FINAL '07 - final 01 BOBBITT, JAMES Due: May 12 2007, 3:00...

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Unformatted text preview: final 01 BOBBITT, JAMES Due: May 12 2007, 3:00 pm 1 Mechanics - Basic Physical Concepts Math: Circle: 2 r , r 2 ; Sphere: 4 r 2 , (4 / 3) r 3 Quadratic Eq.: ax 2 + bx + c = 0, x = b b 2 4 a c 2 a Cartesian and polar coordinates: x = r cos , y = r sin , r 2 = x 2 + y 2 , tan = y x Trigonometry: cos cos + sin sin = cos( ) sin + sin = 2 sin + 2 cos 2 cos + cos = 2 cos + 2 cos 2 sin 2 = 2 sin cos , cos 2 = cos 2 sin 2 1 cos = 2 sin 2 2 , 1 + cos = 2 cos 2 2 Vector algebra: vector A = ( A x ,A y ) = A x + A y Resultant: vector R = vector A + vector B = ( A x + B x ,A y + B y ) Dot: vector A vector B = AB cos = A x B x + A y B y + A z B z Cross product: = k , k = , k = vector C = vector A vector B = vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle k A x A y A z B x B y B z vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle C = AB sin = A B = AB , use right hand rule Calculus: d dx x n = nx n 1 , d dx ln x = 1 x , d d sin = cos , d d cos = sin , d dx const = 0 Measurements Dimensional analysis: e.g. , F = ma [ M ][ L ][ T ] 2 , or F = m v 2 r [ M ][ L ][ T ] 2 Summation: N i =1 ( ax i + b ) = a N i =1 x i + bN Motion One dimensional motion: v = d s dt , a = d v dt Average values: v = s f s i t f t i , a = v f v i t f t i One dimensional motion (constant acceleration): v ( t ) : v = v + at s ( t ) : s = v t = v t + 1 2 at 2 , v = v + v 2 v ( s ) : v 2 = v 2 + 2 as Nonuniform acceleration: x = x + v t + 1 2 at 2 + 1 6 j t 3 + 1 24 st 4 + 1 120 k t 5 + 1 720 pt 6 + ... , (jerk, snap, ... ) Projectile motion: t rise = t fall = t trip 2 = v y g h = 1 2 g t 2 fall , R = v ox t trip Circular: a c = v 2 r , v = 2 r T , f = 1 T (Hertz=s 1 ) Curvilinear motion: a = radicalBig a 2 t + a 2 r Relative velocity: vectorv = vectorv + vectoru Law of Motion and applications Force: vector F = mvectora, F g = mg, vector F 12 = vector F 21 Circular motion: a c = v 2 r , v = 2 r T = 2 r f Friction: F static s N F kinetic = k N Equilibrium (concurrent forces): i vector F i = 0 Energy Work (for all F): W = W AB = W B W A F bardbl s = Fs cos = vector F vectors integraltext B A vector F dvectors (in Joules) Effects due to work done: vector F ext = mvectora vector F c vector f nc W ext | A B = K B K A + U B U A + W diss | A B Kinetic energy: K B K A = integraltext B A mvectora dvectors , K = 1 2 mv 2 K (conservative vector F ): U B U A = integraltext B A vector F dvectors U gravity = mg y , U spring = 1 2 k x 2 From U to vector F : F x = U x , F y = U y , F z = U z...
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FINAL '07 - final 01 BOBBITT, JAMES Due: May 12 2007, 3:00...

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