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 =- =- sin sin dt dv v m b g =- sin c) forces parallel to slope: a v m b g ma bv mg =- =- sin sin at terminal velocity, a = 0 so: b mg v v m b g sin sin = =- d) Note that i) v = 0 at t = 0 ii) b mg v 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 sin sin- = =- =- =- =- = -- Therefore: ( 29 ( 29 1 sin 1-- =- =- = + =---- Bt Bt Bt Bt e b mg e A A Ae C Ae v ( 29 Bt e b mg v-- = 1 sin Using the differential equation from above: dt dv v m b g =- sin Substituting v (t) gives: ( 29 ( 29 A Ae dt d A Ae m b g Bt Bt- =---- sin Bt Bt ABe A m b Ae m b g--- = +- 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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