# Pulleys

## The Power of Pulleys: Making Lifting Heavy Items a Breeze

Lifting heavy materials can be a challenging task, but with the help of simple machines such as pulleys, it can become much more manageable. A pulley consists of a wheel and a fixed axle with a groove along its edges to guide a rope or cable.

Due to their ability to multiply the force applied to lift an object without the use of an engine, pulleys are classified as simple machines. By combining and running a rope around two or more wheels, an excellent lifting tool is created. The load refers to the weight of the object being lifted, while the effort is the force required to move the object.

The number of pulleys in a system directly impacts the force and rope needed to lift a load across a distance. This means that as the number of pulleys increases, the applied force must be sustained for a longer period.

### How Pulleys Work

By adding more pulleys to a system, the mechanical advantage is significantly increased, making it easier to lift the same load. But first, let's clarify the definition of mechanical advantage and the difference between weight and mass.

Weight refers to the gravitational force pulling an object towards the ground, measured in Newtons (N). On the other hand, mass is the amount of substance in an object, measured in kilograms (kg). Mechanical advantage is the measure of how simple machines multiply forces by calculating the ratio of the force that performs the work to the applied force.

For instance, a sack with a mass of 40kg can be calculated as having a weight of 400N due to Earth's gravity being approximately ten times the mass in kilograms.

### The One-Wheel Pulley System

A simple pulley changes the direction of the load, allowing it to be lifted by pulling the rope down. With just one wheel, as seen in the diagram below, the load is moved upwards.

**Image: César Rincón CC BY-SA 3.0**

### The Two-Wheel Pulley System

Adding one more wheel to the system reduces the effort required to lift the same load in a one-wheel pulley system. For example, a 40kg sack with a weight of 400N would now be split between the two pulleys, requiring only half the effort to lift. The more wheels a pulley system has, the greater the mechanical advantage.

If a two-wheel pulley system is used, pulling 5 meters of rope will only move the load 2.5 meters.

**Image: Public Domain**

### The Four-Wheel Pulley System

With the addition of four wheels to a pulley system, the weight of the load is evenly distributed among the wheels, reducing the effort required even further, as shown in the diagram below.

**Image: Public Domain**

In this case, the mechanical advantage is twice as good as a two-wheel system. However, to lift the load across a 5-meter distance, the rope will need to be pulled four times the distance, or 20 meters.

### Types of Pulleys

Pulleys are divided into three types among simple machines:

- Fixed Pulleys: Also known as single spot, these pulleys remain fixed while the load is on one side, and the effort is applied on the other. This means that the same amount of force is needed to lift the object.
- Movable Pulleys: This type of pulley moves with the load, multiplying the force being exerted and making it easier to lift heavier loads.
- Compound Pulleys: Combining the features of both fixed and movable pulleys, compound pulleys not only multiply force, but also change the direction of the load. They are ideal for lifting heavy objects.

### Calculation of Load Acceleration

Here are a few examples of how to determine the acceleration of a load using SUVAT equations:

**Example:** If two particles with different masses are released from rest, what would be the acceleration?

Answer: The heavier particle will drop while the lighter particle will rise. By labeling the 5kg mass as particle a and the 12kg mass as particle b, the acceleration can be calculated.

With the help of simple machines like pulleys, the process of lifting heavy materials becomes much more manageable. By understanding the principles of mechanical advantage and the various types of pulley systems, the required force to lift a load can be significantly reduced.

A pulley is a machine designed to make lifting easier by using a wheel and rope system to distribute the weight of a load. Its mechanics involve the principles of gravity and weight.

Weight is determined by multiplying an object's mass with the acceleration due to gravity, represented by the formula g = 9.8 m/s². For example, a 5kg object would have a weight of 49N (5kg x 9.8 m/s²).

Let's take two particles, a and b, with masses of 5kg and 12kg, respectively. By using the equations T - 5kg x g = 5kg x a and 12kg x g - T = 12kg x a, we can determine their acceleration and tension.

To solve these equations, we simply add them together, eliminating the variable T. This results in the equation 7kg x g = 17kg x a. With a value of g at 9.8 m/s², we can calculate that a = 5 m/s².

## Exploring Different Scenarios

Let's say we have two particles, one with a mass of 8kg and the other with an unknown mass of m, connected by a tight string passing over a smooth peg. If one particle is held at rest and the particles accelerate at a rate of 5 m/s², what is the value of m?

To solve this problem, we must first draw a diagram and label the particles a (with 8kg) and b (with mass m). We know that for one particle to accelerate, the other must either have a greater or lesser mass. Therefore, we will consider both possibilities.

In the scenario where m > 8, we can resolve particle a's acceleration using the SUVAT equations. This gives us T - 4g = 5a and 3g - T = 3a. By adding these equations, we get -g = 8a. With a value of g at 9.8 m/s², we can calculate a = 0.122 m/s².

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