To determine the readings of the two spring scales, A and B, we need to analyze the forces acting on the system. In this setup, scale A is fixed to the floor, and scale B is attached to the ceiling, with a weight of 74 N hanging from the pulley. Let's break down the forces step by step.
Understanding the Forces in the System
First, we recognize that the weight (W) of 74 N is acting downward due to gravity. This weight creates tension in the rope that runs over the pulley. Since the pulley is assumed to be massless and frictionless, the tension in the rope will be the same on both sides of the pulley.
Analyzing Scale A
Scale A is connected to the floor and measures the force exerted on it. Since the weight is hanging from the pulley, the tension in the rope (let's call it T) will be equal to the weight of the object hanging from it. Therefore, the reading on scale A will be equal to the tension in the rope, which is 74 N. This is because scale A is effectively supporting the entire weight through the tension in the rope.
Examining Scale B
Scale B, on the other hand, is attached to the ceiling and measures the force exerted on it by the pulley and the weight. The tension in the rope (T) acts upward on scale B, while the weight (W) acts downward. Since the system is in equilibrium (the weight is not accelerating), the forces must balance out. Thus, the reading on scale B will also be equal to the weight of the object hanging from the pulley, which is again 74 N.
Final Readings of the Scales
- Reading of Scale A: 74 N
- Reading of Scale B: 74 N
In summary, both scales A and B will read 74 N. This is due to the fact that the tension in the rope is equal to the weight of the object hanging from it, and both scales are effectively measuring the same force in this static situation. Understanding these principles of tension and equilibrium is crucial in solving similar problems in physics.
