Final answer:
The magnitude of the torque on a rod due to gravity is determined by the force and the lever arm's length. To produce an 8.0 kN·m torque on a 2.0 meters long rod, a force of 4.0 kN applied at the rod's end is needed.
Step-by-step explanation:
The magnitude of the total torque exerted on a rod due to the gravitational force can be calculated using the lever arm to the point where the force is applied. If a rod is placed along the x-axis and has to produce a given amount of torque about an axis located at one of its ends, we can use the formula τ = rF, where τ is the torque, r is the distance from the axis to the point where the force is applied, and F is the force. For instance, if we need to produce 8.0 kN·m of torque on a 2.0 meters long rod, we can calculate the force that needs to be applied at the end of the rod. In a hypothetical example where the axis is at the collar, and we assume it to have negligible length, the lever arm would be the entire length of the rod. Hence, for a rod of length 2.0 meters, a force of 4.0 kN would need to be applied at the end to create the required torque of 8.0 kN·m.