Mechanical advantage, velocity ratio and efficiency of a fixed pulley

Mechanical Advantage, Velocity Ratio, and Efficiency of a Fixed Pulley

While using a fixed pulley to lift a load, the tension along the entire rope between the effort and the load is the same. Therefore, the weight of the load and the effort needed to lift it are the same. If the load is lifted through a distance of 2 metres, the effort used to lift the load will move down a distance of 2 metres. In this case, the fixed pulley has a mechanical advantage and velocity ratio equal to one.

Example Problem

While using a fixed pulley, a 60 kg load was lifted up through 1 m and the effort moved 1 m down.

Given:

• Load = 60 kg
• Distance moved by the load = 1 m
• Distance moved by the effort = 1 m

Required: To determine the effort, mechanical advantage, velocity ratio, and efficiency.

(a) Calculation of the Effort

Formula: $\text{Effort} = \text{Load}$ $\text{Effort} = 60 \text{ kg}$ Therefore, the effort is 60 kg.

(b) Calculation of Mechanical Advantage

Formula: $\text{Mechanical Advantage} = \frac{\text{Load}}{\text{Effort}}$ $\text{Mechanical Advantage} = \frac{60}{60}$ $\text{Mechanical Advantage} = 1$ The mechanical advantage of the fixed pulley is 1.

(c) Calculation of Velocity Ratio

Formula: $\text{Velocity Ratio} = \frac{\text{Distance moved by effort}}{\text{Distance moved by load}}$ $\text{Velocity Ratio} = \frac{1}{1}$ $\text{Velocity Ratio} = 1$ The velocity ratio of the fixed pulley is 1.

(d) Calculation of Efficiency

Formula: $\text{Efficiency} = \left( \frac{\text{Mechanical Advantage}}{\text{Velocity Ratio}} \right) \times 100\%$ $\text{Efficiency} = \left( \frac{1}{1} \right) \times 100\%$ $\text{Efficiency} = 100\%$ Therefore, for a fixed pulley:

• Mechanical Advantage = 1
• Velocity Ratio = 1
• Efficiency = 100%

However, due to friction between the rope and the wheel of the fixed pulley, the efficiency is always slightly less than 100% in real-world applications.