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FormulaSheet2 - Non-cons W depends on path(friction drag A...

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Measurements and Units SI Prefixes: Mega M 10 6 Kilo K 10 3 centi c 10 -2 milli m 10 -3 micro µ 10 -6 nano n 10 -9 pico p 10 -12 ~ " 10 7 s/yr 1 mi hr × 1 hr 3600 s × 5280 ft mi × 12" ft × 2.54 cm " × 1m 100 cm = 0.447 m s 1-D Motion v = dx dt ; a = dv dt Uniform acceleration x = x 0 + v 0 t + at 2 /2 v = v 0 + at v 2 = v 0 2 + 2 a ( x x 0 ) v av = v f v 0 2&3d motion v = d x dt ; a = d v dt v x = v cos( θ ) v y = v sin( θ ) v = v x 2 + v y 2 x = x 0 + v 0 x t + a x t 2 /2 v x = v 0 x + a x t v x 2 = v 0 x 2 + 2 a x ( x x 0 ) same for y ,z v x = v 1 x + v 2 x v Y = v 1 y + v 2 y sin2 α = 2sin α cos α cos2 α = 1 2sin 2 α Newton’s Laws 1) if F = 0 then v = const 2) F = m a 3) action-reaction Free-body diagrams ma = mg sin θ N = mg cos θ N is normal force m 2 a = m 2 g T m 1 a = T m 1 g Using Newton’s Laws dynamic friction f = μ N direction opp. to v static friction f = μ N direction as needed Circular motion a = v 2 / r centripetal acc. inward v = 2 π r / T = fr ; T = period=2 π / ω = 1 / f ; ma = mv 2 / r = F inward Banked curve mv 2 / r = N sin θ μ N cos θ Drag F = b v drift v = F ext / b Gravity F = GMm / r 2 ( ) ˆ r For spherical obj M is mass enclosed inside r mv 2 / r = GMm / r 2 r 3 /( MT 2 ) = const Work and Energy W = F i d r Cons. force W ind. of path
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Unformatted text preview: Non-cons. W depends on path (friction, drag) A • B = A B cos Spring F = − k ( x − x eq ) If external force accelerates object, W = Δ K = Δ 1 2 mv 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ Work done by external force to change position without accel: W = Δ U U = mgh gravity on earth-GMm r satellites 1 2 k ( x − x eq ) 2 springs ⎧ ⎨ ⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ Conservation of Energy for cons. force K+U=const for non-cons force Δ K + Δ U = W where W is work done by non-cons force Power P=dW/dt Escape velocity 1 2 mv 2 − GMm r =...
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