Question

A 800 kg steel beam is supported by the two ropes shown in (Figure 1). Calculate the tension in the rope.

Answer 1

9029 Newtons

Step-by-step explanation:

To calculate the tension in the rope supporting the 800 kg steel beam, you can use trigonometry and resolve the forces into components. Since you have two ropes each at an angle of 30 degrees, the vertical component of each rope's tension will support the weight of the beam, and the horizontal component will balance out with each other.

First, calculate the force due to gravity acting on the steel beam:

Weight (W) = mass (m) x gravitational acceleration (g)

W = 800 kg x 9.8 m/s² = 7840 N

Next, consider the angle of 30 degrees. The vertical component of the tension force (T_v) will balance the weight, and the horizontal component of each rope's tension will cancel out.

Using trigonometry, you can relate the tension (T) to its components:

T_v = T * cos(30 degrees)

T_h = T * sin(30 degrees)

Now, we can set up an equation to solve for T:

T_v = W

T * cos(30 degrees) = 7840 N

Now, solve for T:

T = 7840 N / cos(30 degrees)

T ≈ 9029 N

So, the tension in each rope supporting the 800 kg steel beam is approximately 9029 Newtons.