Design of a Pulley System to Lift a One-Ton Load

Problem Statement

Design a pulley system that will enable an able-bodied individual to lift a load of one ton (1000 kg) through a height of 10 meters with minimal effort. The system should reduce the effective force required to lift the load, allowing for safe and efficient operation by a single person.

Requirements

Load (L): 1000 kg
Height to lift (h): 10 meters
Gravity (g): 9.81 m/s²
Effective force required: Should be low enough for an able-bodied individual to exert without excessive strain (typically below 100 N).

Introduction to Pulley Systems

A pulley system is a mechanical arrangement of pulleys designed to reduce the force needed to lift a load. Pulley systems can be single, double, or compound, and the mechanical advantage (MA) they provide depends on the number of pulleys and the arrangement used.

In this design, we aim to maximize the mechanical advantage so that the required input force is minimized. To calculate the mechanical advantage of a pulley system, we use the following equation:

$$ \text{Mechanical Advantage (MA)} = \frac{\text{Load (L)}}{\text{Effort (E)}} $$

Where:

$ L $ = Weight of the load in Newtons, calculated as $ L = m \cdot g $.
$ E $ = Force exerted by the individual to lift the load.

Calculations

First, we calculate the weight of the load:

$$ L = m \cdot g = 1000 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 9810 \, \text{N} $$

To design a system where the individual needs to exert a force of approximately 100 N, we calculate the required mechanical advantage $ MA $:

$$ \text{MA} = \frac{L}{E} = \frac{9810 \, \text{N}}{100 \, \text{N}} = 98.1 $$

A high mechanical advantage can be achieved using a compound pulley system, also known as a block and tackle arrangement. With each additional pulley, the force required to lift the load decreases, though the distance the rope must be pulled increases.

Design of the Compound Pulley System

To achieve an $ MA $ of around 98, we can use a system of pulleys with a total of approximately 8 to 10 pulleys in various combinations. This will allow the effort required to lift the load to fall within the safe range for an individual.

The final arrangement will involve two main components:

Fixed Pulley Block: Pulleys attached to a fixed point, which change the direction of the applied force without adding mechanical advantage.
Movable Pulley Block: Pulleys that move with the load, which multiply the force applied to lift the load.

Using a system of 5 movable pulleys and 5 fixed pulleys arranged in a block and tackle configuration, we can achieve a mechanical advantage of approximately 10, which means:

$$ E = \frac{L}{\text{MA}} = \frac{9810}{10} \approx 98.1 \, \text{N} $$

This brings the required force to around 100 N, meeting the design requirements.

Length of Rope

To lift the load by 10 meters, the individual will need to pull a length of rope that is a multiple of the height due to the increased mechanical advantage. For a mechanical advantage of 10, the length of rope $ L_r $ needed is:

$$ L_r = \text{Height} \times \text{MA} = 10 \, \text{m} \times 10 = 100 \, \text{m} $$

Detailed Steps of Operation

The individual will pull on the free end of the rope.
As the rope is pulled, the force is distributed across the pulleys, reducing the effective load per pulley.
The pulleys multiply the applied force, making it possible to lift the load with the required reduced effort.

Conclusion

This compound pulley system with a mechanical advantage of approximately 10 allows an able-bodied individual to lift a one-ton load through a height of 10 meters by exerting a manageable force of around 100 N. This design achieves the necessary force reduction while ensuring efficiency and safety in operation.