Finally, consider the gravitational force generated by a spherically symmetrical massive object. the magnitude and direction of such a force are given by newton's law of gravity: f⃗ g=−gm1m2r2r^, where ds⃗ =drr^; g, m1, and m2 are constants; and r> 0. find u(rf)−u(r0)=−∫rfr0f⃗ g⋅ds⃗ . express your answer in terms of g, m1, m2, r0, and rf. view available hint(s)

Wo audio speakers are placed on a vertical rail. speaker a is placed at head-level while speaker b is place at some variable height, \delta yδy, above speaker a. both speakers receive simultaneous input from a sine-wave generator so the speakers each produce a pure sinusoidal sound wave with a wavelength of 0.531 meters. calculate the lowest height that speaker b can be placed above speaker a to produce a minimum of sound heard by person standing \delta x = 7.86δx=7.86 meters directly in front of speaker a.

What is friction? how does it affect the motion of an object?

Which of these best describes the term ecliptic? a. the circle where "earth meets the sky" b. the change in azimuth and altitude of an object c. the point directly above the geographic north pole d. the path of the sun through the constellations of the zodiac