A 6.0 m–tall traffic-signal pole is subjected to a steady horizontal wind force of…
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A 6.0 m–tall traffic-signal pole is subjected to a steady horizontal wind force of magnitude 85 N directed toward the east at the very top of the pole. Two steel guy wires are attached from the top of the pole to anchors in the pavement:
• Wire A runs due north and slants downward, making an angle of 30° below the horizontal.
• Wire B runs due west and slants downward, making an angle of 40° below the horizontal.
Both wires are in tension and exert forces on the top of the pole along their lengths. Ignore the weight of the wires themselves.
(a) Draw and clearly label all forces acting on the top of the pole. Include the directions of the wind force and the forces exerted by the two wires.
(b) Considering that the pole remains stationary, explain qualitatively why the magnitudes of the tensions in Wire A and Wire B cannot be equal.
(c) Describe in words a systematic procedure you could follow—without performing detailed calculations—to decide whether a chosen pair of tensions TA and TB will keep the top of the pole from accelerating. Specify which components of force you would compare and why.
(d) Suppose the wind picks up so that the horizontal force on the pole doubles while the directions of both wires stay the same. Explain how the magnitudes of TA and TB must change to restore equilibrium, and state which wire will experience the larger percentage increase in tension. Justify your answer using reasoning based on vector components.