Formula Sheet for Linear Motion

Formula Sheet [In some relations, the Ò~Ó symbol is being use to represent a direct proportion] Linear Motion a = Δ v/t vf = vi + at (average acceleration) (final velocity: how fast?) vavg = Δd/t (average velocity) Δd = vavgt (displacement: how far?) Δ d = vit + 1/2 at2 (full displacement formula) d = 1/2 gt2 (falling from rest) Newton’s Laws Fnet = 0 or no acceleration (condition for dynamic OR static equilibrium) Fnet = ma (net force); Ff = µN (friction and normal force relation) [g = -10 m/s2] W = mg (weight and acceleration of gravity) a = (R+W)/m (falling with air resistance; R opposes W) p = mv (momentum); Ft = m(vf-vi) (impulse = change of momentum) m 1 v 1 + m2 v 2 = m 1 v 1 ’ + m 2 v 2 ’ m1v1 + m2v2 = (m1+ m2 )v’ (completely elastic collision) (completely inelastic collision) Work and Energy (and Simple Machines!) W = Fd (work) PE = mgh KE = 1/2mv2 P = W/t = Fd/t (power) (potential and kinetic energy) ΔKE + ΔPE = 0, or KE gained = PE lost, results in: mgh = 1/2mvf 2 %eff = Work output / Work input or AMA / IMA (efficiency) Wout = Frdr Win = Fede (work due to effort and resistance forces and distances) IMA = de/d(Ideal Mechanical Advantage) r AMA = Fr/Fe (Actual Mechanical Advantage) Gravity and Projectile Motion: F = mg F = G m1m2/d2 (Universal Law of Gravity) horizontal: Fnet = 0, ax = 0, vx = const, dx = vxt, ttotal = tup + tdown vertical: Fnet = mg, ay = g, vf = vi + gt, dy = 1/2gt2, (tdown )2 = 2dy/g ] v = fλ = (and Light Basics slides): λ / Τ T = 1/f f = 1/T (wave relationships) fpeak ~ T or λpeak ~ 1/T (blackbody curve) (Color and Light Properties) E = hf c = fλ c = 3.00 x 108 m/s (electromagnetic spectrum) R+G+B=W (primary color addition) R + G = Y; R + B = M; B + G = C (color addition) (Optical Behavior) θi = θ r (law of reflection) n = c/v (index of refraction) n2/n1 ~ θ1/θ2 (law of refraction: if n2>n1, then θ2<θ1) or equivalently, Òthe incident ray bends towards the normal when entering a more optically dense mediumÓ.) 1/f = 1/di + 1/do M = hi/ho = -di/do (the following will NOT appear on the formula sheet for your final exam) Ray Diagram Rules: Rule 1: A parallel ray to the optical axis reflects (or refracts) through (or away from) F Rule -1: A ray through (or away from) F reflects (or refracts) parallel to the optical axis. Rule 2: A ray to the vertex A reflects (or refracts) at the same angle on the other side of the optical axis. (This rule reads exactly the same when reversed!) Rule 3: A ray towards C reflects back on itself (mirrors only, and reads the same if reversed). There were no formulas from the text for Ch 29, but there is a formula governing diffraction (as seen in one of the HW tutorials): pλ = d sin θ , where p is a whole number like 1, 2, 3É and d is the width of a slit. θ represents the amount the diffraction pattern has spread out between the 1st pair of dark fringes (for p = 1). What we saw when playing with the variables was if d increases for the same λ, θ decreases, and if we keep d constant and make λ longer, θ still decreases. In other words, if the wavelengths are long relative to the opening, less diffraction is seen. Thus, (λ/d) ~ θ . Also, hereÕs a reminder about the interference pattern seen from two separate sources of (in phase) waves: As the sources move apart, more nodal lines appear (where deconstructive interference occurs) and so the angle between nodal lines decreases. A similar formula as above can be used; the proportionality still holds if we now take d to mean the separation between sources.