Please help me with question 3 Uniform Circular Motion (UCM) and Universal Gravitation Review Questions1. A spherical stone with a mass of 1.25 kg is attached to one end of a 90 cm string and is the swung in a horizontalcircle. If the maximum force that the string can withstand before breaking is 450 N, what maximum speed can beattained by the stone? (18 m/s)2.A satellite is located 1000 km above the surface of the Earth. How long would it take for the satellite to completeone orbit of the Earth? What is its speed? (6295 s, 7357 m/s)3.Jupiter has a mass of 1.90 x 1027 kg and a radius of orbit of 7.78 x 10¹¹ m. Saturn has a mass of 5.67 x 1026 kg anda radius of orbit of 1.43 x 10¹2 m. What is the gravitational force of attraction between Jupiter and Saturn whenone of the planets is on the exact opposite side of the Sun from the other planet? (1.47 x 10¹⁹ N)4.A hill has a radius of curvature of 60 m. With what maximum speed can a car go over the hill without leaving theground? (24.3 m/s)5.A satellite is orbiting the Earth with a period of 60 h. Determine the height of the satellite above the Earth'ssurface. (7.41 x 107 m)6.Two students with masses of 65 kg and 74 kg are standing 3.00 m apart. What is the gravitational force ofattraction between the students? (3.56 x 10-8 N)7.What would be the acceleration due to gravity on the Earth if Earth's mass was tripled and the radius wasdoubled? (7.36 m/s²)8.An object with a mass of 5.00 kg is swung 22 times in 57.5 s. If the diameter of the circle is 6.00 m, what is thetension in the rope? (86.7 N)9.A merry-go-round is being turned with a frequency of 0.25 Hz. A child, with a mass of 40 kg, is sitting on the floorof the merry-go-round which has a coefficient of friction of 0.35. What is the maximum distance from the centrewhere the child can sit without being thrown off the merry-go-round? Explain why the child would be thrownoff. (1.39 m)10. Two masses, 2000 kg and 5000 kg, are placed 20 m apart. A third mass of 500 kg is placed in between the twolarge masses a distance of 5.0 m from the larger mass. What is the force acting on the 500 kg mass? (6.37 x 10-6N toward the 5000 kg mass)

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one orbit of the Earth? What is its speed? (6295 s, 7357 m/s) 3. Jupiter has a mass of 1.90 x 1027 kg and a radius of orbit of 7.78 a radius of orbit of 1.43 x 10¹2 m. What is the gravitational one of the planets is on the exact opposite side of the Sun from the other x 10¹¹ m. Saturn has a mass of 5.67 x 1026 kg and between Jupiter and Saturn when force of attraction planet? (1.47 x 10¹⁹ N) hill without leaving the

one orbit of the Earth? What is its speed? (6295 s, 7357 m/s) 3. Jupiter has a mass of 1.90 x 1027 kg and a radius of orbit of 7.78 a radius of orbit of 1.43 x 10¹2 m. What is the gravitational one of the planets is on the exact opposite side of the Sun from the other x 10¹¹ m. Saturn has a mass of 5.67 x 1026 kg and between Jupiter and Saturn when force of attraction planet? (1.47 x 10¹⁹ N) hill without leaving the

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter7: Gravity

Section: Chapter Questions

Problem 3PQ: For many years, astronomer Percival Lowell searched for a Planet X that might explain some of the...

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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.
For many years, astronomer Percival Lowell searched for a Planet X that might explain some of the perturbations observed in the orbit of Uranus. These perturbations were later explained when the masses of the outer planets and planetoids, particularly Neptune, became better measured (Voyager 2). At the time, however, Lowell had proposed the existence of a Planet X that orbited the Sun with a mean distance of 43 AU. With what period would this Planet X orbit the Sun?
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?
Two planets in circular orbits around a star have speed of v and 2v . (a) What is the ratio of the orbital radii of the planets? (b) What is the ratio of their periods?
Suppose the gravitational acceleration at the surface of a certain moon A of Jupiter is 2 m/s2. Moon B has twice the mass and twice the radius of moon A. What is the gravitational acceleration at its surface? Neglect the gravitational acceleration due to Jupiter. (a) 8 m/s2 (b) 4 m/s2 (c) 2 m/s2 (d) 1 m/s2 (e) 0.5 m/s2
What is the orbital radius of an Earth satellite having a period of 1.00 h? (b) What is unreasonable about this result?
When Sedna was discovered in 2003, it was the most distant object known to orbit the Sun. Currently, it is moving toward the inner solar system. Its period is 10,500 years. Its perihelion distance is 75 AU. a. What is its semimajor axis in astronomical units? b. What is its aphelion distance?
A massive black hole is believed to exist at the center of our galaxy (and most other spiral galaxies). Since the 1990s, astronomers have been tracking the motions of several dozen stars in rapid motion around the center. Their motions give a clue to the size of this black hole. a. One of these stars is believed to be in an approximately circular orbit with a radius of about 1.50 103 AU and a period of approximately 30 yr. Use these numbers to determine the mass of the black hole around which this star is orbiting, b. What is the speed of this star, and how does it compare with the speed of the Earth in its orbit? How does it compare with the speed of light?
An object of mass m is located on the surface of a spherical planet of mass M and radius R. The escape speed from the planet does not depend on which of the following? (a) M (b) m (c) the density of the planet (d) R (e) the acceleration due to gravity on that planet
Tidal friction is slowing the rotation of the Earth. As a result, the orbit of the Moon is increasing in radius at a rate of approximately 4 cm/year. Assuming this to be a constant rate, how many years will pass before the radius of the Moon's orbit increases by 3.84106 m (1%)?
(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?
What is the gravitational acceleration close to the surface of a planet with a mass of 2ME and radius of 2RE where ME, and RE are the mass and radius of Earth, respectively? Answer as a multiple of g, the magnitude of the gravitational acceleration near Earths surface. (See Section 7.5.)