Chapter 8, Problem 8.18P

Consider a satellite of mass m moving in a circular orbit around the Earth at a constant speed v and at an altitude h above the Earth’s surface as illustrated as shown. (A) Determine the speed of the satellite in terms of G, h, RE (the radius of the Earth), and ME (the mass of the Earth).

A particle is moving on xy plane, with x=15sin(2t), and y = 20cos(2t) In what kind of orbit is this particle moving?

Compute g for the surface of a planet whose radius is half that of the Earth and whose mass is double that of the Earth

Find the magnitude of the initia acceleration of a uniform sphere with mass .010kg if released from rest at point P and acted on only by forces of gravitational attraction of the spheres at A and B.

Consider a pulsar, a collapsed star of extremely high density, with a mass M equal to that of the Sun (1.98 × 1030 kg), a radius R of only 17.4 km, and a rotational period T of 0.0448 s. By what percentage does the free-fall acceleration g differ from the gravitational acceleration ag at the equator of this spherical star?

When solving for the normal force at C, why is there no tangential acceleration?

Verify Kepler’s Laws of Planetary Motion. Assume that each planet moves in an orbit given by the vectorvalued function r. Let r = || r||, let G represent the universal gravitational constant, let M represent the mass of the sun, and let m represent the mass of the planet.

Prove that there is no work done by the Coriolis pseudoforce acting on a particle moving in a rotating frame. If the Coriolis pseudoforce were the only force acting on a particle, what could you conclude about the particle’s speed in the rotating frame?

A merry-go-round is a playground ride that consists of a large disk mounted to that it can freely rotate in a horizontal plane. The merry-go-round shown is initially at rest, has a radius R = 1.3 meters, and a mass M = 291 kg. A small boy of mass m = 42 kg runs tangentially to the merry-go-round at a speed of v = 1.8 m/s, and jumps on. Randomized VariablesR = 1.3 metersM = 291 kgm = 42 kgv = 1.8 m/s Part A- Calculate the moment of inertia of the merry-go-round, in kg ⋅ m2.  Part B- Immediately before the boy jumps on the merry go round, calculate his angular speed (in radians/second) about the central axis of the merry-go-round.  Part C- Immediately after the boy jumps on the merry go round, calculate the angular speed in radians/second of the merry-go-round and boy.  Part D- The boy then crawls towards the center of the merry-go-round along a radius. What is the angular speed in radians/second of the merry-go-round when the boy is half way between the edge and the center of the merry…