Chapter 12 Linear Kinetics of Human Movement Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D. © 2012 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin

12-2 Newton’s Laws What is the law of inertia? A body will maintain a state of rest or constant velocity unless acted on by an external force that changes the state. Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

12-3 Newton’s Laws Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D. A skater has a tendency to continue gliding with constant speed and direction because of inertia.

12-4 Newton’s Laws What is the law of acceleration? A force applied to a body causes 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 F = ma Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

12-5 Newton’s Laws What is the law of reaction? For every action, there is an equal and opposite reaction. When one body exerts a force on a second, the second body exerts a reaction force that is equal in magnitude and opposite in direction on the first body. Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

12-6 Newton’s Laws wt R In accordance with the law of reaction, the weight of a box sitting on a table generates a reaction force by the table that is equal in magnitude and opposite in direction to the weight. Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

12-7 Newton’s Laws Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D. In accordance with Newton’s third law of motion, ground reaction forces are sustained with every footfall during running.

12-8 Mechanical Behavior of Bodies in Contact What is friction? A force acting over the area of contact between two surfaces direction is opposite of motion or motion tendency magnitude is the product of the coefficient of friction (  ) and the normal reaction force (R) F =  R Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

12-9 Mechanical Behavior of Bodies in Contact Static F m =  s R Dynamic F k =  k R Applied external force Friction For static (motionless) bodies, friction is equal to the applied force. For dynamic bodies (in motion), friction is constant and less than maximum static friction. Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

12-10 Mechanical Behavior of Bodies in Contact Is it easier to push or pull a desk across a room? Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D. Pushing a desk Pulling a desk R = wt + P v R = wt - P v wt P P P P PvPv PvPv PHPH PHPH

12-11 Mechanical Behavior of Bodies in Contact What is momentum? quantity of motion possessed by a body measured as the product of a body’s mass and its velocity; M = mv Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

12-12 Mechanical Behavior of Bodies in Contact What is the principle of conservation of momentum? In the absence of external forces, the total momentum of a given system remains constant. M 1 = M 2 (mv) 1 = (mv) 2 Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

12-13 Mechanical Behavior of Bodies in Contact What causes momentum? impulse: the product of a force and the time interval over which the force acts Ft Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

12-14 Mechanical Behavior of Bodies in Contact What is the relationship between impulse and momentum? Ft =  M Ft = (mv) 2 - (mv) 1 Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

12-15 Mechanical Behavior of Bodies in Contact Force-time graphs from a force platform for high (A) and low (B) vertical jumps by the same performer. Force (Body Weight) Time (ms) A Time (ms) B What does the area under the curve represent? Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

12-16 Mechanical Behavior of Bodies in Contact What is impact? a collision characterized by: the exchange of a large force during a small time interval Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

12-17 Mechanical Behavior of Bodies in Contact What happens following an impact? This depends on: the momentum present in the system the nature of the impact Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

12-18 Mechanical Behavior of Bodies in Contact What happens during impact? This is described by the coefficient of restitution, a number that serves as an index of elasticity for colliding bodies; represented as e. Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

12-19 Mechanical Behavior of Bodies in Contact What does the coefficient of restitution (e) describe? relative velocity after impact -e = relative velocity before impact v 1 - v 2 -e = u 1 - u 2 Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

12-20 Mechanical Behavior of Bodies in Contact Ball velocities before impact Ball velocities after impact u 1 u 2 v 1 v 2 v 1 - v 2 = -e ( u 1 - u 2 ) The differences in two balls’ velocities before impact is proportional to the difference in their velocities after impact. The factor of proportionality is the coefficient of restitution. Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

12-21 Mechanical Behavior of Bodies in Contact What kinds of impact are there? perfectly elastic impact - in which the velocity of the system is conserved; (e = 1) perfectly plastic impact - in which there is a total loss of system velocity; (e = 0) (Most impacts fall in between perfectly elastic and perfectly plastic.) Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

12-22 Work, Power, and Energy Relationships What is mechanical work? the product of a force applied against a resistance and the displacement of the resistance in the direction of the force W = Fd units of work are Joules (J) Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

12-23 Work, Power, and Energy Relationships What is mechanical power? the rate of work production calculated as work divided by the time over which the work was done W P = t units of work are Watts (W) Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

12-24 Work, Power, and Energy Relationships What is mechanical energy? the capacity to do work units of energy are Joules (J) there are three forms energy: kinetic energy potential energy thermal energy Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

12-25 Work, Power, and Energy Relationships What is kinetic energy? energy of motion KE = ½mv 2 What is potential energy? energy by virtue of a body’s position or configuration PE = (wt)(ht) Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

12-26 Work, Power, and Energy Relationships Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D. During the pole vault, the bent pole stores potential energy for subsequent release as kinetic energy and thermal energy.

12-27 Work, Power, and Energy Relationships What is the law of conservation of mechanical energy? When gravity is the only acting external force, a body’s mechanical energy remains constant. KE + PE = C (where C is a constant - a number that remains unchanged) Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

12-28 Work, Power, and Energy Relationships Ht(m) PE(J) V(m/s) KE(J) Time Height, velocity, potential energy, and kinetic energy changes for a tossed ball. Note: PE + KE = C Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

12-29 Work, Power, and Energy Relationships What is the principle of work and energy? The work of a force is equal to the change in energy that it produces in the object acted upon. W =  KE +  PE +  TE (where TE is thermal energy) Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.