A force F acts at point A on the tip of a bent metal rod. The angle of the bends in the rod at points B and C are 45°, as shown and each segment, AB, BC, CD is of equal length. Rank the magnitudes of the torques about each of the points A, B, C, D. A means the torque due to F about A, B the torque due to F about B, etc. The direction of the force is directly toward point D, as indicated.
Answer (1)
Answer:1. About Point A:The force acts at A → = 0Torque = 02. About Point B:Distance: 1 segment (length ) The force vector makes a 90° angle with the lever arm from B to AτB = L⋅F⋅sin(90°)=L⋅F3. About Point C:Perpendicular distance is more complex, but geometry helps:Path from C to A: 2 segments bent at 45° eachThe effective perpendicular distance is 2Force is still at 90° to that effective radiusτC = 2L⋅F4. About Point D:Path: 3 segments bent — like a triangleEffective perpendicular distance = ⋅3τD = 3 L⋅FSo The Correct Answer is: A < B < C < D
