The velocity ratio of a single fixed pulley is always 1.
This fundamental characteristic means that the distance the effort force travels is exactly equal to the distance the load moves. A single fixed pulley is a simple machine primarily used to change the direction of the force applied, rather than to provide a mechanical advantage (force multiplication).
Understanding Velocity Ratio (VR)
The velocity ratio (VR) is a theoretical measure of a machine's performance, calculated as the ratio of the distance moved by the effort to the distance moved by the load. It is a dimensionless quantity and does not account for friction or other energy losses.
- Formula:
$$VR = \frac{\text{Distance moved by effort (d}_E)}{\text{Distance moved by load (d}_L)}$$
Why is the Velocity Ratio of a Single Fixed Pulley 1?
In a single fixed pulley system, the rope passes over a wheel that is attached to a fixed support. When you pull one end of the rope (effort), the other end (load) moves an equivalent distance.
Consider these points:
- Equal Rope Segments: For every unit of length you pull down on the effort side, the load side of the rope moves up by the exact same unit of length.
- Direct Translation: There is a direct 1:1 relationship between the movement of the effort and the movement of the load. If you pull 1 meter of rope, the load lifts 1 meter.
Therefore:
- Distance moved by effort (d$_E$) = 1 unit
- Distance moved by load (d$_L$) = 1 unit
- $$VR = \frac{1 \text{ unit}}{1 \text{ unit}} = 1$$
Practical Implications and Characteristics
While the velocity ratio of a single fixed pulley is consistently 1, indicating no multiplication of distance or speed, its utility lies in other areas:
- Changing Direction of Force: This is its primary advantage. It allows you to pull downwards to lift a load upwards, which can be more convenient and safer due to gravity assisting your pulling motion.
- Ease of Use: It simplifies lifting tasks by redirecting the force, making it easier to leverage body weight.
- Mechanical Advantage (MA):
- Ideally, the mechanical advantage (MA) of a single fixed pulley is also 1 (MA = Load / Effort). This means the force you apply is equal to the force needed to lift the load.
- However, in real-world scenarios, due to friction in the pulley's axle and the weight of the rope, the actual mechanical advantage is typically slightly less than 1. This means you need to exert slightly more force than the weight of the load to lift it.
- It is also notable that for a single fixed pulley, the velocity ratio is always less than the mechanical advantage.
Comparison Table: Single Fixed Pulley
| Characteristic | Value | Description |
|---|---|---|
| Velocity Ratio | 1 | Effort distance equals load distance. |
| Mechanical Advantage (Ideal) | 1 | Effort force equals load force (ignoring friction). |
| Primary Use | Change direction of force | Does not multiply force or distance. |
Common Applications
Single fixed pulleys are widely used in everyday life due to their simplicity and ability to redirect force. Examples include:
- Flagpoles: Allowing a person to stand on the ground and pull a rope downwards to raise a flag.
- Window Blinds: Facilitating the raising and lowering of blinds by pulling a cord.
- Well Buckets: Making it easier to draw water from a well by pulling down on a rope to lift the bucket.
- Gym Equipment: Certain weight machines utilize fixed pulleys to guide cables and redirect resistance.
In summary, the velocity ratio of a single fixed pulley remains consistently 1, highlighting its role in altering the direction of force rather than amplifying it.
