The average distance between the Earth and the Sun is about 1.5 x 1011 m, whereas the average distance between the Earth and Mars is about 2.3 x 1011 m. Assume the usual convention that the gravitational potential energy referenced to the Earth is zero when infinitely far away, (a) What is the gravitational potential energy of the Earth-Sun system? (b) What is the gravitational potential energy of the Earth-Mars system? (c) Describe how these values indicate that the Sun has a greater effect on the Earth's motion than Mars does. What is the most dominant factor that causes the Sun to have the greater effect?

A child of mass m = 16 kg slides down a slide of height h = 2.7 m without friction. Let gravitational potential energy be zero at ground level. a)Write an expression for the child's total mechanical energy, E, at the top of the slide, in terms of the variables in the problem and the acceleration due to gravity g.  b)Calculate the change in the child's potential energy, ΔU in joules, from the top to the bottom of the slide at ground level (i.e. ΔU = Uground - Utop).  c)What is the child's final speed, vf in m/s?

A child of mass m = 27 kg slides down a slide of height h = 2.1 m without friction. Let gravitational potential energy be zero at ground level. Write an expression for the child's total mechanical energy, E, at the top of the slide, in terms of the variables in the problem and the acceleration due to gravity g.  Calculate the change in the child's potential energy, ΔU in joules, from the top to the bottom of the slide at ground level (i.e. ΔU = Uground- Utop).  What is the child's final speed, vf in m/s?

A 7.00-kg particle moves from the origin to position ©, having coordinates x = 6.50 m and y = 6.50 m as shown in the figure. One force on the particle is the gravitational force acting in the negative y direction. Using the equation (W = FAr cos 0 = F · Ař), calculate the work done by the gravitational force in going from O to © along the following paths. у (m) B (х, у) x (m) (a) the purple path (o0©) (b) the red path (O®© (c) the blue path (O© (d) Your results should all be identical. Why? This answer has not been graded yet.