Question

Two ropes are connected to a steel cable that supports a hanging weight as shown in figure below. (a) Draw a free-body diagram showing all of the forces acting at the knot that connects the two ropes to the steel cable. Based on your force diagram, which of the two ropes will have the greater tension? (b) If the maximum tension either rope can sustain without breaking is 5000 N, determine the maximum value of the hanging weight that these ropes can safely support. You can ignore the weight of the ropes and the steel cable 160° 40°

Answer 1

The tension in the rope connected to the side with the larger angle will be greater. The maximum weight the ropes can support is 5000 N.

Step-by-step explanation:

Based on the free-body diagram, the two ropes are connected to the steel cable at the knot. The forces acting at the knot are the tension in the left rope (T1), the tension in the right rope (TR), and the weight of the hanging mass (W). Since the system is in equilibrium, the net force in the horizontal direction is zero, meaning T1 and TR have the same magnitude.

To determine which rope has the greater tension, we can consider the vertical forces. The tension in each rope is equal to the weight of the hanging mass. Therefore, the rope connected to the side with the greater angle will have a greater tension. In this case, the rope connected to the side with the larger angle (TR) will have the greater tension.

Given that the maximum tension either rope can sustain without breaking is 5000 N, we can use this value to find the maximum weight the ropes can support. Since the tension in each rope is equal to the weight of the hanging mass, the maximum weight is 5000 N.