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The Work Energy Theorem Textbook: 4.1 - 4.3 Homework: pg. 183 # 2, 5, 6, 7 pg. 188 # 2, 5, 6, 7, 8 pg. 194 # 1 – 7 Work • Work is the energy transferred to an object by a force F, through a displacement d • W=Fdcos – W = [J], F = [N], d = [m] James Prescott Joule (1818 – 1889): - English physicist - Discovered relationship btw. heat & mechanical work (energy) - Conservation of Energy Theorem Mechanical Energy is a combination of two fundamental types of energy: • Kinetic energy (the energy of motion) • Potential energy (energy that is stored) - Gravitational Potential Energy - Elastic Potential Energy Kinetic Energy • Work done by the net force causes a change in speed • The kinetic energy of an object of mass m, in kg, and speed v, in m/s: Gravitational Potential Energy • “stored energy” in an object at a particular height w.r.t. a reference point. W.E.T. (Work-Energy Theorem) • The total work done on an object equals the change in the object’s kinetic energy and/or gravitational potential energy. Wtotal EK Wtotal EK 2 EK 1 1 2 1 2 F d mv2 mv1 2 2 Wtotal Eg Wtotal Eg 2 Eg1 F d mgh2 mgh1 Ek = -Eg Ex 1: By what factor does a cyclist’s kinetic energy increase if the cyclist’s speed: (a) doubles (b) triples (c) increases by 37% Ex 2. A 45-g golf ball leaves the tee with a speed of 43 m/s after a golf club strikes it. (a) Determine the work done by the club on the ball. (b) Determine the magnitude of the average force applied by the club to the ball, assuming that the force is parallel to the motion of the ball and acts over a distance of 2.0 cm. A 27g arrow is shot horizontally. The bowstring exerts an average force of 75 N on the arrow over a distance of 78 cm. Determine, using the workenergy theorem, the maximum speed reached by the arrow as it leaves the bow Elastic Potential Energy & Conservation of Energy Textbook: 4.5 Homework: WS – Spring problems What is Hooke’s LAW A Hookean System (i.e. spring, wire, rod etc) is one that returns to its original configuration after being distorted and then released. Hooke’s Law …cont Fapplied on spring Slope = k = spring constant x, (i.e distance from equilibrium) Potential Elastic Energy Fapplied on spring Work done x, (i.e distance from equilibrium) Elastic Potential Energy • The energy stored in a spring of spring constant k [N/m] compressed or extended from equilibrium a distance x [m] is: The Law of Conservation of Energy • Energy cannot be created or destroyed, but only transferred from one form to another without any loss. • The total energy of a closed system is constant. ET 1 ET 2 Elastic Potential Energy & Simple Harmonic Motion (SHM) Textbook: 4.5 Homework: pg 214-215 # 16 – 21 pg 217-218 # 23 – 28 Simple Harmonics Motion (SHM) - Motion that obeys Hooke’s law - Periodic and follows sinusoidal function Period of SHM 4 2 r ac T2 4 2 r 2 T ac T 4 2 r ac T 2 r ac a x ac , x r T 2 T 2 x ax x Fs m T 2 x kx m T 2 m k SHM & Damping: The effect of friction on SHM is called damping. • Three Types of Damping: 1) Overdamping: Oscillation ceases and the mass slowly returns to equilibrium position 2) Critical damping: Oscillation ceases and the mass moves back to equilibrium position as fast as theoretically possible without incurring further oscillations. This special point is never perfectly reached in nature 3) Underdamping: Oscillation is continually reduced in amplitude Decreasing amplitude “Envelope” of the damping motion Pg 214 # 18.