Problem 11 - Applied Physics

Question

What is the rating in \(\mathrm{kW}\) of a \(2.00\) -hp motor?

Step-by-Step Solution

Answer

The rating of a 2.00-hp motor is approximately 1.492 kW.

Step 1: Understand the Horsepower Unit

Before converting units, it's important to know what a horsepower (hp) represents. In terms of power, 1 horsepower is equivalent to approximately 0.746 kW.

Step 2: Use the Conversion Factor

We use the conversion factor to calculate the power in kilowatts (kW). To do this, multiply the power rating in horsepower by the conversion factor: \(2.00 \text{ hp} \times 0.746 \text{ kW/hp}\).

Step 3: Perform the Calculation

Calculate the result by performing the multiplication: \(2.00 \times 0.746 = 1.492 \text{ kW}\).

Step 4: Verify the Calculation

Ensure that the calculations are correct and that all units have been considered properly. The conversion factor used is correct, and the final result is legitimate.

Key Concepts

Horsepower to Kilowatt Conversion

Converting horsepower (hp) to kilowatts (kW) is a common task in power measurement. A horsepower is a unit of power that originated with James Watt, who used it to compare the output of steam engines to the power of draft horses. In modern terms, one horsepower is equal to approximately 0.746 kilowatts. This conversion factor is crucial for accurate power conversions.

To convert from horsepower to kilowatts, you simply multiply the number of horsepower by the conversion factor (0.746 kW/hp). This straightforward calculation allows engineers and technicians to easily compare engines, motors, and other power-generating equipment that may use different units. Always double-check the conversion factor, as slight variations might exist in different contexts, ensuring the accuracy of your calculation.

Power Measurement

Power measurement is a fundamental concept in both engineering and physics. It involves calculating how much work is done over time or determining how much energy is used per unit time. Power can be measured in various units, including watts, kilowatts, and horsepower. Understanding these units and how to convert between them is critical for those working in fields involving mechanical and electrical systems.

The basic formula for power is \[ P = \frac{W}{t} \] where \[ P \] represents power, \[ W \] is work, and \[ t \] is time. In practical contexts, power measurement helps us calculate the efficiency of systems and machines. It can also play a significant role in reducing energy consumption, as precise knowledge of power usage helps optimize the performance of equipment.

Applied Physics

Applied physics bridges the gap between pure physics theories and practical engineering tasks. It involves the use of physics concepts and methods to solve real-world problems, especially those related to power and energy. In the context of power conversions and measurements, applied physics underpins the design and analysis of systems ranging from household appliances to industrial machinery.

Understanding applied physics principles can help one make informed decisions about power selection, energy efficiency, and technical specifications of devices. For example, converting the power rating of a motor from horsepower to kilowatts can be crucial in engineering design and energy management. With applied physics, theoretical knowledge is transformed into actionable insights that enhance technology and improve everyday life. Whether in optimizing electrical systems or inventing new technologies, applied physics plays a vital role.