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=Fdcos 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: Pg. 226 #3 Pg. 242 #29 - 35

Gravitational Potential Energy “stored energy” in an object at a particular height w.r.t. a reference point. Ex. Pg. 191 #1, 2, 3 Ex. Pg. 194 #7

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. Ek = -Eg

Ex 1: By what factor does a cyclist’s kinetic 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  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 Pg. 211 #8 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: Pg. 211 #10 - 12 Derive formula for Pendulum (Restoring Force) Relate to period of a spring and mass system Pg. 214 #16, 18

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.

Elastic Potential Energy & Simple Harmonic Motion (SHM) Pg. 211 #8 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

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.