8. Centripetal Forces & Gravitation

Which statement correctly compares the acceleration due to gravity on $Earth$ and on the $Moon$?

According to Newton's Law of Gravity, what is the relationship between the gravitational force $F$ and the masses $m_1$ and $m_2$ of two objects?

Two spheres of mass 300 kg and 500 kg are placed in a line 20 cm apart. If another sphere of mass 200 kg is placed between them, 8 cm from the 300 kg sphere, what is the net gravitational force on the 200 kg sphere?

A 2,000-kg spacecraft is blasting away from the surface of an unknown planet the same size as the Earth. At 1500km above the surface, an instrument onboard reads the gravitational force to be 18000 N. What is the planet's mass?

 Two spheres are separated by 10m. If the lighter 40kg sphere feels a gravitational force of 1.6 × 10^-9 N, what is the mass of the heavier sphere?

(II) You are explaining to friends why an astronaut feels weightless orbiting the Earth in a space station, and they respond that they thought gravity was just a lot weaker up there. Convince them that it isn’t so by calculating how much weaker (in %) gravity is 380 km above the Earth’s surface.

The point masses m and 2m lie along the x-axis, with m at the origin and 2m at x = L. A third point mass M is moved along the x-axis. At what point is the net gravitational force on M due to the other two masses equal to zero?

Find the magnitude and direction of the net gravitational force on mass A due to masses B and C in Fig. E13.6. Each mass is 2.00 kg.

Two uniform spheres, each with mass M and radius R, touch each other. What is the magnitude of their gravitational force of attraction?

Two spherical objects have a combined mass of 150 kg. The gravitational attraction between them is 8.00 x 10^-6 N when their centers are 20 cm apart. What is the mass of each?

What is the force of attraction between a 50 kg woman and a 70 kg man sitting 1.0 m apart?

Two 65 kg astronauts leave earth in a spacecraft, sitting 1.0 m apart. How far are they from the center of the earth when the gravitational force between them is as strong as the gravitational force of the earth on one of the astronauts?

The International Space Station orbits 300 km above the surface of the earth. What is the gravitational force on a 1.0 kg sphere inside the International Space Station?

Two uniform spheres, each of mass 0.260 kg, are fixed at points A and B (Fig. E13.5). Find the magnitude and direction of the initial acceleration of a uniform sphere with mass 0.010 kg if released from rest at point P and acted on only by forces of gravitational attraction of the spheres at A and B.

Three stars, each with the mass of our sun, form an equilateral triangle with sides 1.0 x 10¹² m long. (This triangle would just about fit within the orbit of Jupiter.) The triangle has to rotate, because otherwise the stars would crash together in the center. What is the period of rotation?