POLEAS Y POLIPASTOS.
Understanding Pulleys and Mechanical Advantage
Introduction to Pulleys
- The session aims to explain what a pulley is, its uses, the concept of a hoist, and how Newton's first law applies to determine mechanical advantage.
- A pulley is described as a small wheel that allows a rope or cable to change direction when tension is applied.
Types of Pulleys
- Different types of pulleys are introduced: fixed pulleys, mobile pulleys, and combinations thereof (e.g., one mobile and one fixed).
- Systems can consist of multiple pulleys arranged in various configurations (e.g., three fixed and three mobile).
Application of Newton's First Law
- The discussion emphasizes applying Newton's first law to analyze the mechanical advantage provided by pulleys.
- Assumptions include neglecting the mass of the rope and pulley for simplification; it’s stated that weights will move at constant speed without acceleration.
Free Body Diagrams
- A free body diagram is utilized to visualize forces acting on the system. Tension in the rope must equal the force applied if in equilibrium.
- The sum of forces at equilibrium leads to an equation where tension equals weight being lifted.
Calculating Mechanical Advantage
- For a single pulley lifting 120 kg force, an equal force must be applied (120 kg).
- When using two pulleys (one fixed, one mobile), the required force drops to half due to two upward tensions supporting the weight.
Advanced Pulley Systems
- In systems with more pulleys (e.g., six total), each additional tension reduces the required input force further; for six tensions, only 20 kg needs to be applied for a 120 kg weight.
- Analyzing different configurations shows that with four tensions present, only a quarter of the weight needs to be lifted manually (30 kg for 120 kg).
Analysis of Pulley Systems
Understanding the Two-Rope System
- The analysis begins with a two-rope system: a green rope fixed to the ceiling and passing through two pulleys, and a red rope that goes through one pulley holding the weight.
- When cutting one rope, the weight is supported by two tensions, leading to a division of force; each tension is halved.
- For a mass of 120 kg, this results in two tensions of 60 kg each, which are further divided into 30 kg each. Thus, only 30 kg of force needs to be applied.
Exploring the Four-Pulley System
- The discussion shifts to a four-pulley system with three ropes (blue and burgundy), all anchored to the ceiling.
- Each tension in this setup is also divided by two repeatedly; thus, for every division by two, mechanical advantage increases.
- With an initial weight of 120 kg, after multiple divisions (2 by 2), it results in needing only 15 kg of force due to the mechanical advantage being one-eighth.
Conclusion and Application