Question

Which of the following is a correct unit of power? a) $\mathrm{kg}\mathrm{m}/{\mathrm{s}}^2$ c) J e) $W$ b) $N$ d) $\mathrm{m}/{\mathrm{s}}^2$

Short answer

a) $\mathrm{kg}\mathrm{m}/{\mathrm{s}}^2$ b) $N$ c) J d) $\mathrm{m}/{\mathrm{s}}^2$ e) $W$ Answer: e) $W$

Step-by-step solution

Review the formula for power

Recall the formula for power: $P=\frac{W}{t}$. Knowing that work, $W$, has units of Joules (J) and time, $t$, has units of seconds (s), we can derive the unit for power as follows: $$\mathrm{Unit}\mathrm{of}\mathrm{power}=\frac{\mathrm{Unit}\mathrm{of}\mathrm{work}}{\mathrm{Unit}\mathrm{of}\mathrm{time}}$$

Determine work and time units

Work is measured in Joules, which is equivalent to Newton meters ($\mathrm{N}\cdot \mathrm{m}$). Time is measured in seconds (s).

Calculate the unit of power

Using the units for work and time, we can derive the unit for power: $$\mathrm{Unit}\mathrm{of}\mathrm{power}=\frac{\mathrm{Joules}}{\mathrm{seconds}}=\frac{\mathrm{N}\cdot \mathrm{m}}{\mathrm{s}}$$

Express the unit of power in base units

In order to compare the obtained unit of power to the given options, we must express it in terms of base units. Recall that the unit of force, Newton (N), can be expressed as $\mathrm{kg}\cdot \mathrm{m}/{\mathrm{s}}^2$. Substituting this expression into the previous equation, we get: $$\mathrm{Unit}\mathrm{of}\mathrm{power}=\frac{\mathrm{kg}\cdot \mathrm{m}/{\mathrm{s}}^2\cdot \mathrm{m}}{\mathrm{s}}=\mathrm{kg}\cdot {\mathrm{m}}^2/{\mathrm{s}}^3$$

Compare the derived unit with the given options

Now, we can compare the derived unit of power ($\mathrm{kg}\cdot {\mathrm{m}}^2/{\mathrm{s}}^3$) with the given options: a) $\mathrm{kg}\mathrm{m}/{\mathrm{s}}^2$ c) J e) $W$ b) $N$ d) $\mathrm{m}/{\mathrm{s}}^2$ The unit Watt (W) is used to represent power, and 1 Watt is equal to 1 $\mathrm{kg}\cdot {\mathrm{m}}^2/{\mathrm{s}}^3$. Therefore, the correct unit of power in this list of options is:

Conclusion

e) $W$

Key concepts

Physics Education

Physics education dives deep into understanding the nature and properties of energy and matter, with power being a fundamental concept.

To help students like you anchor this concept, one begins with hands-on experience. Imagining physically putting an effort over a set duration helps illustrate power. For example, when you push a box across the floor, you're doing work over a period of time, which involves using power.

The goal in physics education is to translate real-world experiences to mathematical equations, which then can be applied to a wide array of problems, giving students tools to solve complex tasks by breaking them down to basic principles.

Work and Energy

In the realm of physics, 'work' refers to the effect of a force acting over a distance, while 'energy' is the ability to do work. The concept is crucial because it forms the basis for understanding power.

Why Understanding Work and Energy Is Important

When you lift an object or throw a ball, you're exerting a force over a distance, which is essentially 'work'. The energy you use is essentially 'transferred' to the object. This transfer of energy, quantified by 'work', is measured in joules (J).

Understanding this lays the groundwork for comprehending how power, the rate at which work is done over time, is calculated. If you do the same work in less time, you demonstrate greater power, highlighting the importance of defining power in terms of both work and time.

SI Units

The International System of Units (SI) is a standardized system of measurement used globally in science and industry. It provides a common language for scientists and technicians to communicate their findings and specifications clearly.

The Importance of SI Units in Physics

SI Units help ensure consistency in the recording and exchange of scientific information. The standard unit of power in the SI system is the watt (W), named after James Watt, the inventor of the steam engine. A watt is defined as one joule of work per second ($1W=1\frac{J}{s}=1\frac{kg\times m^2}{s^3}$), aligning the practical applications of physics with a universally understood system of measurement.