To solve the problem of finding the weight \( W \) in the given frictionless pulley system, we need to analyze the forces acting on the system. ### Step-by-Step Explanation 1. **Understanding the System**: - The pulley system consists of two weights: one weight \( W \) and another weight of 40N. - Since the system is in equilibrium, the forces acting on both sides of the pulley must be equal. This means that the tension in the rope on both sides of the pulley is the same. 2. **Setting Up the Equation**: - In equilibrium, the weight \( W \) must balance the weight of 40N. Therefore, we can write the equation: \[ W = 40N \] 3. **Conclusion**: - From the equation above, we can directly conclude that the value of \( W \) is 40N. ### Why the Correct Option is C (40.0N) - The system is in equilibrium, which means that the forces must balance out. Since the only weights acting on the system are \( W \) and 40N, and they are connected by a frictionless pulley, they must be equal for the system to remain at rest. ### Why the Other Options are Incorrect - **Option A: 13.3N**: - This value does not satisfy the equilibrium condition. If \( W \) were 13.3N, the system would not be balanced, and the 40N weight would accelerate downwards. - **Option B: 20.0N**: - Similar to option A, if \( W \) were 20N, the 40N weight would still be heavier, causing the system to accelerate rather than remain in equilibrium. - **Option D: 80.0N**: - If \( W \) were 80N, it would exceed the 40N weight, causing the system to accelerate upwards, which contradicts the condition of equilibrium. ### Common Pitfalls - **Misunderstanding Equilibrium**: Students often confuse equilibrium with other states of motion. Remember, equilibrium means that all forces are balanced, and there is no net force acting on the system. - **Ignoring the Pulley**: In a frictionless pulley, the tension is the same on both sides. This is crucial for setting up the correct equations. ### Revision Summary - In a frictionless pulley system, the weights must balance for equilibrium. - The equation for equilibrium is \( W = 40N \). - The correct answer is C (40.0N). - Always check that the forces acting on the system are balanced when analyzing pulley problems.