Chapter 6, Problem 6.4P

Using Figure 13.9, carefull sketch a free body diagram for the case of a simple pendulum hanging at latitude lambda, labeling all forces acting on the point mass,m. Set up the equations of motion for equilibrium, setting one coordinate in the direction of the centripetal accleration (toward P in the diagram), the other perpendicular to that. Show that the deflection angle , defined as the angle between the pendulum string and the radial direction toward the center of Earth, is given by the expression below. What is the deflection angle at latitude 45 degrees? Assume that Earth is a perfect sphere. tan(+)=gg2REtan , where is the angular velocity of Earth.

Answer without rounding off: (COLLAB Gauss's Law for Mass) Journey through the Center of the Earth. A 1024-kg blue ball is dropped from an initial z-position of 3.8 x 106 m through the center of a planet with a radius of 8.5 x 106 m. If the mass of the planet is 48.8 x 1015 kg, measure the displacement of the ball at time t = 7 s?

A seat on the perimeter of a Ferris wheel at the amusement park experiencesan angular displacement of 37o. If the radius of the wheel is 20 m, what arclength is described by the seat?

A satellite in orbit around the earth is at an altitude of 107 percent of the earth's radius. Rounding off our old friend "g" to ten meters per second squared, what is the acceleration due to earth's gravity at the satellite?  Your answer should be in meters per second squared, but do not put the unit, just the number.

Show that the gravitational force exerted on a particle inside a hollow symmetric sphere is zero.

An undiscovered planet, many lightyears from Earth, has one moon in a periodic orbit. This moon takes 2010 × 103 seconds (about 23 days) on average to complete one nearly circular revolution around the unnamed planet. If the distance from the center of the moon to the surface of the planet is 235.0 × 106 m and the planet has a radius of 3.30 × 106 m, calculate the moon's radial acceleration ?c .

Two identical uniform spheres A and B, with mass M=M= 1.00 [kg], are placed 0.500 [m] away from another spherical mass C with mass m=m= 0.300 [kg] as shown: If mass C is released from rest, what is its net acceleration? Assume that only the gravitational forces from spheres A and B act on C. State also the direction if it is upward or downward.

The condition for a sphere to be considered as an isolated sphere is that the outer sphere radius should go to

If a particle be describing an ellipse about a centre of force in the centre, show that the sum of the reciprocates of its angular velocities about foci is constant.