Zero, a hypothetical planet, has a mass of 4.0 x 10^23 kg, a radius of 3.0 x 10^
ID: 1293186 • Letter: Z
Question
Zero, a hypothetical planet, has a mass of 4.0 x 10^23 kg, a radius of 3.0 x 10^6 m, and no atmosphere. A 11 kg space probe is to be launched vertically from its surface. (a) If the probe is launched with an initial kinetic energy of 5.0 x 10^7 J, what will be its kinetic energy when it is 4.0 x 10^6 m from the center of Zero? J (b) If the probe is to achieve a maximum distance of 8.0 x 10^6 m from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero? JExplanation / Answer
(a)
K1 + U1 = K2 + U2
K1 + (- GMm/R1) = K2 + (- GMm/(R2))
K2 = K1 + (- GMm(R2 - R1)/(R2 * R1))
K2 = 5.0 * 107 + (- 6.67 * 10-11 * 4 * 1023 * 11(4 * 106 - 3 * 106)/(4 * 106 * 3 * 106))
K2 = 5.0 * 107 - 2.935 x 1020 / (12 * 1012)
K2 = 5.0 x 107 - 2.446 x 107
K2 = 2.554 x 107 J
(b)
K1 + U1 = U2
K1 = U2 - U1
K1 = - GMm/(8 x 106) + GMm/(3.0 x 106)
K1 = GMm * 5/(24 x 106)
K1 = 6.67 * 10-11 * 4 * 1023 * 11 * 5/(24 x 106)
K1 = 6.11 * 107 J
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