A steel cable is tightly tied (horizontally) to two trees that are 8 meters apart. A 40-kg child hangs from the center of the cable-causing the center of the cable to be 1 cm below the original location (before the child grabbed the cable). The tension in the cable is
A) 78,000 N.
B) 400 N.
C) 1200 N.
D) 12,000 N.

Question

Quizplus · Accepted Answer

The tension in the cable can be calculated using the formula for the tension in a horizontal cable with a weight hanging from its center, which is $T = \frac{w}{2} \times \frac{L}{d}$, where $w$ is the weight of the object hanging from the cable (in this case, the child), $L$ is the half-length of the cable, and $d$ is the displacement of the cable due to the weight. Given that the weight of the child is 40 kg (which corresponds to a force due to gravity of $w = mg = 40 \times 9.8 = 392$ N), the half-length of the cable is 4 meters (since the total length between the trees is 8 meters), and the displacement is 0.01 meters (1 cm), the tension in the cable is calculated as $T = \frac{392}{2} \times \frac{4}{0.01} = 196 \times 400 = 78,400$ N, which is approximately 78,000 N, indicating a very high tension due to the small displacement and the mechanics of the system.

A Steel Cable Is Tightly Tied (Horizontally) to Two Trees