2 and VO2 is the volume of O2 consumed Difficult, accurate, expensive, invasive Physiological Work = c (VO2) Where, c is the energy released by metabolizing O2 and VO2 is the volume of O2 consumed Biomechanics Lab, U. of Ottawa Mouthpiece for collecting expired gases and physiological costs Measure both mechanical and physiological costs ME = mechanical cost divided by physiological cost times 100% ME = mechanical cost divided by physiological cost times 100% Monark ergometer used to measure mechanical work done Biomechanics Lab, U. of Ottawa Internal work + External work ME = —————————————— × 100 % Physiological cost Internal work is measured by adding up the work done by all the joint moments of force. Most researchers ignore the internal work done. Biomechanics Lab, U. of Ottawa Work of a Force is product of force (F) and displacement (s) when F and s are in the same direction. Work = F s (when F is parallel to s) = F s cos f (when F is not parallel to s and is f angle between F and s) = F . s = Fx sx + Fy sy+ Fz sz (dot product) = Ef – Ei (change of energy) = P t (power times time) Biomechanics Lab, U. of Ottawa Work of a Moment of Force is product of moment of force (M) and angular displacement (q). Work = Mq = r F (sin f) q (f is angle between r and F) = P t (power times time) = S (Mw Dt) (time integral of moment power) Biomechanics Lab, U. of Ottawa Power is the rate of doing work. measured in watts (W), 1 watt = 1 joule per second (J/s) Power = work / time (work rate) = (Ef – Ei) / time (change in energy over time) = (F s) / t = F v (force times velocity) = (Mq) / t = Mw (moment of force times angular velocity) Power = work / time (work rate) = (Ef – Ei) / time (change in energy over time) = (F s) / t = F v (force times velocity) = (Mq) / t = Mw (moment of force times angular velocity) Biomechanics Lab, U. of Ottawa Power = F v (when F is parallel to v) = F v cos f (when F is not parallel to v and is f angle between F and v) = F . v = Fx vx + Fy vy+ Fz vz (dot product) = Mw (moment times angular velocity) Biomechanics Lab, U. of Ottawa KinCom 500H Controls speed of motion therefore lever has constant angular velocity (w) Measures force against a lever arm Moment = force times lever arm Instantaneous Power = moment times angular velocity Measures force against a lever arm Moment = force times lever arm Instantaneous Power = moment times angular velocity hydraulically controlled motion lever arm force sensor Biomechanics Lab, U. of Ottawa For SlideServe users

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