Mechanical advantage, velocity ratio and efficiency of a movable pulley

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

When using a movable pulley to lift a load, two pulleys are required. The tension in all parts of the rope is the same, which means the effort needed to lift the load in part A of the rope is equal to the effort needed to lift the load in part B of the rope. Both efforts combine to lift the load.

A two-pulley system

1. Effort in part A + Effort in part B = Load
2. Effort + Effort = Load
3. 2 × Effort = Load
4. Effort = ½ × Load

Thus, the effort needed to lift the load is half the load. As the number of movable pulleys in a system increases, the effort required to lift the load decreases.

Mechanical Advantage (MA)

The mechanical advantage of the movable pulley in this system is 2, as the effort is halved compared to the load.

Velocity Ratio (VR)

Similarly, the distance moved by the load is half the distance moved by the effort when lifting the load:

1. Distance moved by load = ½ × Distance moved by effort
2. Distance moved by effort = 2 × Distance moved by load

Thus, the velocity ratio of the movable pulley is 2.

Example 1

Calculate the effort needed to lift an 800-kilogram load using a movable pulley.

Solution:

Formula: $\text{Effort} = \frac{1}{2} \times \text{Load}$

Given: Load = 800 kg

Required: Effort

$\text{Effort} = \frac{1}{2} \times 800$ $\text{Effort} = 400 \text{ kg}$

Therefore, the effort is 400 kg.

Example 2

Calculate the load when the effort used to lift the load using a movable pulley is 350 kg.

Solution:

Formula: $\text{Load} = 2 \times \text{Effort}$

Given: Effort = 350 kg

Required: Load

$\text{Load} = 2 \times 350$ $\text{Load} = 700 \text{ kg}$

Therefore, the weight of the load is 700 kg.

Example 3

Calculate the distance moved by the load when the distance moved by the effort while lifting the load is 2 metres.

Solution:

Given: Distance moved by the effort = 2 m

Required: Distance moved by the load

Formula: $\text{Distance moved by the load} = \frac{1}{2} \times \text{Distance moved by the effort}$ $\text{Distance moved by the load} = \frac{1}{2} \times 2$ $\text{Distance moved by the load} = 1 \text{ m}$

Example 4

Find the mechanical advantage and velocity ratio of a movable pulley.

Solution:

From Example 1:

Given: Load = 800 kg Effort = 400 kg

Required: Mechanical advantage

Formula: $\text{Mechanical advantage} = \frac{\text{Load}}{\text{Effort}}$ $\text{Mechanical advantage} = \frac{800}{400}$ $\text{Mechanical advantage} = 2$

Thus, the mechanical advantage of the movable pulley is 2.

From Example 3:

Given: Distance moved by the effort = 2 m Distance moved by the load = 1 m

Required: Velocity ratio

Formula: $\text{Velocity ratio} = \frac{\text{Distance moved by effort}}{\text{Distance moved by load}}$ $\text{Velocity ratio} = \frac{2}{1}$ $\text{Velocity ratio} = 2$

Therefore, for a movable pulley, the mechanical advantage is 2, and the velocity ratio is also 2. This suggests that the efficiency of the pulley system is 100%. However, in practice, due to friction between the rope and pulley, the actual efficiency is always less than 100%.