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Exam 10: Dynamics of Rotational Motion

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Question 1

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Satellites: A satellite of mass m has an orbital period T when it is in a circular orbit of radius R around the earth. If the satellite instead had mass 4m, its orbital period would be

A) 4T.
B) 2T.
C) T.
D) T/2.
E) T/4.

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C

Question 2

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Escape speed: A certain planet has an escape speed V. If another planet of the same size has twice the mass as the first planet, its escape speed will be

A) 2V.
B) V.
C) V.
D) V/2.
E) V/

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Question 3

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Kepler's laws: The moons of Mars, Phobos (Fear) and Deimos (Terror) , are very close to the planet compared to Earth's Moon. Their orbital radii are 9,378 km and 23,459 km respectively. What is the ratio of the period of revolution of Phobos to that of Deimos?

Satellites: The reason an astronaut in an earth satellite feels weightless is that

Gravitational potential energy: An astronaut is standing on the surface of a planetary satellite that has a radius of 1.74 × 10⁶ m and a mass of 7.35 × 10²² kg. An experiment is planned where a projectile needs to be launched straight up from the surface. What must be the minimum initial speed of the projectile so it will reach a height of 2.55 × 10⁶ m above this satellite's surface? (G = 6.67 × 10^-11 N ∙ m²/kg²)

Gravitational force: An astronaut is in equilibrium when he is positioned from the center of asteroid X and from the center of asteroid Y, along the straight line joining the centers of the asteroids. What is the ratio of the masses X/Y of the asteroids?

Satellites: Jupiter completes one revolution about its own axis every 9.92 hours. What is the radius of the orbit required for a satellite to revolve about Jupiter with the same period? Jupiter has a mass of 1.90 × 10²⁷ kg and G = 6.67 × 10^-11 N ∙ m²/kg².

Gravitational potential energy: A 910-kg object is released from rest at an altitude of 1200 km above the north pole of the earth. If we ignore atmospheric friction, with what speed does the object strike the surface of the earth? (G = 6.67 × 10^-11 N ∙ m²/kg², M_earth = 5.97 × 10²⁴ kg, the polar radius of the earth is 6357 km)

Satellites: Find the orbital speed of an ice cube in the rings of Saturn. The mass of Saturn is 5.68 × 10²⁶ kg and the rings have an average radius of 100,000 km. (G = 6.67 × 10^-11 N ∙ m²/kg²)

Satellites: A satellite that weighs 4900 N on the launchpad travels around the earth's equator in a circular orbit with a period of 1.667 h. The earth's mass is 5.97 × 10²⁴ kg, its equatorial radius is 6.3 × 10⁶ m, and G = 6.67 × 10^-11 N ∙ m²/kg². (a) Calculate the magnitude of the earth's gravitational force on the satellite. (b) Determine the altitude of the satellite above the Earth's SURFACE

Gravitational potential energy: A meteoroid, heading straight for Earth, has a speed of 14.8 km/s relative to the center of Earth as it crosses our moon's orbit, a distance of 3.84 × 10⁸ m from the earth's center. What is the meteroid's speed as it hits the earth? You can neglect the effects of the moon, Earth's atmosphere, and any motion of the earth. (G = 6.67 × 10^-11 N ∙ m²/kg², M_earth = 5.97 × 10²⁴ kg)

Satellites: Suppose we want a satellite to revolve around the earth 5 times a day. What should be the radius of its orbit? (The mass of the earth is 5.97 × 10²⁴ kg, G = 6.67 × 10^-11 N ∙ m²/kg², and you can neglect the presence of the moon.)

Weight and g: By how many newtons does the weight of a 100-kg person change when he goes from sea level to an altitude of 5.0 km if we neglect the earth's rotational effects? (The mean radius of the Earth is 6.38 × 10⁶ m, G = 6.67 × 10^-11 N ∙ m²/kg².)

Gravitational force: If the mass of the earth and all objects on it were suddenly doubled, but the size remained the same, the acceleration due to gravity at the surface would become

Escape speed: What is the ratio of the escape speed of a rocket launched from sea level to the escape speed of one launched from Mt. Everest (an altitude of 8.85 km) ? The radius of the earth is 6.38 × 10⁶ m.

Kepler's laws: A planet has two small satellites in circular orbits around the planet. The first satellite has a period 12.0 hours and an orbital radius 6.00 × 10⁷ m. The second planet has a period 16.0 hours. What is the orbital radius of the second satellite?

Satellites: A satellite is orbiting the earth. If a payload of material is added until it doubles the satellite's mass, the earth's pull of gravity on this satellite will double but the satellite's orbit will not be affected.

Weight and g: An object drops a distance h in a time of 6.3 s on the surface of the earth (neglecting air effects) . How long would it take the same object to drop the same distance on the surface of spherical asteroid X having a mass of 1.1 × 10²² kg and a radius of 4.0 × 10⁵ m? (G = 6.67 × 10^-11 N ∙ m²/kg², M_earth = 5.97 × 10²⁴ kg, R_earth = 6.38 × 10⁶ m)

Kepler's laws: Ekapluto is an unknown planet that has two moons in circular orbits. The table summarizes the hypothetical data about the moons. The orbital period of Moon B is closest to

Satellites: The moons of Mars, Phobos (Fear) and Deimos (Terror) , are very close to the planet compared to Earth's Moon. Their orbital radii are 9,378 km and 23,459 km respectively. What is the ratio of the orbital speed of Phobos to that of Deimos?