Exam 5: Circular Motion; Gravitation

Mass Radius Orbital radius Orbital period Moon A 4.0\times1 unknown 2.0\times1 4.0\times1 Moon B 1.5\times1 2.0\times1 3.0\times1 unknown Mithra is an unknown planet that has two moons, A and B , in circular orbits around it. The table summarizes the hypothetical data about these moons. What is the mass of Mithra? $( G = 6.67 \times$ $\left. 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

Suppose NASA wants a satellite to revolve around Earth 5 times a day. What should be the radius of its orbit if we neglect the presence of the Moon? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } , M _ { \text {earth } } = 5.97 \times \right.$ $10 ^ { 24 } \mathrm {~kg} \text { ) }$

Planet Z-34 has a mass equal to one-third that of Earth and a radius equal to one-third that of Earth. With g representing, as usual, the acceleration due to gravity at the surface of Earth, the acceleration due to gravity at the surface of Z-34 is

Two moons orbit a planet in circular orbits. Moon A has orbital radius R, and moon B has orbital radius 4R. Moon A takes 20 days to complete one orbit. How long does it take moon B to Complete an orbit?

The mass of the Moon is $7.4 \times 10 ^ { 22 } \mathrm {~kg}$ its radius is $1.74 \times 10 ^ { 3 } \mathrm {~km}$ and it has no atmosphere. What is the acceleration due to gravity at the surface of the Moon? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

You are making a circular turn in your car on a horizontal road when you hit a big patch of ice, causing the force of friction between the tires and the road to become zero. While the car is on the Ice, it

If NASA wants to put a satellite in a circular orbit around the sun so it will make 2.0 orbits per year, at what distance (in astronomical units, AU) from the sun should that satellite orbit? The Earth's orbit is 1.0 AU from the sun.

When a spacecraft is launched from the earth toward the sun, at what distance from the earth will the gravitational forces due to the sun and the earth cancel? Earth's mass is $5.97 \times 10 ^ { 24 } \mathrm {~kg}$ the sun's mass is $1.99 \times 10^{30} \mathrm {~kg}$ and the Earth-sun distance is 1.5 x $10 ^ { 11 } \mathrm {~m}$

What is the proper banking angle for an Olympic bobsled to negotiate a 100-m radius turn at 35 m/s without skidding?

A 2.0-kg ball is moving with a constant speed of 5.0 m/s in a horizontal circle whose diameter is 1.0 m. What is the magnitude of the net force on the ball?

Mass Radius Orbital radius Orbital period Moon A 4.0\times1 unknown 2.0\times1 4.0\times1 Moon B 1.5\times1 2.0\times1 3.0\times1 unknown Mithra is an unknown planet that has two moons, A and B , in circular orbits around it. The table summarizes the hypothetical data about these moons. What is the magnitude of the maximum gravitational force that Moon A exerts on Moon B? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

What would be the weight of a 59.1-kg astronaut on a planet twice as massive as Earth and having twice Earth's radius?

As you know, the earth has an orbital period of 1.0 year at an orbital radius of 1.0 AU (astronomical unit, the average distance between the earth and the sun). If a new "minor planet" were to be found in a circular orbit with radius 13 AU, what would be its orbital period?

Satellite A has twice the mass of satellite B, and moves at the same orbital distance from Earth as satellite B. Compare the speeds of the two satellites.

At their closest approach, Venus and Earth are $4.20 \times 10^{10}$ $10^{24} \mathrm {~kg} ,$ the mass of Earth is $5.97 \times 10 ^ { 24 } \mathrm {~kg}$ and $G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 }$ What is the magnitude of the gravitational force exerted by Venus on Earth at that point?

The earth has radius R. A satellite of mass 100 kg is in orbit at an altitude of 3R above the earth's surface. What is the satellite's weight at the altitude of its orbit?

In another solar system, a planet has an airless moon Zygo that is $4.0 \times 10 ^ { 5 }$ m in diameter. Experiments reveal that a freely falling object at the surface of Zygo accelerates at $0.20 \mathrm {~m} / \mathrm { s } ^ { 2 }$ What is the mass of Zygo? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

If you stood on a planet having a mass four times that of Earth's mass, and a radius two times that of Earth's radius, you would weigh

The acceleration due to gravity on Planet A is one-sixth what it is on Planet B, and the radius of the Planet A is one-fourth that of Planet B. The mass of Planet A is what fraction of the mass of Planet B?

At a given point above Earth's surface, the acceleration due to gravity is equal to $7.8 \mathrm {~m} / \mathrm { s } ^ { 2 }$ the altitude of this point above Earth's surface? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } , M _ { \text {earth } } = 5.97 \times 10 ^ { 24 } \right.$ $\mathrm { kg } , R _ { \text {earth } } = 6.38 \times 10 ^ { 6 } \mathrm {~m} \text { ) }$