Problem 8 - University Physics with Modern Physics

Question

Which of the following is not a unit of energy? a) newton-meter b) joule c) kilowatt-hour d) \(\operatorname{kg} \mathrm{m}^{2} / \mathrm{s}^{2}\) e) all of the above

Step-by-Step Solution

Answer

A) Newton-meter B) Joule C) Kilowatt-hour D) \(\operatorname{kg} \mathrm{m}^{2} / \mathrm{s}^{2}\) E) All of the above Answer: E) All of the above

Step 1: Option A: Newton-meter

The Newton-meter (N.m) is also known as the joule (J), which is the SI unit of energy. A Newton is a unit of force and can be expressed as \(\operatorname{kg} \mathrm{m} / \mathrm{s}^{2}\). When we multiply force by the distance (meter), we get the unit of energy, which is \(\operatorname{kg} \mathrm{m}^{2} / \mathrm{s}^{2}\). Hence, the newton-meter is a unit of energy.

Step 2: Option B: Joule

As mentioned in the previous option, the joule (J) is the SI unit of energy and is equal to \(\operatorname{kg} \mathrm{m}^{2} / \mathrm{s}^{2}\). Thus, the joule is a unit of energy.

Step 3: Option C: Kilowatt-hour

The kilowatt-hour (kWh) is a unit of energy used in measuring electrical energy. It represents the amount of energy consumed by a device using 1 kilowatt (\(10^{3}\) watts) for 1 hour. A watt is a unit of power, which is equal to one joule per second. To convert kilowatt-hour into joules, we multiply by the number of seconds in an hour and the conversion factor from kilowatts to watts: \(1 \, \mathrm{kWh} = 1 \times 10^{3} \, \mathrm{W} \times 3600 \, \mathrm{s} = 3.6 \times 10^{6} \, \mathrm{J}\). Therefore, the kilowatt-hour is a unit of energy.

Step 4: Option D: \(\operatorname{kg} \mathrm{m}^{2} / \mathrm{s}^{2}\)

The unit \(\operatorname{kg} \mathrm{m}^{2} / \mathrm{s}^{2}\) is the same as the unit of the joule, which is the SI unit of energy. Hence, this option is also a unit of energy.

Step 5: Conclusion

After analyzing each option, it is clear that all of the given units are units of energy. Therefore, the correct answer is option E: "all of the above" is not a unit of energy since it implies that not any of the options is a unit of energy, but in fact, all of them are.

Key Concepts

Joule

The joule is the basic unit of energy in the International System of Units (SI). It is denoted by the symbol \( J \). The joule measures the amount of energy transferred when a force of one Newton is applied over a distance of one meter. In mathematical terms, it's equivalent to \( \text{N} \cdot \text{m} \) or \( \text{kg} \cdot \text{m}^2/ \text{s}^2 \).
This means that if you apply a force of one Newton to move an object one meter, you are using one joule of energy to do it.

• 1 joule = 1 newton-meter
• 1 joule = 1 \( \text{kg} \cdot \text{m}^2/ \text{s}^2 \)

This measurement is particularly important in physics, as it helps us understand how energy is used and transferred in various applications.

Kilowatt-hour

A kilowatt-hour (kWh) is a unit of energy commonly used to express electrical energy consumption. One kilowatt-hour equals the amount of energy consumed by running a 1,000-watt appliance for one hour.
This is particularly useful for measuring electricity consumption in homes and businesses because electrical appliances are often rated in watts.

• 1 kilowatt = 1,000 watts
• 1 kilowatt-hour = 3.6 million joules

To convert kWh into other energy units, remember that 1 kilowatt-hour equals \( 3.6 \times 10^6 \) joules. Understanding this measurement helps to interpret energy bills or plan energy usage more efficiently.

Newton-meter

The Newton-meter, abbreviated as \( \text{N} \cdot \text{m} \), is both a unit of torque and energy. In the context of energy, one Newton-meter equals one joule.
A Newton-meter represents the energy transferred when a force of one Newton moves an object one meter.
This dual use can sometimes be confusing because:

• In energy: 1 N.m = 1 joule
• In torque: Used to describe the rotational force

Despite these different contexts, when considering energy, the Newton-meter is fundamentally linked to the joule as a unit of work or energy transfer.

Energy Conversion

Energy conversion is the process of changing energy from one form to another. It is a fundamental aspect of many systems in engineering and environmental science. Understanding energy conversion helps us comprehend how energy flows in systems like engines, power plants, and even living organisms.
An example of energy conversion is in electricity generation:

• Mechanical energy of wind is converted into electrical energy in wind turbines.
• Chemical energy in fuels is converted into thermal, then mechanical and electrical energy in power plants.

Being able to interchange between units of measure is essential too. Different applications might use different units such as kilowatt-hours for electricity or joules for other types of energy, requiring conversions to understand the flow and use of energy properly.

SI Units

The International System of Units (SI) is the globally accepted standard for measurement, which includes units for energy. The SI units simplify the process of comparing and communicating measurement results worldwide.
Among the many SI units, the joule is the standard for energy.
Here are key SI units related to energy:

• The joule (J), which is \( \text{kg} \cdot \text{m}^2/ \text{s}^2 \)
• The watt (W), which is a unit of power equivalent to joule per second
• The kilowatt-hour (kWh), a derived unit for energy especially for electrical usage

SI units ensure consistency and clarity in scientific and technological communications, making it essential for anyone working with measurements to understand them.