2007MechSolutions - 2006 AP Physics Mechanics Exam FN 1) a)...

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Unformatted text preview: 2006 AP Physics Mechanics Exam FN 1) a) F1 µ FN mg vertical forces: FN + F1 sin θ = mg → FN = mg − F1 sin θ b) c) d) horizontal forces: F1 cos θ − µFN = ma → µ = constant acceleration v-t graph: linear, positive slope through origin x-t graph: 2nd order polynomial through origin F1 cos θ − ma F1 cos θ − ma = FN mg − F1 sin θ e) Lose contact with ground: FN = 0: FN = mg − F1 sin θ = 0 → F1 = mg ma = F1 cos θ − µFN = F1 cos θ − µmg + µF1 sin θ = sin θ mg cos θ mg cos θ ma = − µmg + µmg = = mg cot θ → sin θ sin θ mg sin θ F1 cos θ − µFN = ma → ma = F1 cos θ − µFN = F1 cos θ − µ ( mg − F1 sin θ ) mg cos θ − µmg + µ sin θ sin θ a = g cot θ 2) a) b) v= 2πR T → R= vT 3.4 × 10 3 7.08 × 10 3 = = 3.83 × 10 6 m 2π 2π ( )( ) mv 2 GmM = R R2 mv 2 GmM = R R2 Rv 2 3.83 × 10 6 3.4 × 10 3 → M= = G 6.67 × 10 −11 → mv 2 = ( )( ) 2 = 6.64 × 10 23 kg c) GmM 1 GmM → mv 2 = R 2 2R 1 GmM GmM GmM GmM = − =− Total Energy: E = K + U = mv 2 − 2 R 2R R 2R −11 23 GmM 6.67 × 10 ( 930 ) 6.64 × 10 E=− =− = −5.4 × 10 9 J 6 2R 2 3.83 × 10 ( ( ) ( ) ) d) mv GmM = R R2 2 → v2 = GM 2πR 4π 2 R 2 = = R T2 T 2 → T2 = 4π 2 R 3 GM Decreasing the orbital radius decreases the orbital period The new orbital period would be LESS THAN the given period. e) R1 = 4.36 x 105 + 3.43 x 106 = 3.866 x 106 m R2 = 3.71 x 105 + 3.43 x 106 = 3.801 x 106 m 2 Total Energy: E = K + U = mv1 − 1 2 GmM 1 GmM 2 = mv 2 − R1 2 R2 1 1 1 1 2 2 −11 3 v 2 = 2GM 6.64 × 10 23 − + 3.4 × 10 R − R + v1 = 2 6.67 × 10 6 6 3.801 × 10 3.866 × 10 2 1 2 v 2 = 1.12 × 10 7 ( )( ) ( ) 2 → v 2 = 3.34 × 10 3 m s 3) a) c) d) 121 kx = mv 2 2 2 k 4.9 k 40 slope = ≈ = 196 → m = = = 0.204 kg m .025 slope 196 1 1 mg ( h + x sin θ ) + kx 2 = mv 2 i) 2 2 121 mgh + mgx sin θ + kx = mv 2 2 2 1 1 ii) For all values of v, mv 2 > kx 2 2 2 1 1 and the difference mv 2 − kx 2 = mgh + mgx sin θ increases as v increases 2 2 Therefore the graph would NOT be linear. ...
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This note was uploaded on 08/29/2010 for the course PHYS 45925 taught by Professor Ramesh during the Spring '10 term at University of California, Berkeley.

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2007MechSolutions - 2006 AP Physics Mechanics Exam FN 1) a)...

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