To determine the maximum weight of the object that can be sustained without breaking the strings, we need to analyze the forces acting on the object and how the tension in the strings contributes to supporting its weight. Given that the strings are inclined at an angle of 120 degrees to each other, we can break down the problem step by step.
Understanding the Setup
Imagine the object is hanging from two strings that are attached to it at an angle of 120 degrees. Each string can handle a maximum tension of 20 N. The goal is to find out how much weight the object can have without exceeding the tension limits of the strings.
Force Analysis
When the object is at rest, the forces acting on it must be balanced. The weight of the object (W) acts downward, while the tensions in the two strings (T1 and T2) act upward at angles. Since the strings are inclined at 120 degrees to each other, each string makes an angle of 60 degrees with the vertical line drawn from the object.
Breaking Down the Forces
We can resolve the tensions into their vertical components. The vertical component of the tension in each string can be calculated using trigonometry:
- Vertical component of T1 = T1 * cos(60°)
- Vertical component of T2 = T2 * cos(60°)
Since both strings can withstand a maximum tension of 20 N, we have:
- Vertical component of T1 = 20 N * cos(60°) = 20 N * 0.5 = 10 N
- Vertical component of T2 = 20 N * cos(60°) = 20 N * 0.5 = 10 N
Calculating the Total Support Force
The total vertical force that supports the weight of the object is the sum of the vertical components of the tensions from both strings:
Total vertical support = Vertical component of T1 + Vertical component of T2 = 10 N + 10 N = 20 N
Determining Maximum Weight
For the object to remain at rest, its weight must be equal to the total vertical support force provided by the strings. Therefore, the maximum weight (W) that can be sustained without breaking the strings is:
W = Total vertical support = 20 N
Conclusion
Given the options provided (10 N, 20 N, 40 N), the maximum weight of the object that can be sustained without breaking the strings is 20 N. This means that if the object weighs more than 20 N, the tension in the strings would exceed their maximum capacity, leading to a potential breakage.
