The potential energy of a particle as a function of position will be given as U (x) = A x2 + B x + C, where U will be in joules when x is in meters. A, B, and C are constants. show answer No Attempt 50% Part (a) Enter an expression for the x-component of the force as function of position F (x), in terms of the constants A, B, and C.

Question

Physics

Rowan Lyons

24 September, 19:28

The potential energy of a particle as a function of position will be given as U (x) = A x2 + B x + C, where U will be in joules when x is in meters. A, B, and C are constants. show answer No Attempt 50% Part (a) Enter an expression for the x-component of the force as function of position F (x), in terms of the constants A, B, and C.

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Answers (1)

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Kiki · Answer 1

F = - 2 A x - B

Explanation:

The force and potential energy are related by the expression

F = - dU / dx i ^ - dU / dy j ^ - dU / dz k ^

Where i ^, j ^, k ^ are the unit vectors on the x and z axis

The potential they give us is

U (x) = A x² + B x + C

Let's calculate the derivatives

dU / dx = A 2x + B + 0

The other derivatives are zero because the potential does not depend on these variables.

Let's calculate the strength

F = - 2 A x - B