Calculating Tension in Ropes Supporting a Hanging Mass: A Physics Problem

Since the girl is in equilibrium, the net force acting on her must be zero:

$$\sum F = 0$$

In the vertical direction:

$$T_1 + T_2 - 200 = 0$$

where \(T_1\) and \(T_2\) are the tensions in the two strands of rope.

Solving for \(T_1\):

$$T_1 = 200 - T_2$$

We can also write the equilibrium equation in the horizontal direction:

$$\sum F = 0$$

$$T_1 \sin \theta - T_2 \sin \theta = 0$$

Dividing both sides by \(sin\theta\):

$$T_1 = T_2$$

Combining this result with the previous one, we get:

$$200 - T_2 = T_2$$

$$200 = 2T_2$$

$$T_2 = 100 \mathrm{N}$$

Therefore, the tension in each strand of rope is 100 N.