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.

This question involves the concepts of derivatives, work done, and vector algebra.

The expression for the x-component of the force as a function of the position is .

According to the simple formula of the work done:

where,

U = Work done

F = Force

x = displacement

Hence, in order to find out the expression for the x-component of force, we must take the derivative of the work done with respect to 'x'.

Learn more about work done here:

link

The attached picture explains the work done formula.

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

v 154.9= 0.9 length length s little over 154.9cm