8. Centripetal Forces & Gravitation

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?

The two stars in a binary star system have masses 2.0 x 10³⁰ kg and 6.0 x 10³⁰ kg. They are separated by 2.0 x 10¹² m. What are The speed of each star?

Two spherical objects have a combined mass of 400 kg. The gravitational attraction between them is 6.00 x 10^-7 N and their gravitational potential energy is ₋1.20 x 10^-6 J. What is the mass of each?

What is the net gravitational force on the 20.0 kg mass in FIGURE P13.36? Give your answer using unit vectors.

Use the binomial expansion ${(1\pm x)}^n=1\pm nx+\frac{n(n-1)}{2}{x}^2\pm \dots$ to show that the value of g is altered by approximately $\Delta g\approx -2g\frac{\Delta r}{r_E}$ at a height ∆r above the Earth’s surface, where r_E is the radius of the Earth, as long as ∆r ≪ r_E.

The value of g is altered by approximately $\Delta g\thickapprox-2g\frac{\Delta r}{r_{E}}$ at a height ∆r above the Earth’s surface, where r_E is the radius of the Earth, as long as ∆r ≪ r_E. What is the meaning of the minus sign in this relation?

Use this result to compute the effective value of g at 125 km above the Earth’s surface. Compare to a direct use of Eq. 6–1.

A plumb bob (a mass m hanging on a string) is deflected from the vertical by an angle θ due to a massive mountain nearby (Fig. 6–37). Estimate the angle θ of the plumb bob if it is 5 km from the center of Mt. Everest.

A plumb bob (a mass m hanging on a string) is deflected from the vertical by an angle θ due to a massive mountain nearby (Fig. 6–37). Find an approximate formula for θ in terms of the mass of the mountain, m_M, the distance to its center, D_M, and the radius and mass of the Earth.

(II) Suppose the maximum distance you can throw a particular ball on Earth is 45.0 m. When you travel to another planet, the maximum distance for the same ball is 36.5 m. If the planet is the same size as Earth, what is its mass?