Calculating Tension In Fixed Pulleys: A Physics Guide

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Hey there, physics enthusiasts! Today, we're diving into a classic problem: calculating the tension in a cable that's running over fixed pulleys. This is a fundamental concept in physics, so whether you're a student, a curious mind, or just brushing up on your knowledge, this guide is for you. We'll break down the problem step-by-step, making sure you understand the concepts and can solve similar problems with confidence. Let's get started!

Understanding the Basics: Fixed Pulleys and Tension

First off, let's get our terms straight. A fixed pulley is one that's attached to a stationary point – like a ceiling or a wall. Its primary function is to change the direction of a force. Think about it: when you pull down on a rope that's looped over a fixed pulley, the object attached to the other end of the rope goes up. The magic here is that the tension in the rope is the same throughout, assuming we're dealing with an ideal, massless rope and frictionless pulley (which is a pretty good approximation for many real-world scenarios).

Now, what about tension? Tension is the force transmitted through a rope, string, cable, or similar object when it's pulled tight by forces acting from opposite ends. It's essentially the 'pulling force' within the rope. The key thing to remember is that, in an ideal scenario with a fixed pulley, the tension is uniform throughout the rope. This means that the force pulling down on one side of the pulley is equal to the force pulling up on the other side. So, if you're holding a bucket of water up with a rope and a fixed pulley, the tension in the rope is equal to the weight of the bucket and the water. This concept is fundamental to understanding how these systems work, as it allows us to analyze the forces at play. Understanding the principles of fixed pulleys and tension is a building block for more complex mechanical systems.

We need to also consider the effect of gravity, which acts downwards on any object with mass. This force is what causes the tension in the cable to resist gravity. The mass of the object and the acceleration due to gravity are the key components used to determine the total force pulling the object downwards.

The Problem: Calculating Tension with a 7 kg Block

Alright, let's get to the specific problem. We want to calculate the tension in a cable that's passing over fixed pulleys. We're given that the block has a mass of 7 kg, and the acceleration due to gravity (g) is 10 m/s². The possible answers are a. 35 N b. 40 N c. 60 N d. 70 N e. 80 N. This is a classic example of applying Newton's laws of motion. This problem will help illustrate how the tension in a cable is directly related to the weight of the object it supports when fixed pulleys are used. This allows us to determine the tension by calculating the weight, which is the force exerted on the object due to gravity.

To solve this, we'll use a simple formula, and it's super important to understand where it comes from. The force due to gravity (also known as weight) is calculated as:

  • Force (Weight) = mass * acceleration due to gravity or F = m * g

Where:

  • F is the force (in Newtons, N)
  • m is the mass (in kilograms, kg)
  • g is the acceleration due to gravity (in meters per second squared, m/s²)

In our case, the mass (m) is 7 kg, and the acceleration due to gravity (g) is 10 m/s². Let's plug these values into the formula.

Step-by-Step Solution

Let's apply the formula F = m * g step-by-step. This straightforward approach will guide us to determine the tension in the cable. This ensures we don't miss any critical steps. Here's how it breaks down:

  1. Identify the given values:

    • Mass (m) = 7 kg
    • Acceleration due to gravity (g) = 10 m/s²

  2. Apply the formula:

    • F = m * g
    • F = 7 kg * 10 m/s²

  3. Calculate the force (weight):

    • F = 70 N

So, the force (or the weight of the block) is 70 N. Because the pulley is fixed, the tension in the cable is equal to the weight of the block. The tension in the cable is equal to the force exerted by the block due to gravity, which we have calculated to be 70 N. Remember, in a fixed pulley system, the tension in the cable is the same throughout the entire cable. Hence, the tension is the same as the weight of the object. Therefore, the correct answer is 70 N.

The Answer and Explanation

Based on our calculations, the tension in the cable is 70 N. This corresponds to option d. The reason is simple: the fixed pulley only changes the direction of the force. It doesn't reduce or increase the force itself. The tension in the cable has to support the weight of the 7 kg block, which we calculated to be 70 N. The simplicity of this system allows you to easily understand the concepts of force, weight, and tension.

Further Considerations and Practical Applications

  • Ideal vs. Real-World: Remember, this solution assumes an ideal scenario. In the real world, factors like the mass of the pulley, friction in the pulley, and the mass of the cable itself can affect the tension. However, in most introductory physics problems, we make these simplifying assumptions to focus on the core concepts.
  • Applications: Fixed pulleys are incredibly useful in many applications, from simple things like raising a flag to more complex systems like construction cranes. They allow us to lift heavy objects with less effort because they change the direction of the force.
  • Varying Mass: If the mass of the block changes, so will the tension. Double the mass, and you double the tension (assuming the same g). This demonstrates the direct relationship between mass and tension in a system with fixed pulleys. If the mass of the block were different, say 10 kg, the calculation would change: F = 10 kg * 10 m/s² = 100 N.
  • Multiple Pulleys: You can also have systems with multiple pulleys (both fixed and movable). In those cases, the mechanical advantage increases, meaning you can lift heavy objects with even less force. However, the tension calculation becomes more complex.

Understanding the tension in cables with fixed pulleys is a fundamental building block in physics. By mastering this concept, you can solve many related problems and understand how forces interact in a variety of mechanical systems. Keep practicing, and you'll become a pro in no time! Keep exploring, keep questioning, and most importantly, keep having fun with physics!

I hope this guide has been helpful. If you have any more questions, feel free to ask. Happy learning, and keep exploring the fascinating world of physics!