Question

For a three-force body to be in equilibrium, identify the condition that must be true.

a) The sum of the forces must be zero.
b) The sum of the torques must be zero.
c) Both the sum of the forces and the sum of the torques must be zero.
d) The forces must be parallel.

Answer 1

For a three-force body to be in equilibrium, both the sum of the forces and the sum of the torques must be zero, ensuring no linear or rotational acceleration.

Step-by-step explanation:

For a three-force body to be in equilibrium, the condition that must be true is c) Both the sum of the forces and the sum of the torques must be zero. This is because equilibrium requires two conditions to be met:

• The sum of all external forces acting on the body must be zero (first condition of equilibrium), which ensures that there is no linear acceleration.
• The sum of all external torques due to these forces must also be zero (second condition of equilibrium), which ensures that there is no rotational acceleration.

These conditions are represented by the equations net F = 0 and net T = 0, respectively. In practical terms, this means that for an object to be in equilibrium, it should not be moving or rotating; it should be completely at rest or moving with a constant velocity.