Question

two ropes in a vertical plane exert equal-magnitude forces on a hanging weightbut pull with an angle of 86° betweenthem what pull does each one exertif their resultantpull 372N directlyupward?

Answer 1

To find the tension in each rope, you can use the concept of vector addition. Since the two ropes exert equal-magnitude forces at an angle of 86 degrees between them and the resultant pull is 372 N directly upward, you can break down the problem into components.

Let T be the magnitude of tension in each rope.

1. The vertical component of tension in each rope (T_vertical) opposes the weight and should be equal to the weight (372 N) for the system to be in equilibrium.

T_vertical = 372 N

2. The horizontal component of tension in each rope (T_horizontal) is the force due to the angle between the ropes. This component is given by:

T_horizontal = 2 * T * sin(86 degrees)

Now, you can solve for T using the vertical component:

T = T_vertical / (2 * sin(86 degrees))

T = 372 N / (2 * sin(86 degrees))

Calculate the value of T:

T ≈ 372 N / (2 * 0.9962)

T ≈ 186 N

So, each rope exerts a tension of approximately 186 N.