arlene is walking across a "high wire" strung horizontally between 2 buildings 10.0 meters appart. the sag in the rope when she is @ midoint is 10 degrees. her mas is 50.0 kg. what is the tension in the rope

To calculate the tension in the rope, we need to consider the gravitational force acting on Arlene and the force due to the sag in the rope. Let's break it down step by step.

Step 1: Calculate the gravitational force:
The gravitational force acting on Arlene can be calculated using the formula: F = m * g, where
F is the gravitational force,
m is the mass of Arlene, and
g is the acceleration due to gravity which is approximately 9.8 m/s².

Given that Arlene's mass (m) is 50.0 kg, we can calculate the gravitational force (F) using the formula:
F = 50.0 kg * 9.8 m/s²

Step 2: Calculate the horizontal component of the gravitational force:
Since the rope is horizontal, the sag in the rope will create a vertical component of the gravitational force. This vertical component needs to be balanced by the tension in the rope. However, we have to find the horizontal component of the gravitational force because it provides the tension in the rope.

To calculate the horizontal component of the gravitational force, we can use the angle of sag (θ) provided, which is 10 degrees. Since the sag forms a right triangle with the horizontal, the horizontal component is given by:
Horizontal component = F * cos(θ)

Step 3: Calculate the tension in the rope:
The tension in the rope is equal to the horizontal component of the gravitational force. So, the tension is given by:
Tension = Horizontal component

By substituting the value of the horizontal component from Step 2, we can obtain the tension in the rope.

Please note that you may need a scientific calculator or use trigonometric tables to find the cosine of the angle if you don't have one.