Concept explainers
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 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:
Here,
Write the expression for static equilibrium condition of the force in the y-component as follows:
Here,
Write the expression for static equilibrium condition of the torques as follows:
Here,
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.
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