The force exerted by an electric charge at the origin on a charged particle at the point KT (x, y, z) with position vector 7 = (x, y, z) is F(7) where K is constant. · Assume K = 30. Find the work done as the particle moves along a straight line from (3,0,0) to (3,4,5) %3D

A force field is given by F = Fo (x°i + xyj + z°k), find the work perform by this force on a circle of radius R centered at (0,0,1) on the plane z = 1. Repeat the calculation along a circle with radius R on the ry-plane with z = 0. Is this a conservative force field?

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.

8-) three point particles are in empty space located at the following coordinates. Q1 = 20nC in A (2, -5.4) m; Q2 = 30 nC in B (-3, -4, -2) m and Q3 = 40nC in C (4, -3.7) m. What is the work of bringing a fourth 50 nC particle to the point P (1,1,1) m One of these answers: 55.4 nJ 55.4 µJ 5.54 µJ

A spring with k = 15 N/m with equilibrium length 30 cm is attached vertically to a surface and then allowed to come to equilibrium, after which a weight with mass 0.2 kg is attached to the top side of the spring. → How much work does the Earth do on the weight via gravity between its initial position and the new equilibrium height? Explicitly compute the work with an integral.

Two persons were practicing social distancing to alleviate the spread of COVID-19. Social distancing requires a minimum of 3 feet distance from person to person. However, due to their eagerness to share some rumors, the two persons decided to approach each other and now within the intimate distance (12 inches). If person A weighs 60 kg. and person B weighs 68 kg., determine the work done for this act. Take G = 6.67408 × 10-11 m³ kg-ls-2. A. 6.8076 ergs C. 5.9559 ergs D. 5.5599 ergs B. 8.0766 ergs

07 Prove that the force F = 2ex(- yzi + zj + yk) follows from a function potential energy and to determine it.

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 Thirteen. A potential energy function is given by U(r)=U2 where o = 2.00 m r r and U, = 1.00 J. Find the magnitude of the force at r= 1.00 m. Give an answer in kN. 25.) (A) 280 (В) 106 (С) 420 (D) 470 (E) 530

To move a load of 6c from point a (2,1,1) to point b (4,3,1) along the path y = x-1, z = 1 in E = 4xax +2zay+ 2yaz V / m Find the Work has done