Consider the 56 N weight held by two cables shown below. The left hand cable is horizontal. What is the tension in the cable slanted at an angle of 38degrees
You know weight can be derived from the force of Newtons. 56N/9.8=5.174. That is the weight in kg.
To determine the tension in the slanted cable, we can use the concept of resolving forces into their components. Here's how you can calculate it step by step:
1. Start by labeling the given information:
- Weight of 56 N (acting downward)
- Angle of 38 degrees between the slanted cable and the vertical
- Tension in the slanted cable (unknown)
2. Resolve the weight into its vertical and horizontal components:
- Vertical component: W * sin(θ) = 56 N * sin(38°) = 56 N * 0.6157 = 34.49 N (acting downward)
- Horizontal component: W * cos(θ) = 56 N * cos(38°) = 56 N * 0.7880 = 44.07 N (acting to the right)
3. Since the cables are in equilibrium, the sum of the horizontal components of tension force should be equal to the horizontal component of the weight. Therefore:
- Tension in the slanted cable * cos(38°) = 44.07 N
- Tension in the slanted cable = 44.07 N / cos(38°)
- Tension in the slanted cable ≈ 55.56 N (rounded to two decimal places)
Therefore, the tension in the slanted cable is approximately 55.56 N.