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In their physics classroom, students want to hang a heavy sign of mass M and length L as shown in the figure above. The sign makes an angle θ with the wall. Without any support, the sign would rotate clockwise while its pivot would remain connected to the wall. The students can connect one support cable vertically from one of the hooks above the sign, as indicated by the dotted lines in the diagram. (a) Rank the three hook locations according to the amount of tension the support cable would experience if the students decided to support the sign from that location. Use 1 for the least tension and 3 for the greatest tension. If two locations would have the same tension, give them the same ranking.
In their physics classroom, students want to hang a heavy sign of mass M and length L as shown in the figure above. The sign makes an angle θ with the wall. Without any support, the sign would rotate clockwise while its pivot would remain connected to the wall. The students can connect one support cable vertically from one of the hooks above the sign, as indicated by the dotted lines in the diagram. (a) Rank the three hook locations according to the amount of tension the support cable would experience if the students decided to support the sign from that location. Use 1 for the least tension and 3 for the greatest tension. If two locations would have the same tension, give them the same ranking.
The tension in the support cable is highest at Location A (closest to the pivot), intermediate at Location B, and lowest at Location C (farthest from the pivot). The choice of hook location affects the load borne by the cable, with closer locations experiencing greater tension.Location A: This hook is closest to the pivot point (where the sign rotates). The torque due to the weight of the sign is maximum here. Therefore, the tension in the cable at Location A would be the greatest.Location B: Location B is farther away from the pivot than A but closer than C. The torque due to the weight of the sign is less than at Location A. Hence, the tension in the cable at Location B would be less than at A but more than at C.Location C: This hook is farthest from the pivot. The torque due to the weight of the sign is the least here. Therefore, the tension in the cable at Location C would be the least.Ranking:Location A: 3 (greatest tension)Location B: 2Location C: 1 (least tension)The tension in the cable depends on the distance from the pivot point. Closer locations require more tension to balance the gravitational torque, while farther locations require less tension.In summary, the tension in the support cable is highest at Location A (closest to the pivot), intermediate at Location B, and lowest at Location C (farthest from the pivot). The choice of hook location affects the load borne by the cable, with closer locations experiencing greater tension....