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 ?escvesc 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 ?=4.10×106 g/m3ρ=4.10×106 g/m3 and volume ?=1.25×1012 m3V=1.25×1012 m3 . Recall that the universal gravitational constant is ?=6.67×10−11 N·m2/kg2G=6.67×10−11 N·m2/kg2 .
How fast would you need to fire a 80 g Hot Wheels car down a straight track in order for it to successfully coast through a circular vertical loop of track with a radius of 30 cm? Draw a diagram and construct a force balance to determine your answer?
An 8000 kg satellite is launched from the surface of the Earth into outer space. What initial kinetic energy is needed by the satellite in order to reach a great (i.e., infinite) distance from the Earth, neglecting the effects of air resistance in the atmosphere? (G = 6.67 × 10−11 N·m2/kg2, ME = 5.97 × 1024 kg, RE = 6.37 × 106 m.)
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