Gravitation MCs

A satellite of mass m orbits a moon of mass M in uniform circular motion with a constant tangential speed of v. The gravitational field strength at a distance R from the center of moon is gR. The satellite is moved to a new circular orbit that is 2R from the center of the moon. What is the gravitational field strength of the moon at this new distance? A. gR/4 B. gR/2 C. 2gR D. 4gR

A. Correct. According to the relationship g=GM/R², if the distance of the satellite's orbit from the center of the moon is doubled, then the gravitational acceleration is one-fourth of the original gravitational field strength

A satellite is a large distance from a planet, and the gravitational force from the planet is the only significant force exerted on the satellite. The satellite begins falling toward the planet, eventually colliding with the surface of the planet. As the satellite falls, which of the following claims is correct about how the force that the planet exerts on the satellite Fps changes and how the force that the satellite exerts on the planet Fsp changes, if at all? What reasoning supports this claim? A. Fps and Fsp both increase. The gravitational forces that two objects exert on one another decrease as the separation between the objects increases, and these forces are always equal in magnitude. B. Fps increases while Fsp remains constant. The gravitational force exerted by a planet on a satellite decreases as the separation between the two objects increases, and the force exerted by the satellite on the planet remains negligibly small. C. Fps remains constant while Fsp increases. The gravitational force exerted by a planet on a satellite is a constant equal to the weight of the satellite, and the gravitational force exerted by the satellite on the planet decreases as the separation between the two objects increases. D. Fps and Fsp both remain constant. The gravitational forces that a planet and a satellite exert on one another is a constant equal to the weight of the satellite.

A. Correct. Claim: The force that the planet exerts on the satellite will increase, and the force that the satellite exerts on the planet will increase. Evidence: The satellite moves toward the planet from far away until it hits the planet's surface. The planet's gravity provides the only significant force exerted on the satellite. By Newton's third law, If an object exerts a force on a second object, the second object exerts a force of equal magnitude and opposite direction back on the first object. Reasoning: The force of gravity has an inverse-square dependence on the distance between two objects, decreasing at larger separations and increasing as the objects get closer together. The forces that the two objects exert on each other are always equal in magnitude.

A payload of mass m, where m<M, is delivered to the space station. Soon after, the space station's orbit is adjusted so that it is 50 km farther away from Earth's surface than before. Which of the following best describes the effects of these changes on Earth's gravitational field strength at the space station's new location? A. The increase in mass of the space station has no effect on the field strength, and the increase in orbital radius decreases the field strength. B. The increase in mass increases the field strength, and the increase in orbital radius decreases the field strength; however, the field strength decreases overall. C. The increase in mass increases the field strength, and the increase in orbital radius decreases the field strength; however, the field strength increases overall. D. The field strength is unchanged because there is no gravitational field in space.

A. Correct. Earth's gravitational field, g=GM/r², is an inverse square relationship. The mass in the equation refers to the mass of Earth, not the mass of the space station. The change in mass of the space station has no effect on the field strength. The radius of the orbit, which is measured from the center of Earth, increases and therefore the gravitational field strength decreases

Planet X has twice Earth's mass and three times Earth's radius. The magnitude of the gravitational field near Planet X's surface is most nearly A. 2 N/kg B. 7 N/kg C. 10 N/kg D. 20 N/kg

A. 2 N/kg

Two identical stars, a fixed distance D apart, revolve in a circle about their mutual center of mass, as shown above. Each star has mass M and speed v. G is the universal gravitational constant. Which of the following is a correct relationship among these quantities?

A. v²=GM/D B. v²=GM/2 C. v²=GMD² D. v²=MGD E. v²=2GM²/D

A planet travels in an elliptical orbit around its star, as shown above. Which arrow best shows the direction of the net force exerted on the planet?

C. Correct. The gravitational force between the planet and its sun, which is directed along a line joining the sun and planet, is the only force exerted in this situation. Since Newton's second law is a vector relation, the direction of the planet's acceleration must be in the direction of the net force, in this case, only the gravitational force, which is directed toward the sun from the planet. For the elliptical orbit, there are only two points at which this force would be normal to the path of the planet. At all other points the force would have a component tangent to the path, which would speed up or slow down the planet, as well as a component normal to the path, which would cause the path to curve.

A planet has two moons, Moon A and Moon B, that orbit at different distances from the planet's center, as shown. Astronomers collect data regarding the planet, the two moons, and their obits. The astronomers are able to estimate the planet's radius and mass. What additional information is needed to determine the time required for one of the moons to make one complete revolution around the planet? A. The mass of each moon B. The radius of each moon C. The distance between the center of each moon and the planet. D. No additional information is needed.

C. Correct. The time it takes for a moon to make one complete revolution around the planet is found by applying Newton's second law of motion for an object that experiences a centripetal force due to the force due to gravity. The force due to gravity can be represented by applying Newton's law of universal gravitation: |Fg| =Gm₁m₂/r². Gm₁m₂/r²=mv²/R and v=2πR/T, so T=2π√R³/GM. The mass of the planet is known, and G is a known constant. Therefore, the only additional quantity that is needed is the distance R between the center of the moon and the center of the planet.

