A particle moves in a conservative force field where its potential energy is given by U = 20yz / x. Find the force vector acting on the particle.

(20yz/x²) i_hat + (20z/x) j_hat + (20y/x) k_hat
(20yz/x²) i_hat - (20z/x) j_hat - (20y/x) k_hat
-(20yz/x²) i_hat - (20z/x) j_hat - (20y/x) k_hat
-(20yz/x²) i_hat + (20z/x) j_hat + (20y/x) k_hat

Correct answer: (20yz/x²) i_hat - (20z/x) j_hat - (20y/x) k_hat

Solution

U = 20yz/x. grad(U): dU/dx = 20yz*(-1/x²) = -20yz/x²; dU/dy = 20z/x; dU/dz = 20y/x. F = -grad(U) = (20yz/x²) i_hat - (20z/x) j_hat - (20y/x) k_hat.

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