407_Physics ProblemsTechnical Physics

407_Physics ProblemsTechnical Physics - 409 Chapter 13...

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Chapter 13 409 P13.70 (a) The gravitational force exerted on m 2 by the Earth (mass m 1 ) accelerates m 2 according to: mg Gm m r 22 12 2 = . The equal magnitude force exerted on the Earth by m 2 produces negligible acceleration of the Earth. The acceleration of relative approach is then g Gm r 2 1 2 11 24 7 2 6 67 10 5 98 10 120 10 277 == ×⋅ × × = .. . . Nm kg kg m ms 2 ej e j . (b) Again, m 2 accelerates toward the center of mass with g 2 = . m s 2 . Now the Earth accelerates toward m 2 with an acceleration given as Gm m r g Gm r 11 2 1 2 2 11 24 7 2 6 67 10 2 00 10 0926 = × × = . . m 2 e j The distance between the masses closes with relative acceleration of gg g rel 2 =+= + = 370 ... . P13.71 Initial Conditions and Constants: Mass of planet: 5 98 10 24 . × kg Radius of planet: 6 37 10 6 . × m Initial x : 0.0 planet radii Initial y : 2.0 planet radii Initial v x : +5 000 m/s Initial v y : 0.0 m/s Time interval: 10.9 s FIG. P13.71 t (s) x (m) y (m) r (m) v x (m/s) v y (m/s) a x 2 a y 2 0.0 0.0 12 740 000.0 12 740 000.0 5 000.0 0.0 0.000 0 –2.457 5 10.9 54 315.3 12 740 000.0 12 740 115.8 4 999.9 –26.7 –0.010 0 –2.457 4 21.7 108 629.4 12 739 710.0 12 740 173.1 4 999.7 –53.4 –0.021 0 –2.457 3 32.6 162 941.1
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