1. A child is on a playground swing, motionless at the highest point of his arc. What energy transformation takes place as he swings back down to the lowest point of his motion? A. K→U̟ B. Ug→K С. Еһ —К D. Ug→Eth

REMARKS Only simple geometries-rectangles and triangles-can be solved exactly with this method. More complex shapes require calculus or the square-counting technique in the next worked example. QUESTION When stretching springs, does half the displacement require half as much work? (Select all that apply.) U > Yes, because the work is equal to the force times the distance. Yes, because the spring exerts a constant force. Yes, because half the displacement means the force from the spring is half as large. No, because the spring does not exert a constant force. No, because the force of the spring is proportional to x. No, because the force exerted by the spring is proportional to x². X Consider the expression for the work done by an applied force. Under what conditions is the work done equal to simply a value of the force multiplied by the displacement? Do those conditions apply to the present problem - consider why or why not. Consider how the force exerted by the spring depends on its…

Show and explain the complete solution with the formulas. Label the symbols used accordingly.

Indicate the one with more potential energy and explain why. A full plane or an empty plane (both are flying )?

How to get the solution for these problems? (Answers are given)

How did you solve D? Wouldn't it's distance be different from that of Point 1 to Point 2 as would be Point 3 to Point 2 and shouldn't that effect the answer for work needed to be done?

Please explain  An electrically charged particle is held fixed at the origin. Let V = 1/r be the potential energy of a second particle with unit electric charge located at (x, y, z), where r = sqrt(x^2 + y^2 + z^2). The force on this second particle is given by −∇V . Calculate the force on the particle when it is at (1, 2, −2). Show working

Problem 2: A horizontal force keeps a 3.71 kg box traveling at a constant speed up a frictionless incline for a vertical height change of 3.4 m.

A 20m rope is hanging over the edge of a 50m building. Attached to the end is 2 kg bucket carrying 30kg of sand. There is a whole in the bucket that allows the sand to leak out at 0.5 kg/m. Disregarding the rope, how much work is done lifting the bucket to the top of the building? Show all work. Include units. Method of solving: fnint(), rounded to nearest whole number or Fundamental Theorem. Your choice

Show all work for parts a and b. Follow directions as stated. Thank you