Zero, a hypothetical planet, has a mass of 4.1 ×10 23 kg, a radius of 2.9 × 10 6
ID: 1747245 • Letter: Z
Question
Zero, a hypothetical planet, has a mass of 4.1 ×1023 kg, a radius of 2.9 × 106 m, andno atmosphere. A 2.3 kg space probe is to be launched verticallyfrom its surface. (a) If the probe is launchedwith an initial kinetic energy of 5.5 × 107 J,what will be its kinetic energy when it is 4.2 ×106 m from the center of Zero? (b) Ifthe probe is to achieve a maximum distance of 7.3 ×106 m from the center of Zero, with what initial kineticenergy must it be launched from the surface of Zero?
(a)
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(b)
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Chapter 13, Problem 38Explanation / Answer
the energy conservation for the situation isgiven by K1 + U1 =K2 + U2 K1 - (G m M / r1) =K2 - (G m M / r2) (a) if K1 = 5.5 ×107 J and K2 = 4.2 ×106 J then we get that K2 = K1 + G M m [(1 /r2) - (1 / r1)] = .........J (b) in this case K2 = 0 r2 = 7.3 × 106m K1 = K2 + G M m [(1 /r1) - (1 / r2)] = .........J K1 - (G m M / r1) =K2 - (G m M / r2) (a) if K1 = 5.5 ×107 J and K2 = 4.2 ×106 J then we get that K2 = K1 + G M m [(1 /r2) - (1 / r1)] = .........J (b) in this case K2 = 0 r2 = 7.3 × 106m K1 = K2 + G M m [(1 /r1) - (1 / r2)] = .........J = .........JRelated Questions
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