A 2.0 rigid rod with negligible weight is subject to forces in three different ways as shown in diagrams 1-3 below.
diagrams:
1- middle point: 2.0 N
distance on both sides: 1.0 m apart
forces below at the end of each side: 1.0 N
2- distance on both sides: 1.0 m apart
force above at end of side 1: 2.0 N
force below at the end of side 2: 2.0 N
3- distance on both sides: 1.0 m apart
forces below at the end of each side: 2.0 N
For the rod to be in equilibrium which of the diagrams above is /are correct and say why.
To determine which diagram(s) result in equilibrium for the 2.0 rigid rod, we need to analyze the forces acting on each diagram.
In order for the rod to be in equilibrium, the sum of the forces acting on the rod must be zero. Additionally, the sum of the torques (or moments) applied to the rod about any point must also be zero.
Let's analyze each diagram one by one:
1. In diagram 1, there is a force of 2.0 N acting at the middle point of the rod and forces of 1.0 N acting at the ends of each side. To check for equilibrium, we examine the forces and torques. The total force acting at the middle point is 2.0 N. Since there are equal and opposite forces of 1.0 N acting on each side, the net force is indeed zero. However, when we consider torques, the torques exerted by the forces at the ends of each side are equal in magnitude but opposite in direction, resulting in a net torque of zero. Therefore, diagram 1 achieves equilibrium.
2. In diagram 2, there is a force of 2.0 N acting above at the end of side 1 and a force of 2.0 N acting below at the end of side 2. To check for equilibrium, we once again examine forces and torques. The sum of the forces in the vertical direction is zero (2.0 N upward and 2.0 N downward), satisfying the condition of equilibrium for forces. However, when it comes to torques, the forces at the ends of each side generate torques that are equal in magnitude but opposite in direction. These torques do not cancel each other out. Therefore, diagram 2 does not achieve equilibrium.
3. In diagram 3, there are forces of 2.0 N acting at the ends of each side. Again, we examine forces and torques. The forces at the ends are equal and opposite, resulting in a net force of zero. Additionally, there are no external forces acting on the rod, so the sum of forces is zero. When it comes to torques, the torques exerted by the forces at the ends of each side are equal in magnitude but opposite in direction, resulting in a net torque of zero. Therefore, diagram 3 achieves equilibrium.
Based on the analysis, both diagrams 1 and 3 result in equilibrium for the 2.0 rigid rod. Diagram 2 does not achieve equilibrium due to the unbalanced torques.