Chapter 6, Problem 6.13P

Show that hooks law has the form of the general equation for a straight line. What would be the slope and y intercept of this straight-line relationship?

Using Figure 13.9, carefully 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 acceleration (toward P in the diagram), the other perpendicular to that. Show that the deflection angle ε , 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(λ + ε) = (g / (g − ω2 RE)) . tanλ , where ω is the angular velocity of Earth.

Find the distance from the point (-7,2,8) to the yz-plane

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.

How far above the Earth’s surface must we be before “g” has decreased significantly by dropping 10%? Show all work.

. Consider a system of N particles in a uniform gravitational field. Prove that the total gravitational torque about center of mass(CM) is zero.?​

Consider a satellite in elliptical orbit around a planet of mass M, and suppose that physical units are so chosen that GM D 1 (where G is the gravitational constant). If the planet is located at the origin in the xy-plane, then Explain the equations of motion of the satellite?

The Brachistochrone Problem: Show that if the particle is projected withan initial kinetic energy 1/2 m v02 that the brachistochrone is still a cycloidpassing through the two points with a cusp at a height z above the initialpoint given by v02 = 2gz.