8. Centripetal Forces & Gravitation

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.

Which of the following best illustrates how Newton's Law of Gravity demonstrates a cause-and-effect relationship?

According to Newton's Law of Gravity, in what direction does the gravitational force $F$ act between two orbiting objects?

What is the ratio of the sun's gravitational force on you to the earth's gravitational force on you?

A typical adult human has a mass of about 70 kg. (a) What force does a full moon exert on such a human when it is directly overhead with its center 378,000 km away? (b) Compare this force with the force exerted on the human by the earth

According to Newton's Law of Gravity, which factor most directly influences the gravitational force that causes a safety boat to tend to lie abeam to the wind? $F=\frac{\mathrm{G\; m\_1\; m\_2}}{r^2}$

According to Newton's Law of Gravity ($F=\frac{\mathrm{Gm\_1m\_2}}{r^2}$) and the Coriolis effect, in which direction is the path of motion of an ocean current deflected in the Northern Hemisphere?

Which of the following best describes the force between two masses according to Newton's Law of Gravity?

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

Which force is responsible for keeping the planets in orbit around the $\mathrm{Sun}$ and preventing them from flying out of the solar system?

A car of mass $m$ travels over the top of a hill with radius of curvature $r$. What is the maximum speed $v$ the car can have at the top of the hill without losing contact with the road (i.e., without flying off)?

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?

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. Why don’t the two stars crash into one another due to the gravitational force between them?