The gravitational field of a spherical object  at any distance from it points back to the center of the object.  That is, in the field simulator it has arrows toward the center of the sphere.  Put a test mass in this field and  it will fall toward the center with increasing speed following the line of force.  Locally, the field is the acceleration of gravity at that point. Now,  how would you move a small mass so that you would not have to do work on it during the move? That work would be the change its energy.     You would move it radially

Two protons start out a distance of 3 m from eachother; inititally the protons are at rest. They both start to move away from eachother at the same speed.  What is the initial potential energy of this system? What will the final velocity of the protons be when they are 10 m from eachother?

Compute the work performed in moving a particle al ong the path r(t) = (r*,te,2-t) for 0St54 by the force field F = {cos z,yz,(x+y)*}. Include a plot of the path and the force field on the same axis.

Kepler’s laws of planetary motion can be derived from Newton’s laws of motion and Newton’s universal law of gravitation. Since gravity is a conservative force, mechanical energy is conserved throughout a planet’s orbit. a) Is the gravitational potential energy of the planet-Sun system greater at perihelion (the point of closest approach to the Sun) or aphelion (the point of farthest approach from the Sun)? b) Is the kinetic energy of the planet-Sun system greater at perihelion or aphelion? c) Is your answer consistent with Kepler’s second law of planetary motion? Justify your answers.

A 1200 kg roller coaster car starts at point A, then travels 165 ft at 40.0° below the horizontal to point B. (a) Taking point B to be the level where the gravitational potential energy of the car-Earth system is zero, what is the potential energy (in J) of the system when the car is at points A and B, and the change in potential energy (in J) as the coaster moves between these points? at point A at point B change in potential energy J (b) Repeat part (a), setting the zero configuration with the car at point A. at point A J at point B J change in potential energy J

In the figure, a 3.97 g ice flake is released from the edge of a hemispherical bowl whose radius ris 13.7 cm. The flake-bowl contact is frictionless. (a) How much work is done on the flake by the gravitational force during the flake's descent to the bottom of the bowl? (b) What is the change in the potential energy of the flake-Earth system during that descent? (c) If that potential energy is taken to be zero at the bottom of the bowl, what is its value when the flake is released? (d) If, instead, the potential energy is taken to be zero at the release point, what is its value when the flake reaches the bottom of the bowl? (a) Number (b) Number -5.34e-3 (c) Number 5.34e-3 (d) Number 5.34e-3 Units Units Units Ice flake- Mik Units J

You pull a wagon across a floor with a force of 25 N over a distance of 30 meters.The handle of the wagon you are pulling on has an angle of 35 degrees above the horizontal.a) How much work do you do on the wagon?You now let your wagon roll down a frictionless slope from rest. The height of the slope is 5 meters, and the angle of the slope with the horizontal is 10 degrees. Assume the mass of the wagon is 10 kg.b) What is the final velocity of the suitcase (hint: use the work-energy theorem).

In the figure, a frictionless roller coaster car of mass m - 992 kg tops the first hill with speed vo- 11.9 m/s at heighth-47.0 m. How much work does the gravitational force do on the car from that point to (a) point A, (b) point B, and (c) point C? If the gravitational potential energy of the car-Earth system is taken to be zero at C, what is its value when the car is at (d) Band (e) A? First

You are meeting your friends at a 49er football game. You start near the top of the seating area (8.9 m above the field) and walk down the steps to where your friends are sitting (3.4 m above the field). Assume that your mass is 60 kg. What is the change in your gravitational potential energy as you walk down the steps? Give your answer in J and report your answer to 1 decimal place. Make sure you include the sign if that is important for your answer.

particle in the xy plane travels along a spiral path C beginning at a point P that is 8 units from the origin and ending at a point Q that is 2 units from the origin. The particle makes 2.5 revolutions around the origin along the way. What is the work done by the gravitational field F(x,y) = -x/(x^2=y^2)^3/2 i + -y/(x^2+y^2)^3/2 j in moving the particle along its path. Enter your answer as an integer or a deimal rounded to 3 places