A girl weighing 310 N sits on a hammock supprted by two ropes. Each tied 60 degree from vertical posts. What is the tension on each rope?

You should draw a free-body diagram.

Represent the unknown forces with variables.
Let F1 = force on the left side
Let F2 = force on the right side

Since the ropes are tied 60 degrees from the vertical, it's 90 - 60 = 30 degrees from the horizontal.
Summation of all forces on x:
-F1*cos(30) + F2*cos(30) = 0
F1*cos(30) = F2*cos(30)
F1 = F2
This is true since the diagram is symmetric.

Summation of all forces on y:
F1*sin(30) + F2*sin(30) - 310 = 0
Since F1 = F2,
F1*sin(30) + F1*sin(30) - 310 = 0
2*F1*sin(30) = 310

Now solve for F1. Units in N.
Hope this helps~ `u`

To find the tension on each rope, we can use the concepts of equilibrium and resolving forces. Let's break down the steps to solve the problem:

Step 1: Identify the forces acting on the girl.
In this scenario, there are three forces acting on the girl:
1. Her weight (310 N), acting vertically downward.
2. The tension in the left rope.
3. The tension in the right rope.

Step 2: Resolve the weight of the girl into horizontal and vertical components.
Since the ropes are at angles, we need to consider the vertical and horizontal components of the girl's weight. The vertical component is given by the equation:
Vertical component = Weight × sin(angle)
Plugging in the values, we get:
Vertical component = 310 N × sin(60°)

Step 3: Calculate the tension in each rope.
Since the hammock is in equilibrium, the vertical components of the tensions in the ropes should balance the vertical component of the girl's weight. Therefore, the tension in each rope is equal to half the vertical component of the girl's weight.
Tension in each rope = 0.5 × Vertical component

Now, let's calculate the tension in each rope using the given values:
Vertical component = 310 N × sin(60°)
Tension in each rope = 0.5 × Vertical component

By solving these equations, you will obtain the values for the tension in each rope.