the figure above shows a uniform meterstick that is set on a fulcrum at its center. a force of magnitude f toward the bottom of the page is exerted on the meterstick at the position shown. at which of the labeled positions must an upward force of magnitude 2f be exerted on the meterstick to keep the meterstick in equilibrium?
Answer: To keep the meterstick in equilibrium, an upward force of magnitude 2f needs to be exerted on the meterstick at a specific position. In this case, we need to analyze the torques acting on the meterstick to determine the position where the force should be applied.
The torque can be calculated by multiplying the force applied to an object by the distance from the fulcrum. In this scenario, the force f is applied downward at a specific position on the meterstick. To balance this force and keep the meterstick in equilibrium, an upward force of magnitude 2f needs to be applied.
To achieve equilibrium, the sum of the torques acting on the meterstick should be zero. Since the meterstick is uniform and the fulcrum is at its center, the torques exerted on each side of the fulcrum will be equal in magnitude but opposite in direction.
Let’s consider the position labeled “A” on the meterstick. If an upward force of magnitude 2f is exerted at position A, it will create a clockwise torque. At the same time, the force f downward at the shown position creates a counterclockwise torque. For equilibrium, these torques should balance each other.
Considering the principle of moments, the clockwise torque created by the 2f force at position A can be balanced by the counterclockwise torque created by the force f at the shown position. The distance between the fulcrum and position A should be twice the distance between the fulcrum and the shown position to ensure that the torques are equal.
Therefore, the upward force of magnitude 2f should be exerted at the labeled position “A” on the meterstick to keep it in equilibrium.