Volcanoes on lo. lo, 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 (see Figure 7.45 ). Due to the satellite’s small mass, the acceleration due to gravity on lo is only 1.81 m/s 2 , and lo 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? (b) If the gravitational potential energy is zero at the surface, what is the potential energy for a 25 kg fragment at its maximum height on lo? How much would this gravitational potential energy be if it were at the same height above earth? Figure 7.45 Problem 39.
Volcanoes on lo. lo, 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 (see Figure 7.45 ). Due to the satellite’s small mass, the acceleration due to gravity on lo is only 1.81 m/s 2 , and lo 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? (b) If the gravitational potential energy is zero at the surface, what is the potential energy for a 25 kg fragment at its maximum height on lo? How much would this gravitational potential energy be if it were at the same height above earth? Figure 7.45 Problem 39.
Volcanoes on lo. lo, 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 (see Figure 7.45 ). Due to the satellite’s small mass, the acceleration due to gravity on lo is only 1.81 m/s2, and lo 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? (b) If the gravitational potential energy is zero at the surface, what is the potential energy for a 25 kg fragment at its maximum height on lo? How much would this gravitational potential energy be if it were at the same height above earth?
A team of astronauts is on a mission to land on and explore a large asteroid. In addition to collecting samples and performing experiments, one of their tasks is to demonstrate the concept of the escape speed by throwing rocks straight up at various initial speeds. With what minimum initial speed ?esc will the rocks need to be thrown in order for them never to "fall" back to the asteroid? Assume that the asteroid is approximately spherical, with an average density ?=2.93×106 g/m3 and volume ?=1.94×1012 m3 . Recall that the universal gravitational constant is ?=6.67×10-11 N·m2/kg2 .vesc = ? m/s
Venus is slightly smaller and lighter than the Earth. As a result, the gravitational acceleration at the surface of Venus gv = 8.9 m/s2 indicating a gravitational attraction slightly weaker than that of Earth. It is also closer than Earth, to the sun. The atmosphere of Venus is composed predominantly of carbon dioxide with very little nitrogen. Why might that be the case?
Rick is an Aerospace Engineer at NASA’s Jet Propulsions Laboratory (JPL), and is designing
the next mission to Pluto called “New Horizons 2: The Sequel". This time Rick plans to
study Pluto's largest moon Charon. Charon has a mass of 1.586 ×1021 kg and a mean radius
of 606 km, and might have a nitrogenous atmosphere (N2) just like Pluto. If, for a massive
object to have an atmosphere its escape speed must be 12 times greater than the root-mean-
square (rms) velocity of the gas (otherwise the gas will slowly leak away over time), what is
the maximum temperature that Charon can have and still have a nitrogenous atmosphere?
[Charon has a temperature of -281 °C = 55 K, day or night.]
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