Exam 6: Gravity

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? (G = 6.67 × 10^-11 N ∙ m²/kg², M_earth = 5.97 × 10²⁴ kg)

A 20-g bead is attached to a light 120 cm-long string as shown in the figure. If the angle α is measured to be 18°, what is the speed of the mass?

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?

A jet plane flying 600 m/s experiences an acceleration of 4.0 g when pulling out of a circular dive. What is the radius of curvature of the circular part of the path in which the plane is flying?

In a carnival ride, passengers stand with their backs against the wall of a cylinder. The cylinder is set into rotation and the floor is lowered away from the passengers, but they remain stuck against the wall of the cylinder. For a cylinder with a 2.0-m radius, what is the minimum speed that the passengers can have so they do not fall if the coefficient of static friction between the passengers and the wall is 0.25?

A highway curve of radius 100 m, banked at an angle of 45°, may be negotiated without friction at a speed of

The curved section of a speedway is a circular arc having a radius of 190 m. This curve is properly banked for racecars moving at 34 m/s. At what angle with the horizontal is the curved part of the speedway banked?

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?

One way that future space stations may create artificial gravity is by rotating the station. Consider a cylindrical space station 380 m in diameter that is rotating about its longitudinal axis. Astronauts walk on the inside surface of the space station. How long will it take for each rotation of the cylinder if it is to provide "normal" gravity for the astronauts?

Planet A has twice the mass of Planet B. From this information, what can we conclude about the acceleration due to gravity at the surface of Planet A compared to that at the surface of Planet B?

Mass Radius Orbital radius Orbital period Moon A 4.0\times1020 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? (G = 6.67 × 10^-11 N ∙ m²/kg²)

Asteroid Ida was photographed by the Galileo spacecraft in 1993, and the photograph revealed that the asteroid has a small moon, which has been named Dactyl. From the dimensions of Ida and its general features, one can estimate the mass of Ida to be 4.5 × 10¹⁶ kg, and the distance between Dactyl and Ida is approximately 90 km. Assuming a circular orbit, what would be the orbital speed of Dactyl? (G = 6.67 × 10^-11 N ∙ m²/kg²)

The mass of the Moon is 7.4 × 10²² kg, its radius is 1.74 × 10³ km, and it has no atmosphere. What is the acceleration due to gravity at the surface of the Moon? (G = 6.67 × 10^-11 N ∙ m²/kg²)

A satellite that is in a circular orbit 230 km above the surface of the planet Zeeman-474 has an orbital period of 89 min. The radius of Zeeman-474 is 6.38 × 10⁶ m. What is the mass of this planet? (G = 6.67 × 10^-11 N ∙ m²/kg²)

A car traveling at a steady 20 m/s rounds an 80-m radius horizontal unbanked curve with the tires on the verge of slipping. What is the maximum speed with which this car can round a second unbanked curve of radius 320 m if the coefficient of static friction between the car's tires and the road surface is the same in both cases?

Suppose our sun had 4 times its present mass but the earth orbited it at the same distance as it presently does. What would be the length of the year on the earth under those conditions?

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

A small 175-g ball on the end of a light string is revolving uniformly on a frictionless surface in a horizontal circle of diameter 1.0 m. The ball makes 2.0 revolutions every 1.0 s. (a) What are the magnitude and direction of the acceleration of the ball? (b) Find the tension in the string.

A Ferris wheel has radius 5.0 m and makes one revolution every 8.0 s with uniform rotation. A person who normally weighs 670 N is sitting on one of the benches attached at the rim of the wheel. What is the apparent weight (the normal force exerted on her by the bench) of the person as she passes through the highest point of her motion?

A hypothetical planet has a mass of one-half that of the earth and a radius of twice that of the earth. What is the acceleration due to gravity on the planet in terms of g, the acceleration due to gravity at the surface of the earth?