Chapter 14, Problem 1PQ

What Is Static Equilibrium?

Problems 1–3 are grouped.

1. C A ball is attached to a strong, lightweight rod (Fig. P14.1). The rod is supported by a horizontal pin near the top. The ball is at rest. Is the ball in static equilibrium? If not, why not? If so, which type of equilibrium is it—stable, unstable, or neutral? Hint: What would happen if you displaced the ball slightly?

FIGURE P14.1

To determine

Whether the ball is in static equilibrium and if so the type of equilibrium in which the ball is present.

Answer to Problem 1PQ

The ball is in static equilibrium and it is stable equilibrium.

Explanation of Solution

Equilibrium is a special case of motion in which an object’s translational momentum and angular momentum are both constant. Static equilibrium is a special case in which the object’s translational momentum and angular momentum are zero. This also implies that for an object to be in static equilibrium, the total force and the total torque acting on the object must be zero. There are three types of static equilibrium namely stable static equilibrium, unstable static equilibrium and neutral static equilibrium. If an object returns to its equilibrium position after being released, it will be in stable equilibrium. If an object moves farther away from the equilibrium position after being released, it will be in unstable equilibrium. If an object is moved and released from a new position and does not move toward or away from its equilibrium position, then the object is in neutral equilibrium.

It is given that the ball in the figure is at rest so that it has no acceleration. This implies the net force and the torque acting on the ball are zero and the ball must be in static equilibrium. If the ball is displaced slightly, it will return to or pass through the equilibrium position. According to the definition, it is stable equilibrium.

Conclusion:

Thus, the ball is in stable static equilibrium since the net force and the torque acting on it is zero and it returns to its equilibrium position when it is displaced slightly.