Gravity Work required to move a mass radially outward from the c.m. of a planet

A uniform spherical planet has mass M= 8.5 E 25 kg and radius R= 7.5 E 6 m. A hole is drilled from the surface to mass m= 360 kg at an initial position r1= 2.5 E 6 m from the center. PART a. Find the initial gravity force F that the planet exerts on mass m. PART b. Find the work required to bring mass m to the surface at a constant speed. PART c. Find the work required to move mass m at constant speed from initial distance r2= 8.2 E 6 m to distance r3= 9.4 E 6 m, from the center of the planet. See attachment #1 for diagram showing parameters.

Satellite in circular orbit around Earth Find period, speed, height etc.

An observation satellite whose mass m= 4800 kg is to be put into a circular orbit around the earth at a height h= 322000 m above the surface in a precise north-south orbit. See attachment #1. PART a. In this orbit, find the force of gravity exerted by the earth on the satellite. PART b. Find the speed, v, and the period, T, of the satellite. PART c. During one cycle the satellite is directly above Mt Kenyatta on the equator. Exactly one period later, the satellite is directly above Mt Jomo on the equator. Find the distance on land from Mt Kenyatta to Mt Jomo. PART d. If the longitude of Mt Kenyatta is 5 degrees West, find the longitude of Mt Jomo.

A cube suspended in water by a cord. Buoyant force and equilibrium.

A cube of aluminum, whose volume is Va= .125 m^3, and whose density is Da= 2700 kg/m^3 is suspended from a cord which holds it stationary with the top surface horizontal and h= 2.2 m below the surface of fresh water. See attachment #1 showing known parameters. PART a. Find the mass of the aluminum. PART b. Find C, the force in the supporting cord.

Archimedes' Principle for a block in two different liquids

A solid block of mass M= 21 kg floats with 80% if its volume submerged in carbon tetrachloride, whose density is Dc= 1600 kg/m^3. When this block is submerged in liquid X however, it requires an upward pull by a cord of F= 72 newtons to hold it stationary, completely submerged. a. Find Db, the density of the block. b. Find Dx, the density of liquid X. See attachment #1 for diagram showing parameters.

Friction problem

The asking problem: A block of weight W=60 lb rests on a rough plane as shown. Knowing that "alpha"= 20° and Us(coefficient of static friction) = 0.30, determine the magnitude and direction of the smallest force P required to start the block up the plane. The answer of this problem for verification:35.9 lb at 36.7° directed up and to the right.