8. Centripetal Forces & Gravitation

(II) Two objects attract each other gravitationally with a force of 6.5 x 10^-9 N when they are 0.25 m apart. Their total mass is 6.50 kg. Find their individual masses.

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.

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?

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.

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.

(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?

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?

Three meteorites in outer space lie along a straight line. At a certain instant in time, the meteorite on the right is 53 m from the center meteorite and the lefthand meteorite is 21 m from the center meteorite. If the mass of the righthand meteorite is 1300 kg and the net gravitational force on the center meteorite is zero, what is the mass of the lefthand meteorite?

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?

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.

Binary star: Two equal-mass stars maintain a constant distance D apart (Fig. 6–34) of 8.0 x 10¹¹ m and revolve about a point midway between them at a rate of one revolution every 14.2 yr. What must be the mass m of each star?

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