Two $25.0$ -N weights are suspended at opposite ends of a rope that passes over a light, frictionless pulley. The pulley is attached to a chain from the ceiling. What is the tension in the rope?

검증된 단계별 안내

Identify the forces acting on the system: Each weight exerts a downward force of 25.0 N due to gravity. The rope transmits this force to the pulley, creating tension in the rope.

Recognize that the pulley is light and frictionless: This means the tension in the rope is the same on both sides of the pulley, as there is no energy loss or additional forces introduced by the pulley.

Apply the equilibrium condition for the weights: Since the weights are stationary, the upward tension in the rope must exactly balance the downward gravitational force on each weight. Therefore, the tension in the rope on each side is equal to the weight of one of the objects, which is 25.0 N.

Analyze the tension in the rope as a whole: The tension in the rope is uniform throughout because the pulley is frictionless. Thus, the tension in the rope is the same as the force exerted by one of the weights, which is 25.0 N.

Conclude that the tension in the rope is 25.0 N: This is because the system is in equilibrium, and the forces on each side of the rope are balanced.

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주요 개념

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Tension in a Rope

Tension is the force transmitted through a rope or string when it is pulled tight by forces acting from opposite ends. In a system with weights suspended on either side of a pulley, the tension in the rope is equal to the weight of the objects if they are in equilibrium, meaning they are not accelerating.

Equilibrium

Equilibrium occurs when the net force acting on an object is zero, resulting in no acceleration. In the context of the pulley system, both weights being equal means that the forces balance each other out, allowing us to determine the tension in the rope as equal to the weight of one of the objects.

Pulley Systems

A pulley system consists of a wheel on an axle or shaft designed to support movement and change the direction of force. In this scenario, the pulley is frictionless, meaning it does not add any additional forces to the system, allowing for a straightforward calculation of tension based solely on the weights involved.