Question

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. (a) What is the tension in the rope? (b) What is the tension in the chain?

Short answer

(a) 25.0 N; (b) 50.0 N

Step-by-step solution

Understanding the System

The setup consists of two identical weights, each with downward force due to gravity, suspended by a rope over a pulley. The pulley is frictionless and light (meaning its mass is negligible) and does not affect the tension directly.

Analyzing Forces on the Weights

Each weight exerts a force due to gravity on the rope. Both weights are 25.0 N. Since the pulley is massless and frictionless, the tension throughout the rope must be the same.

Calculating the Tension in the Rope

Since the system is symmetrical with identical weights on both sides, the tension in the rope supports the 25.0 N force from each weight. Therefore, the tension in the rope is equal to the weight of one block, 25.0 N.

Determining the Tension in the Chain

The chain supports the entire system, including the tensions from both halves of the rope which both equal the weight of 25.0 N. Thus, the tension in the chain is the total downward force: 25.0 N + 25.0 N = 50.0 N.

Key concepts

Force of Gravity

In physics, understanding the force of gravity is crucial when analyzing how objects interact with one another. Gravity is a force that pulls objects toward each other. On Earth, it gives weight to physical objects and affects their motion.
For instance, in the given exercise, each of the weights hanging from the pulley experiences a force due to gravity. This force is directed downwards toward the center of the Earth and is calculated as the product of the mass of an object and the gravitational acceleration, which is approximately 9.81 m/s².
Because both weights are 25.0 N, this value represents the gravitational force acting on them. In simpler terms, each weight "feels" a pull from the Earth that amounts to 25.0 N. Understanding how gravity operates here helps us determine the tension in the rope and chain.

Frictionless Pulley

A frictionless pulley is an ideal concept used in physics to simplify the analysis of motion. When a pulley is termed "frictionless," it means that it has no resistance to the movement of the rope passing over it.
This characteristic is crucial for solving the exercise involving weights suspended over a pulley. The absence of friction ensures that the tension in the rope is the same on both sides because no energy is lost in overcoming friction. This setup allows us to consider only the gravitational forces and the tension without complicating factors.
The frictionless nature of the pulley in the problem allows the weights' forces to balance each other out smoothly, meaning the tension supporting both weights is identical at 25.0 N. Such a simplification helps in focusing on the key aspects of equilibrium without extra noise.

System Equilibrium

When a system is in equilibrium, all forces acting on it balance each other out, and there is no net movement. In mechanical systems like the one described in the exercise, equilibrium implies that the forces on both sides of the pulley are equal, so the system remains stationary.
In the problem with the suspended weights, the weights are balanced because each has the same gravitational force pulling downwards. The tensions created by these forces are equal and opposite, ensuring stability.
We found that the tension in the rope is 25.0 N on either side because each weight is exerting that amount of force downward. As a whole, the chain holds the combined tension from both weights, 50.0 N, reflecting the total gravitational pull. Achieving this perfect balance, or equilibrium, is essential for ensuring systems function predictably and comprehensibly.