Conceptual Physics
3.0×10^4 N. (a) How much will the cable stretch when the helicopter is hovering? (b) If the yield strength of the steel in the c ...
12.0 - Introduction The topic of gravity has had a starring role in some of the most famous tales in the history of physics. Gal ...
12.1 - Newton’s law of gravitation Newton’s law of gravitation: The attractive force of gravity between two particles is proport ...
What is the gravitational force between the Earth and the Moon? F = 1.98×10^20 N Each body attracts the other How much gravitati ...
12.2 - G and g Newton’s law of gravity includes the gravitational constant G. In this section, we discuss the relationship betwe ...
Our calculations show that g equals 9.78 m/s^2. The value for g varies by location on the Earth for reasons you will learn about ...
12.4 - Shell theorem: inside the sphere Another section discussed how to calculate the force of gravity exerted on an object on ...
What is the strategy? Use the shell theorem. Compute the ratio of the volume of the Earth to the volume of the sphere defined b ...
12.6 - Earth’s composition and g The force of gravity differs slightly at different locations on the Earth. These variations mea ...
12.7 - Newton’s cannon In addition to noting that the Earth exerts a force on an apple, Newton also pondered why the Moon circle ...
12.8 - Interactive problem: Newton’s cannon Imagine that you are Isaac Newton. It is the year 1680, and you are staring up at th ...
Speed in circular orbit m = mass of satellite v = satellite speed G = gravitational constant M = mass of body being orbited r = ...
Step-by-step solution We start by determining the satellite’s orbital radius. Careful: this is not the satellite’s height above ...
There are a few things you may find worth observing. You will learn more about them when you study orbital energy. First, what i ...
(Both terms come from the Greek, “far from the Sun” and “near the Sun” respectively.) Halley’s comet has an eccentricity of 0.97 ...
What is the perihelion distance of Halley’s Comet? The comet’s semimajor axis is 17.8 AU. rmin = 2aírmax rmin = 2(17.8 AU) í 35. ...
12.16 - Kepler’s third law The law of periods: The square of the period of an orbit is proportional to the cube of the semimajor ...
T = satellite period (in seconds) G = gravitational constant M = mass of central body a = semimajor axis 12.17 - Orbits and ener ...
For a given circular orbit BothPE,KE constant Total energy increases with radius Energy in circular orbits G = gravitational con ...
Energy in elliptical orbits Etot = total energy a = semimajor axis 12.18 - Escape speed Escape speed: The minimum speed required ...
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