Problem 12 - Applied Physics

Question

A wattmeter shows that a motor is drawing \(2200 \mathrm{~W}\). What horsepower is being delivered?

Step-by-Step Solution

Answer

The motor delivers approximately 2.95 horsepower.

Step 1: Understand the relationship between watts and horsepower

Horsepower (hp) is a unit of power in the Imperial system, whereas watts (W) are in the metric system. To convert watts to horsepower, we can use the conversion factor: 1 horsepower is approximately equal to 746 watts.

Step 2: Set up the conversion

Given that the motor is drawing 2200 watts, we can use the relationship between watts and horsepower to set up the conversion: \[ \text{Horsepower} = \frac{\text{Watts}}{746} \]

Step 3: Perform the calculation

Substitute 2200 W into the conversion formula { \[ \text{Horsepower} = \frac{2200 \, \text{W}}{746} \approx 2.95 \text{ hp} \] This tells us the equivalent power in horsepower.

Key Concepts

Watt to Horsepower Conversion

To comprehend watt to horsepower conversion, we first need to acknowledge that these are units of power measurement in different systems. Watts (W) are a standard unit of power in the metric system, quite prevalent globally, and commonly used for measuring electric power. Horsepower (hp), on the other hand, is a unit from the Imperial system, traditionally used in the United States to refer to the power output of engines and motors.

The conversion between these units is straightforward once we know the conversion factor, which is crucial for moving between these two power values. As mentioned, 1 horsepower is approximately equal to 746 watts. So, to convert watts into horsepower, the formula is relatively simple: divide the wattage by this conversion factor:

• \[ \text{Horsepower} = \frac{\text{Watts}}{746} \]

Using this understanding, anyone can convert watt measurements (say, from an electric motor) into horsepower, making it easier to compare power ratings across different systems. This conversion finds practical use especially in contexts involving international product specifications or when dealing with varied equipment standards.

Imperial and Metric Units

Imperial and Metric units are two predominant measurement systems used around the world. Each serves unique purposes and is based on different standards. The Metric system, using units like meters for distance, kilograms for weight, and watts for power, is widespread in most countries due to its simplicity and uniformity. The Metric system is decimal-based, making calculations straightforward and conversions among units consistent.

In contrast, the Imperial system, which uses units like pounds for weight, inches for length, and horsepower for power, is mainly used in the United States and a few other countries. This system isn't as uniform as its metric counterpart, often requiring specific conversion factors, like in the case of watts to horsepower conversion, making it a bit more challenging for certain calculations.

• Metric System:
  • Meters, grams, watts
• Imperial System:
  • Feet, pounds, horsepower

Understanding these units is essential not just in academic contexts, but also in daily applications, such as buying appliances, measuring building materials, or calculating fuel costs. Recognizing how to transition between these systems enhances precision and reduces errors in professional and personal scenarios.

Electric Motor Power Measurement

Electric motor power measurement is a vital aspect of both engineering and everyday applications. Being able to measure how much power a motor is producing or consuming gives us insight into its efficiency, capability, and potential energy consumption costs. The two common units used for expressing power—watts and horsepower—help quantify an electric motor's performance in both the metric and Imperial systems respectively.

A wattmeter is a tool often used to determine a motor's power draw in watts. Knowing this value is the first step in assessing or comparing motor efficiency. For instance, the exercise provided involves an electric motor drawing 2200 watts. To understand this power level in terms of the Imperial system, a conversion to horsepower is necessary, providing a clearer picture of the motor's capacity for those familiar with that unit.

• Common Measurement Units:
  • Watts (W)
  • Horsepower (hp)
• Measurement Tools:
  • Wattmeter

By understanding how electric motor power is measured, individuals and professionals can make informed decisions when selecting or maintaining equipment, ensuring the right power output for the needed task while keeping energy consumption under control.