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Chapter 9: Q10Q (page 230)

Figure 9–38 shows a cone. Explain how to lay it on a flat table so that it is in (a) stable equilibrium, (b) unstable equilibrium, (c) neutral equilibrium.

Short Answer

Expert verified

The following are the positions of the cone in (a) stable equilibrium (b) unstable equilibrium, and (c) neutral equilibrium.

Step by step solution

01

Understanding stable and unstable equilibrium

Stable equilibrium takes place only if an object returns to its original position after been displaced.

On the other hand, in unstable equilibrium, the object will accelerate away from its original location as soon as it gets slightly displaced.

02

Explanation for the position of the cone in stable equilibrium

If the cone is placed flat at the base of the table, it will be in stable equilibrium. To return to its original position, the cone is tilted slightly from this position and then released.

03

Explanation for the position of the cone in unstable equilibrium

When the cone is balanced on its tip, it can be said that it is in unstable equilibrium. Also, considerable displacement in the cone from this position makes it fall and collapse.

04

Explanation for the position of the cone in neutral equilibrium

In order to achieve neutral equilibrium, the cone is to be placed on its side.

The following diagram represents the position of the cone.

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Most popular questions from this chapter


In a mountain-climbing technique called the “Tyrolean traverse,” a rope is anchored on both ends (to rocks or strong trees) across a deep chasm, and then a climber traverses the rope while attached by a sling as in Fig. 9–91. This technique generates tremendous forces in the rope and anchors, so a basic understanding of physics is crucial for safety. A typical climbing rope can undergo a tension force of perhaps 29 kN before breaking, and a “safety factor” of 10 is usually recommended. The length of rope used in the Tyrolean traverse must allow for some “sag” to remain in the recommended safety range. Consider a 75-kg climber at the center of a Tyrolean traverse, spanning a 25-m chasm. (a) To be within its recommended safety range, what minimum distance x must the rope sag? (b) If the Tyrolean traverse is set up incorrectly so that the rope sags by only one-fourth the distance found in (a), determine the tension in the rope. Ignore stretching of the rope. Will the rope break?

(II) (a) Calculate the magnitude of the force, required of the “deltoid” muscle to hold up the outstretched arm shown in Fig. 9–72. The total mass of the arm is 3.3 kg. (b) Calculate the magnitude of the force exerted by the shoulder joint on the upper arm and the angle (to the horizontal) at which it acts.

(II) Calculate\({F_{\rm{A}}}\)and\({F_{\rm{B}}}\)for the uniform cantilever shown in Fig. 9–9 whose mass is 1200 kg.

(II) A 172-cm-tall person lies on a light (massless) board which is supported by two scales, one under the top of her head and one beneath the bottom of her feet (Fig. 9–64). The two scales read, respectively, 35.1 and 31.6 kg. What distance is the center of gravity of this person from the bottom of her feet?

(II) The Achilles tendon is attached to the rear of the foot as shown in Fig. 9–73. When a person elevates himself just barely off the floor on the “ball of one foot,” estimate the tension\({F_{\bf{T}}}\) in the Achilles tend on (pulling upward), and the (downward) force\({F_{\rm{B}}}\) exerted by the lower leg bone on the foot. Assume the person has a mass of 72 kg and Dis twice as long as d.
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