{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

PHY 303K - Midterm #2

PHY 303K - Midterm #2 - midterm 02 FIERRO JEFFREY Due Mar 5...

This preview shows pages 1–2. Sign up to view the full content.

midterm 02 – FIERRO, JEFFREY – Due: Mar 5 2008, 9:00 pm 1 Mechanics - Basic Physical Concepts Math: Circle: 2 π r , π r 2 ; Sphere: 4 π r 2 , (4 / 3) π r 3 Quadratic Eq.: a x 2 + b x + c = 0, x = b ± b 2 4 ac 2 a Cartesian and polar coordinates: x = r cos θ, y = r sin θ , r 2 = x 2 + y 2 , tan θ = y x Trigonometry: cos α cos β + sin α sin β = cos( α - β ) sin α + sin β = 2 sin α + β 2 cos α β 2 cos α + cos β = 2 cos α + β 2 cos α β 2 sin2 θ = 2 sin θ cos θ, cos2 θ = cos 2 θ - sin 2 θ 1 - cos θ = 2 sin 2 θ 2 , 1 + cos θ = 2 cos 2 θ 2 Vector algebra: vector A = ( A x , A y ) = A x ˆ ı + A y ˆ Resultant: vector R = vector A + vector B = ( A x + B x , A y + B y ) Dot: vector A · vector B = A B cos θ = A x B x + A y B y + A z B z Cross product: ˆ ı × ˆ = ˆ k , ˆ × ˆ k = ˆ ı , ˆ k × ˆ ı = ˆ vector C = vector A × vector B = vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle ˆ ı ˆ ˆ k A x A y A z B x B y B z vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle C = A B sin θ = A B = A B , use right hand rule Calculus: d dx x n = n x n 1 , d dx ln x = 1 x , d sin θ = cos θ , d cos θ = - sin θ , d dx const = 0 Measurements Dimensional analysis: e.g. , F = m a [ M ][ L ][ T ] 2 , or F = m v 2 r [ M ][ L ][ T ] 2 Summation: N i =1 ( a x i + b ) = a N i =1 x i + b N Motion One dimensional motion: v = ds dt , a = dv 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 0 + a t s ( t ) : s = ¯ v t = v 0 t + 1 2 a t 2 , ¯ v = v 0 + v 2 v ( s ) : v 2 = v 2 0 + 2 a s Nonuniform acceleration: x = x 0 + v 0 t + 1 2 a t 2 + 1 6 j t 3 + 1 24 s t 4 + 1 120 k t 5 + 1 720 p t 6 + . . . , (jerk, snap, . . . ) Projectile motion: t rise = t fall = t trip 2 = v 0 y g h = 1 2 g t 2 fall , R = v ox t trip Circular: a c = v 2 r , v = 2 π 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 = m g, vector F 12 = - vector F 21 Circular motion: a c = v 2 r , v = 2 π r T = 2 π r f Friction: F static μ s N F kinetic = μ k N Equilibrium (concurrent forces): i vector F i = 0 Energy Work (for all F): Δ W = W AB = W B - W A F bardbl s = Fs cos θ = 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 m v 2 K (conservative vector F ): U B - U A = - integraltext B A vector F · dvectors U gravity = m g 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 F gravity = - ∂ U ∂y = - m g , F spring = - ∂ U ∂x = - k x Equilibrium: ∂ U ∂x = 0, 2 U ∂x 2 > 0 stable, < 0 unstable Power: P = dW dt = F v bardbl = F v cos θ = vector F · vectorv (Watts) Collision Impulse: vector I = Δ vector p = vector p f - vector p i integraltext t f t i vector F dt Momentum: vector p = mvectorv Two-body: x cm = m 1 x 1 + m 2 x 2 m 1 + m 2 p cm M v cm = p 1 + p 2 = m 1 v 1 + m 2 v 2 F cm F 1 + F 2 = m 1 a 1 + m 2 a 2 = M a cm K 1 + K 2 = K 1 + K 2 + K cm Two-body collision:

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}