Previously it was considered a force of the form f = ixy + jcx^2 + kz^3, and found a value of "c" from the following list such that this was a conservative force.
Note: there must really be extra 'constants' in front of each term, with magnitude 1 but the proper units (such as Newton m^-2 for the first term) to make "F" have the right units of force. For this problem ignore these unit conversion constants and just use the right numerical magnitude of c, and these other constants.)
[A]: c = 1/4, [B]: c = 1/2
[C]: c = 1, [D]: c = 3

Now given the correct 'c', and using (x,y,z) = (0, 0,0) as the reference position, find the potential energy U(x, y, z) by computing the appropriate line integral from the reference position to the final (x, y, z).
Do the line integral even if you can see what the final U must be just by examing "F".

It finds the potential energy of conservative force via line integral. It then shows that the gradient field of the potential energy is the force. The solution is detailed and has a '5/5' rating.

A particle is under the influence of a force F = -kx+(kx^3)/a^3 where k and a are constants and k is positive.
1) Find U(x) the potentialenergy
2) What happens when E (total energy) = (1/4)ka^3

Which of the following forces is conservative?
(a)F=k(x,2y,3z) where k is a constant.
(b)F=k(y,x,0)(c)F=k(-y,x,0).
For those which are conservative, find the corresponding potentialenergy U, and verify by direct differentiation that F=-gadU.

A particle moves along the x-axis while acted on by a single conservativeforce parallel to the x-axis. The force corresponds to the potential-energy function graphed in the figure. The particle is released from rest at point A.
a). What is the direction of the force on the particle when it is at point A? (Positive or Negativ

Explain the concept of Work, Energy and Power. Also describe various types of mechanical energy compared to kinetic energy and potentialenergy and inter relation between them.

The force exerted by a one-dimensional spring, fixed at one end, is F=-kx, where x is the displacement of the other end from its equilibrium position. Assuming that this force is conservative (which it is) show that the corresponding potentialenergy is U=1/2kx^2, if we choose U to be zero at the equilibrium position. (b) Suppos

I need perfect step by step solution please.
A force is given by: (vector)F(x, y, z) = (yz)x(^) + (xz)y(^) + (yx)z(^).
a. Find the work done by this force when a particle is taken from (0, 0, 2) to (2, 4, -3). Can you choose any path, or does the answer depend on the path?
b. Can a potentialenergy function be specified

Question: Two protons are moving directly towards one another. When they are very far apart, their initial speeds are 3.00 x 10^6 m/s. What is the distance of closest approach?

A force of 5 Newtons acts in the direction of a = -7i+3j+4k, moving a particle from point B(1, 7, 1) to point C(-7, 5,-2). What is the work done on the particle given that the displacement is measured in meters?

A particle at rest is attracted toward a center of force according to the relation F=-mk^2/x^33. Calculate the time required for the particle to reach the force center from a distance d.