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Chapter 5: Q37. (page 134)
A hypothetical planet has a mass 2.80 times that of Earth, but has the same radius. What is g near its surface?
The gravitational acceleration of the planet is .
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(a)Show that if a satellite orbits very near the surface of a planet with period \({\bf{T}}\), the density (= mass per unit volume) of the planet is \({\bf{\rho = m/V = }}\frac{{{\bf{3\pi }}}}{{{\bf{G}}{{\bf{T}}^{\bf{2}}}}}\) (b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of \({\bf{85}}{\rm{ }}{\bf{min}}\). Approximate the Earth as a uniform sphere.
Two blocks with massesand, are connected to each other and to a central post by thin rods as shown in Fig. 5鈥�41. The blocks revolve about the post at the same frequency f (revolutions per second) on a frictionless horizontal surface at distancesandfrom the post. Derive an algebraic expression for the tension in each rod.
FIGURE 5-41. Problem 17
Four 7.5-kg spheres are located at the corners of a square of side 0.80 m. Calculate the magnitude and direction of the gravitational force exerted on one sphere by the other three.
People sometimes ask, "What keeps a satellite up in its orbit around the Earth?" How would you respond?
A car rounds a curve at a steady 50 km/h. If it rounds the same curve at a steady 70 km/h, will its acceleration be any different? Explain.
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