Chapter 8, Problem 1CQ

An object is acted upon by two (and only two) forces that are of equal magnitude and oppositely directed. Is the object necessarily in static equilibrium?

To determine

To confirm: Whether the object is in static equilibrium condition or not.

Answer to Problem 1CQ

The object will not be in static equilibrium condition.

Explanation of Solution

Given data:

An object is acted upon by two forces. The two forces are equal in magnitude and opposite in direction.

The following are the conditions for an object to be in static equilibrium condition.

• The net force in the x-component (horizontal direction) must be zero.
• The net force in the y-component (vertical direction) must be zero.
• The net torque about every point must be zero.

The conditions are expressed mathematically as follows:

Write the expression for static equilibrium condition of the force in the x-component as follows:

${\displaystyle \sum F_x}=0$

Here,

${\displaystyle \sum F_x}$ is the sum of the forces acting on the object in the x-component (horizontal direction).

Write the expression for static equilibrium condition of the force in the y-component as follows:

${\displaystyle \sum F_y}=0$

Here,

${\displaystyle \sum F_y}$ is the sum of the forces acting on the object in the y-component (vertical direction).

Write the expression for static equilibrium condition of the torques as follows:

${\displaystyle \sum \tau }=0$

Here,

${\displaystyle \sum \tau }$ is the sum of the torques acting on the object.

All the three conditions must be satisfied in order for the object to be in static equilibrium condition.

From the given data, two equal forces are acted upon; the object is in the opposite directions. Therefore, the two forces cancel with each other, and the net force on the object is zero. Even though the net force is zero, the sum of the torques may not be zero.

Refer to Figure 8.1 c in the textbook, the net force on the object is zero, but the net torque is not zero. It leads to the rotational movement of the object. Therefore, the object is not in the static equilibrium condition.

From the analysis, it is clear that the object may not be in static equilibrium condition even though the net force on the object is zero.

Conclusion:

Thus, the object will not be in static equilibrium condition.