Horsepower (HP) is a unit of measurement for power, commonly used to quantify the output of engines or motors. It was originally defined by James Watt in the late 18th century to compare the output of steam engines with the power of draft horses. Today, horsepower remains a standard unit in the automotive industry for describing the power output of internal combustion engines.

The formula for calculating horsepower is:

\[ HP = \frac{Torque \times RPM}{5252} \]

Where:

- \( HP \) is Horsepower
- \( Torque \) is the rotational force, measured in pound-feet (lb-ft)
- \( RPM \) is Revolutions Per Minute, the rotational speed of the engine
- 5252 is a constant derived from the definition of horsepower

Let's calculate the horsepower for an engine with the following specifications:

- Given:
- Torque = 250 lb-ft
- RPM = 5500

- Apply the horsepower formula: \[ HP = \frac{Torque \times RPM}{5252} \]
- Substitute the known values: \[ HP = \frac{250 \text{ lb-ft} \times 5500 \text{ RPM}}{5252} \]
- Perform the calculation: \[ HP = \frac{1,375,000}{5252} \approx 261.8 \]

Let's visualize the relationship between torque, RPM, and horsepower:

This graph illustrates:

- The x-axis represents the engine's RPM
- The y-axis represents power output
- The red curve shows horsepower, which typically increases with RPM
- The blue curve shows torque, which often peaks at lower RPM than horsepower
- The point where the curves intersect is at 5252 RPM, due to the constant in the horsepower formula

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