8. Centripetal Forces & Gravitation

(II) What is the apparent weight of a 75-kg astronaut 2800 km from the center of the Moon in a space vehicle accelerating toward the Moon at 1.8m/s²? State “direction” in each case.

You have been visiting a distant planet. Your measurements have determined that the planet's mass is twice that of earth but the free-fall acceleration at the surface is only one-fourth as large. What is the planet's radius?

You decide to visit Santa Claus at the north pole to put in a good word about your splendid behavior throughout the year. While there, you notice that the elf Sneezy, when hanging from a rope, produces a tension of 395.0 N in the rope. If Sneezy hangs from a similar rope while delivering presents at the earth's equator, what will the tension in it be? (Recall that the earth is rotating about an axis through its north and south poles.)

What is the approximate value of the acceleration due to gravity on the surface of $\mathrm{Earth}$?

What is the approximate value of the acceleration due to gravity at the surface of the Earth?

Which of the following is closest to the acceleration due to gravity on the surface of Pluto?

What is the approximate value of the acceleration due to gravity at the surface of the Earth?

If an object is dropped from rest near the surface of Mars, where the free-fall acceleration is $3.7 m/s^2$, what will be its velocity after falling for $4 s$?

Titania, the largest moon of the planet Uranus, has 1/8 the radius of the earth and 1/1700 the mass of the earth. What is the average density of Titania? (This is less than the density of rock, which is one piece of evidence that Titania is made primarily of ice.)

How far would you have to be above Earth's surface for g to be ½ of its surface value?

For an object in free fall near the surface of the Earth (ignoring air resistance), what is the gain in speed per second, also known as the acceleration due to gravity?

Given that the average distance between the Moon and the Earth is approximately $3.84\times {10}^{8}m$ and the mass of the Earth is $5.97\times {10}^{24}\mathrm{kg}$, what is the magnitude of the acceleration of the Moon towards the Earth due to gravity? (Use $G=6.67\times {10}^{-}N{m}^2/{\mathrm{kg}}^2$)

Jupiter is about 320 times as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter because people cannot survive more than a few g’s. Calculate the number of g’s a person would experience at Jupiter’s equator, using the following data for Jupiter: mass = 1.9 x 10²⁷ kg, equatorial radius = 7.1 x 10⁴ km, rotation period = 9 hr 55 mins. Take the centripetal acceleration into account.

You stand on the surface of a mysterious planet with a mass of 6 ×10²⁴ kg and measure the surface gravity to be 7 m/s². What must the radius of the planet be?