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Chapter 1: Q23DQ (page 228)

The potential energy function for a force F鈫� isU=伪x3 , where伪 is a positive constant. What is the direction of F鈫�?

Short Answer

Expert verified

F鈫� is directed to the negative direction of the x-axis.

Step by step solution

01

Significance of the force

Force can be described as the negative gradient of the potential function for any object.

02

Determination of the direction of the force

The equation of the potential energy function is expressed as:

U=伪x3

Here, U is the potential energy, 伪 is the constant and x is the distance moved by the object.

The formula for the magnitude of force is

F=-鈭�U鈭�x

Here F鈫�is the force exerted.

Substitute 伪x3for U in the above equation.

F=-鈭�伪x3鈭�x=-3伪x

The negative sign indicates that the force is directed to the negative direction of the x-axis.

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