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Chapter 6: Q54P (page 279)

Under certain conditions the interaction between a "polar" molecule such asHCllocated at the origin and an ion located along the x axis can be described by a potential energy U=-b/x2, where b is a constant. What is Fx, the xcomponent of the force on the ion? What is Fy, the ycomponent of the force on the ion?

Short Answer

Expert verified

Fx, the x component of the force on the ion is -2bx

Fy, the y component of the force on the ion is 0

Step by step solution

01

Identification of given data

Potential energyU=-b/x2

02

concept of the potential energy

Potential energy is calculated when the energy kept in an object due to the position of an object is related to zero.

03

Determination of Fx, thex component of the force and Fy, the y component of the force

Thexcomponent of the force,

Fx=-∂U∂x

=-∂∂x-bx2

=b∂→∂xx-2

=b(-2x)

=-2bx

Hence, the x component of the force on the ion is -2bx

The y component of the force,

Fy=-∂U∂y

=-∂∂y-bx2

=b∂∂yx-2

=0

Hence, the ycomponent of the force on the ion is 0.

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