ECE 105 Fall 2012 3/4 Course Notes

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University of Waterloo
Electrical and Computer Engineering
ECE 105
Michael Balogh

ECE 105 - Physics of Electrical Engineering 1 Kevin Carruthers Fall 2012 Forces and Motion Force is a vector, and therefore includes direction. For any vector a, ▯a has the same magnitude but opposite direction. Coordinate Systems Given AB we can ▯nd A or B’s position based on the position of the other one ~ ~ ~ OB= O +AAB for any Oxis the location of x relative to the origin. Components We can break any vector into components by ▯nding the angle between it and the plane we want to model it o▯ of. ▯ Example: for A = [email protected] , we can ▯nd it’s components with relation to the standard x-y plane with ~ ~ ▯ A y Acos20 A = Asin20 ▯ x 1 Constant Acceleration ▯~v a = ▯t ~f▯ v~i a = ▯t a▯t = v ~ ▯ v~ f i ~f= v ~i+~a▯t For the position vector d;d =fd + vi ~i▯t + ~1a(▯t) 2 2 2 2 ▯ ▯ vf = v~i+ 2~ a ▯d ~ Relative Motion For any three objects a;b; and c v~ = v~ + v~ ca cb ba read "the velocity of c with respect to a is equal to the velocity of c with respect to b plus the velocity of b with respect to a. Circular Motion 2 ac= v 4x ▯ ▯ r for very close points. For circle with center O and radius r 0r 1:: connected to object on circumferance with velocity ~0;v~1::: tangent to circumferance, a = v1 ▯0. For arc length between object (at di▯erent times s t t0;t1:::) s, ▯ =r. For small ▯ ▯ 1;jv ~1▯ v ~0j = ▯v: jaj = v▯ t a is perpendicular to ~v r1▯r0 r▯ v = t = t v▯ v2 ) ~a = r ▯ = r v 2 s = r▯ ds d▯ dt = v = rdt = r! d▯ ! = dt 2 v a = r 2 = (r!) r = r!2 Types of Forces A force is a push or pull interaction between two objects, reponsible for changing motion. Springs When unstretched, no spring forces exist. When a string is pushed from equilibrium, its spring force pushes back toward equilibrium. F = ▯k▯x s Tension The tension force pulls an object toward a rope and a rope toward an object. Ropes can never push. Normal The normal force "pushes back" against other objects via molecular electromagnetism. It is always perpendicular to the surface for any surface-to-surface contact. Technically, it is a type of spring force. 3 Friction Friction is the interaction between an object and a surface. It is a real force which acts opposite the direction of sliding, and is always tangent to surface. f / N is an experimental fact. f = ▯N, where ▯ is the coe▯cient of friction. ▯ is dependant on the type of objects and must be determined experimentally. Kinetic friction is when objects are sliding relative to each other and static friction is when objects are not yet sliding fs▯ ▯ s Example: A 50kg person is in a 1000kg elevator at rest. When the elevator begins to rise, the person notices her weight is 600N. How far does the elevator move in 3s? ~ ▯F = m~ a F ▯ mg ~a = n m 600 ▯ 50g = 50 2 = 2:2m=s 1 2 d = i t + at 2 1 = 0 + 22:2)9 = 9:9m Energy An object can be said to have a total energy equal to the sum of the various forms of energy it may posess. Kinetic Energy The kinetic energy of an object is determined by its mass and velocity 2 K = mv 2 4 For any object with a changing velocity 2 2 vf = vi+ 2ad 1 mv = 1 mv + mad 2 f 2 i ~ K f K + iFd ~ ▯K = ▯Fd Potential Gravitational Energy Potential gravitational energy is a measure of stored energy of an object based on its height. It is essentially non-sensical to determine an object’s "absolute" potential gravita- tional energy, thus we often simply solve for the di▯erence in energy. For a distance
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