Question

A 45.0-kg person takes a nap in a backyard hammock. Both ropes supporting the hammock are at an angle of 21.0° above the horizontal. What is the tension in each rope?

Answer 1

To calculate the tension in each rope supporting the hammock, we can use the principles of equilibrium. By resolving the forces, we can use trigonometry to find the tension in each rope. The tension in each rope is dependent on the weight of the person and the angle of the ropes.

Step-by-step explanation:

To calculate the tension in each rope supporting the hammock, we can use the principles of equilibrium.

We can break down the forces acting on the person and the hammock into vertical and horizontal components.

The vertical component of the person's weight is balanced by the tension in the ropes, while the horizontal component does not affect the tension in the ropes.

By resolving the forces, we can use trigonometry to find the tension in each rope.

• tension = (weight / 2) / sin(angle)

• Substituting the given values, the tension in each rope is

• tension = (45.0 kg x 9.8 m/s^2 / 2) / sin(21.0°)

• Calculating this expression gives us the tension in each rope.