2008MechSolutions

# 2008MechSolutions - 2008 AP Physics Mechanics Exam 1 a b...

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Unformatted text preview: 2008 AP Physics Mechanics Exam 1) a) b) forces parallel to slope: a v m b g ma bv mg =- → =- θ θ sin sin dt dv v m b g =- → θ sin c) forces parallel to slope: a v m b g ma bv mg =- → =- θ θ sin sin at terminal velocity, a = 0 so: b mg v v m b g θ θ sin sin = → =- d) Note that i) v = 0 at t = 0 ii) b mg v θ sin = at t → ∞ v ( t ) is a function whose derivative looks like itself but is negative. Guess: C Ae v Bt + =- where A, B, and C are constants to be determined. Set t = 0: C A C A C Ae C Ae v Bt- = → = + = + = + =- Therefore: A Ae C Ae v Bt Bt- = + =-- Set t = ∞: b mg A b mg A A A Ae A Ae v Bt θ θ sin sin- = → =- =- =- =- = ∞-- Therefore: ( 29 ( 29 1 sin 1-- =- =- = + =---- Bt Bt Bt Bt e b mg e A A Ae C Ae v θ ( 29 Bt e b mg v-- = → 1 sin θ Using the differential equation from above: dt dv v m b g =- θ sin Substituting v (t) gives: ( 29 ( 29 A Ae dt d A Ae m b g Bt Bt- =---- θ sin Bt Bt ABe A m b Ae m b g--- = +- θ sin This works if : b mg A A m b...
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2008MechSolutions - 2008 AP Physics Mechanics Exam 1 a b...

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