The figure shows three cases where two spheres are touching and attract each other with the gravitational force. The radii of the spheres in each case are shown. All of the spheres are made of material with the same density. Which of the following correctly ranks these cases based on the gravitational force between the spheres? A: R R B: 2R 2R C: 3R R A. (A=B)>C( B. A>C>B C. B>C>A D. C>(A=B)

C. p=m/v M=pV M=p(4/3πR³) Fg= Gm₁m₂/r²

A satellite of mass 1000 kg is in a circular orbit around a planet. The centripetal acceleration of the satellite in its orbit is 5 m/s² What is the gravitational force exerted on the satellite by the planet? A. 0 N B. 200 N⁢ C. 5000 N D. 10,000 N

C. Correct. The centripetal acceleration of the satellite is due to the centripetal force due to gravity that the planet exerts on the satellite. The centripetal acceleration of the object also represents the strength of the gravitational field at the satellite's location. Therefore, the following equation may be used to determine the gravitational force that the planet exerts on the satellite: Fg=mg Fg=(1000 kg)(5 ms/s² Fg=5000 N

A meteoroid is in a circular orbit 600 km above the surface of a distant planet. The planet has the same mass as Earth but has a radius that is 90% of Earth's (where Earth's radius is approximately 6370 km). The acceleration of the meteoroid due to the gravitational force exerted by the planet is most nearly: A. 9 m/s² toward the center of the planet B. 9 m/s² in the direction of the meteoroid's motion C. 10 m/s² toward the center of the planet D. 10 m/s² in the direction of the meteoroid's motion

C. 10 m/s² toward the center of the planet The meteoroid's acceleration must be in the same direction as the net force exerted on the meteoroid. The net force is entirely due to the gravitational force exerted by the planet, which is toward the center of the planet. Newton's law of universal gravitation can be used to determine the magnitude of the meteoroid's acceleration. First, note that the distance from the meteoroid to the planet's center is (0.9×6370+600) km=6333 km, which is very nearly (99.4% of) the radius of Earth. The gravitational force on the meteoroid is then Fg=Gm1m2/r²≈GmEmMeteoroid/rEarth² a= F/m = G*mEarth/rEarth² = g

An astronaut in the space station appears weightless because the astronaut seems to float. Which of the following claims is true about the force exerted on the astronaut by Earth? A. There is no force exerted on the astronaut by Earth because the astronaut is 400km above Earth's surface. B. The force exerted on the astronaut by Earth is less than the force exerted on Earth by the astronaut because the astronaut is 400km above Earth's surface. C. The force exerted on the astronaut by Earth is equal to the force exerted on Earth by the astronaut. D. The force exerted on the astronaut by Earth is equal to the gravitational force of the space station that is exerted on the astronaut; the two equal forces balance to cause the astronaut to float.

C. Correct. The force of gravity exerted on the astronaut due to Earth is present 400km above the surface of Earth in space. This is an action-reaction pair described by Newton's third law, so these two forces must be equal.

B. Two experiments are performed on an object to determine how much the object resists a change in its state of motion while at rest and while in motion. In the first experiment, the object is pushed with a constant known force along a horizontal surface. There is negligible friction between the surface and the object. A motion sensor is used to measure the speed of the object as it is pushed. In a second experiment, the object is tied to a string and pulled upward with a constant known force, and a motion sensor is used to measure the speed of the object as it is pulled upward. The student uses the data collected from the motion sensor to determine the mass of the object in both experiments. Which of the following classifies the type of mass that was determined in each experiment? Experiment 1 and Experiment 2 A. Gravitational mas & gravitational mas B. Inertial mass & gmass C. Gmass & Imass D. Imass & Imass

Correct. An experiment that can be used to determine the acceleration of a mass when there is a net force applied to the object will determine the inertial mass Fnet=ma, where m is the inertial mass. An experiment that can be used to the determine the force of gravity on a mass when it is in a gravitational field will determine the gravitational mass Fg=mg, where m is the gravitational mass.

On the surface of Planet X, a 2 kg object is thrown upward with a speed of 20 m/s. The object's vertical velocity as a function of time is shown in the graph. Which of the following free-body diagrams represents the gravitational force exerted on the object while it is in free fall? m=-4

Correct. To determine the force due to gravity on the object near the surface of Planet X, the object's mass must be multiplied by the acceleration due to gravity while in free fall as shown by Fg=mg. Since the mass is known, the acceleration due to gravity must be determined from the vertical velocity versus time graph that has been given. The slope of a velocity versus time graph is the acceleration of the object that is in motion. The slope of the graph is −4 m/s². Therefore, Fg=mgFg=(2 kg)(−4 ms²) Fg=−8 So, the magnitude is 8 N and the direction is downward

A newly discovered planet is found to have density 2/3 PE and radius 2RE, where pE and RE are the density and radius of Earth, respectively. The surface gravitational field of the planet is most nearly A 1.7 N/kg B 3.3 N/kg C 6.7 N/kg D 13 N/kg

D. This option is correct. Other things being equal, doubling a planet's radius would cut the gravitational field to one-fourth, due to the square in g = Fgrav / m = GM/r². But the new planet also has more mass than Earth. Doubling the radius increases the volume by a factor of 8; but this does not mean the mass increases by 8 times, because the planet's density is two-thirds that of Earth. Instead, the new planet's mass is two-thirds of 8 times the Earth's, i.e., 2/3 * 8 = 5.3 times the mass of Earth. Taking both mass and radius into account, the new planet's g is (5 3.)/4 times the Earth's: 9 8. . m/s² * (5 3)/4 = 13 N/kg.

An astronaut performs an experiment near the surface of a moon by releasing an object at rest above a motion detector such that data can be collected about the object's vertical velocity as a function of time. The data are provided in the table. Which of the following graphs most likely represents the shape of the curve of the magnitude of the gravitational field strength near the surface of the moon as a function of time? Time (s): 0,1,2,3,4,5,6 Vertical Velocity: 0.0, -4.9, -10.2, -15.6, -19.7, -24.4, -30.9

constant positive line x= time y= gravitational field strength