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Chapter 1: Q17DQ (page 228)

Figure 7.22a shows the potential energy function for the force Fx=-Kx. Sketch the potential energy function for the force Fx=+Kx. For this force, is x=0a point of equilibrium? Is this equilibrium stable or unstable? Explain.

Short Answer

Expert verified

x=0is a point of equilibrium.

The equilibrium is unstable.

Step by step solution

01

Significance of the potential energy

Potential energy is described as the energy that an object possesses while at rest. It is also termed as the energy that is stored inside an object.

02

Sketching the potential energy function

The force kx=+kxhas been drawn below:


The potential energy function has been sketched below:

Thus,

03

Determination of the equilibrium point

According to the sketches, at the point x=0, the value of Fxwill also become zero.

Thus, x=0is a point of equilibrium.

04

Determination of the stability of the equilibrium

According to the sketches, at the point x=0, the value of the function of the potential energy Uxwill also become maximum. Hence, Fxwill get pushed away from the point of equilibrium.

Thus, the equilibrium is unstable.

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Most popular questions from this chapter

A shaft is drilled from the surface to the center of the earth (see Fig. 13.25). As in Example 13.10 (Section 13.6), make the unrealistic assumption that the density of the earth is uniform. With this approximation, the gravitational force on an object with mass m, that is inside the earth at a distance r from the center, has magnitude Fg=GmEmr/RE3(as shown in Example 13.10) and points toward the center of the earth. (a) Derive an expression for the gravitational potential energyU(r)of the object鈥揺arth system as a function of the object鈥檚 distance from the center of the earth. Take the potential energy to be zero when the object is at the center of the earth. (b) If an object is released in the shaft at the earth鈥檚 surface, what speed will it have when it reaches the center of the earth?

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