Io, a satellite of Jupiter, is the most volcanically active moon or planet in th

Question

Io, a satellite of Jupiter, is the most volcanically active moon or planet in the solar system. It has volcanoes that send plumes of matter over 500 km high. Due to the satellite's small mass, the acceleration due to gravity on Io is only 1.81 m/s2, and Io has no appreciable atmosphere. Assume that there is no variation in gravity over the distance traveled.

A) What must be the speed of material just as it leaves the volcano to reach an altitude of 500 km ? Express your answer in meters per second to three significant figures.

B) If the gravitational potential energy is zero at the surface, what is the potential energy for a 35 kg fragment at its maximum height on Io? Express your answer in Joules to two significant figures.

C) How much would this gravitational potential energy be if it were at the same height above earth? Express your answer in Joules two significant figures.

Explanation / Answer

h =500km

(a) If it leaves the surface of volcano then the total potential energy converted into kinetic energy.

mgh = (1/2) mv2

v =[2gh]1/2

here g =1.81 m/s^2

v = [2x1.81x5x105]1/2

v =1.34x103 m 1340 m

(b) m =35 kg, g =1.81 m/s^2

U =mgh = (35)(1.81)(5x105)

U= 3.2X107 J

(c) m =35 kg,

object is on earth so we should consider g value as 9.8 m/s^2

U =mgh = (35)(9.8)(5x105)

U = 1.7x108 J

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