Which one of the following statements describes the condition(s) for which a rigid body is in equilibrium?
Only internal forces can be present.
The sum of the externally applied forces must be zero, and the sum of the externally applied torques must be zero.
Each external force may be non-zero, but the sum of the forces must be zero.
Each external torque may not be non-zero, but the sum of the torques must be zero.
Each external torque acting on the body must be zero.
The sum of the externally applied forces must be zero, and the sum of the externally applied torques must be zero.
The statement that describes the condition(s) for which a rigid body is in equilibrium is: The sum of the externally applied forces must be zero, and the sum of the externally applied torques must be zero.
To determine which statement describes the condition(s) for which a rigid body is in equilibrium, we need to understand the concept of equilibrium for a rigid body.
A rigid body is said to be in equilibrium when it is not experiencing any net translation or rotation. This means that the body remains stationary and doesn't rotate due to the forces applied to it.
Now, let's evaluate each statement to determine which one accurately describes the condition(s) for a rigid body to be in equilibrium:
1. Only internal forces can be present: This statement is incorrect. Both internal and external forces can be present on a rigid body in equilibrium.
2. The sum of the externally applied forces must be zero, and the sum of the externally applied torques must be zero: This statement accurately describes the condition(s) for a rigid body to be in equilibrium. In other words, for a rigid body to be in equilibrium, the total sum of the external forces acting on it must be zero (resultant force is zero) and the total sum of the external torques acting on it must be zero (the net torque is zero).
3. Each external force may be non-zero, but the sum of the forces must be zero: This statement is incorrect. The sum of the external forces acting on a rigid body in equilibrium must be zero, not each individual force.
4. Each external torque may not be non-zero, but the sum of the torques must be zero: This statement is unclear and contradictory. It is not a valid explanation for the condition(s) of equilibrium.
5. Each external torque acting on the body must be zero: This statement is incorrect. The individual external torques acting on a rigid body can be non-zero, but their sum must be zero for equilibrium.
So, the correct statement that accurately describes the condition(s) for which a rigid body is in equilibrium is: "The sum of the externally applied forces must be zero, and the sum of the externally applied torques must be zero."