The potential energy of a particle is given by U = (40 + x² + y² + z²) joules, where x, y, z are in metres. Find the magnitude of the conservative force acting on the particle when it is located at the point (1.0 m, 0.5 m, -1.0 m).

sqrt(6) N
3 N
sqrt(5.25) N
sqrt(7) N

Correct answer: sqrt(6) N

Solution

Taking the negative gradient of U: Fₓ = -2x, F_y = -2y, F_z = -2z. At (1, 0.5, -1): F = (-2, -1, 2) N. Magnitude = sqrt(4+1+4) = sqrt(9) = 3 N.

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