EXAMPLE A Robot Spacecraft Leaves an Asteroid A robot spacecraft lands on an asteroid, picks up a sample, and blasts off to return to Earth; its total mass is 1500 kg. When it is 200 km (2 x 105 m) from the center of the asteroid, its speed is 5.0 m/s, and the rockets are turned off. At the moment when it has coasted to a distance 500 km (5 x 105 m) from the center of the asteroid, its speed has decreased to 4.1 m/s. (a) Draw and label a diagram showing your choice of initial and final states. (b) Calculate the mass of the asteroid.

EXAMPLE A Robot Spacecraft Leaves an Asteroid A robot spacecraft lands on an asteroid, picks up a sample, and blasts off to return to Earth; its total mass is 1500 kg. When it is 200 km (2 x 105 m) from the center of the asteroid, its speed is 5.0 m/s, and the rockets are turned off. At the moment when it has coasted to a distance 500 km (5 x 105 m) from the center of the asteroid, its speed has decreased to 4.1 m/s. (a) Draw and label a diagram showing your choice of initial and final states. (b) Calculate the mass of the asteroid.

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter13: Gravitation

Section: Chapter Questions

Problem 70AP: Space debris left from old satellites and their launchers is becoming a hazard to other satellites....

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Astronomical observatrions of our Milky Way galaxy indicate that it has a mass of about 8.01011 solar masses. A star orbiting on the galaxy’s periphery is about 6.0104 light-years from its center. (a) What should the orbital period of that star be? (b) If its period is 6.0107 years instead, what is the mass of the galaxy? Such calculations are used to imply the existence of other matter, such as a very massive black hole at the center of the Milky Way.
Integrated Concepts Space debris left from old satellites and their launchers is becoming a hazard to other satellites. (a) Calculate the speed of a satellite in an orbit 900 km above Earth's surface. (b) Suppose a loose rivet is in an orbit of the same radius that intersects the satellite's orbit at an angle of 90° relative to Earth. What is the velocity of the rivet relative to the satellite just before striking it? (c) Given the rivet is 3.00 mm in size, how long will its collision with the satellite last? (d) If its mass is 0.500 g, what is the average force it exerts on the satellite? (e) How much energy in joules is generated by the collision? (The satellite's velocity does not change appreciably, because its mass is much greater than the rivet's.)
Native people throughout North and South America used a bola to hunt for birds and animals. A bola can consist of three stones, each with mass m, at the ends of three light cords, each with length . The other ends of the cords are tied together to form a Y. The hunter holds one stone and swings the other two above his head (Figure P11.41a, page 308). Both these stones move together in a horizontal circle of radius 2 with speed v0. At a moment when the horizontal component of their velocity is directed toward the quarry, the hunter releases the stone in his hand. As the bola flies through the air, the cords quickly take a stable arrangement with constant 120-degree angles between them (Fig. P11.41b). In the vertical direction, the bola is in free fall. Gravitational forces exerted by the Earth make the junction of the cords move with the downward acceleration g. You may ignore the vertical motion as you proceed to describe the horizontal motion of the bola. In terms of m, , and v0, calculate (a) the magnitude of the momentum of the bola at the moment of release and, after release, (b) the horizontal speed of the center of mass of the bola, and (c) the angular momentum of the bola about its center of mass. (d) Find the angular speed of the bola about its center of mass after it has settled into its Y shape. Calculate the kinetic energy of the bola (e) at the instant of release and (f) in its stable Y shape. (g) Explain how the conservation laws apply to the bola as its configuration changes. Robert Beichner suggested the idea for this problem. Figure P11.41
Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.1011 solar masses. A star orbiting on the galaxy's periphery is about 6.0104 light years from its center. (a) What should the orbital period of that star be? (b) If its period is 6.0107 instead, what is the mass of the galaxy? Such calculations are used to imply the existence of "dark matter" in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies.
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Does the kinetic energy of an object depend on the frame of reference in which its motion is measured? Provide an example to prove this point.
Consider the Earth and the Moon as a two-particle system, a. How far from the center of the Earth is the gravitational field of this two-particle system zero? b. Sketch gravitational field vectors g along the line joining the Earth and the Moon. Indicate the point at which g=0 (Do not consider positions inside either object.)
(a) The Sun orbits the Milky Way galaxy once each 2.60108 y, with a roughly circular orbit averaging 3.00104 light years in radius. (A light year is the distance traveled by light in 1 y.) Calculate the centripetal acceleration of the Sun in its galactic orbit. Does your result support the contention that a nearly inertial frame of reference can be located at the Sun? (b) Calculate the average speed of the Sun in its galactic orbit. Does the answer surprise you?
Two identical particles, each of mass 1 000 kg, are coasting in free space along the same path, one in front of the other by 20.0 m. At the instant their separation distance has this value, each particle has precisely the same velocity of 800 m/s. What are their precise velocities when they are 2.00 m apart? Figure P13 74
According to the National Academy of Sciences, the Earths surface temperature has risen about 1F since 1900. There is evidence that this climate change may be due to human activity. The organizers of World Jump Day argue that if the Earth were in a slightly larger orbit, we could avoid global warming and climate change. They propose that we move the Earth into this new orbit by jumping. The idea is to get people in a particular time zone to jump together. The hope is to have 600 million people jump in a 24-hour period. Lets see if it will work. Consider the Earth and its inhabitants to make up the system. a. Estimate the number of people in your time zone. Assume they all decide to jump at the same time; estimate the total mass of the jumpers. b. What is the net external force on the Earthjumpers system? c. Assume the jumpers use high-tech Flybar pogo sticks (Fig. P8.32), which allow them to jump 6 ft. What is the displacement of the Earth as a result of their jump? d. What happens to the Earth when the jumpers land?
I need help with all parts. Thank you
A 750 kg spacecraft has total energy -0.55 TJ and is in circular orbit around the Sun. Part A Find its orbital radius. Express your answer in meters. femplates Symbols uado redo reset keyboard shortcuts help r = m Submit Request Answer • Part B Find its kinetic energy. Express your answer in joules. Templates Symbols undo redo reset keyboard shortcuts help K = J Submit Request Answer Part C Find its speed.