Question2. (II) Arlene is to walk across a "high wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is $10.0^{\circ}$, as shown in Fig. 4-39. If her mass is 50.0 kg , what is the tension in the rope at this point?

Studdy Solution
Solve for the tension $T$:
$$2T \sin(10.0^{\circ}) = 490 \, \text{N}$$
$$T = \frac{490 \, \text{N}}{2 \sin(10.0^{\circ})}$$
Calculate $\sin(10.0^{\circ})$ and then find $T$:
$$\sin(10.0^{\circ}) \approx 0.1736$$
$$T = \frac{490 \, \text{N}}{2 \times 0.1736}$$
$$T \approx \frac{490 \, \text{N}}{0.3472}$$
$$T \approx 1411 \, \text{N}$$
The tension in the rope at the midpoint is:
$$\boxed{1411 \, \text{N}}$$