Power
You should be able to describe the transfer of energy into, out of, or within a system in terms of power.
Power
Power is the time rate of change of energy: \[\begin{align} \text{power} &= \dfrac{\Delta \text{work or energy}}{\Delta \text{time}} \\ P &= \dfrac{\Delta W}{\Delta t} \end{align}\]
Power is the rate at which energy changes with respect to time, either by transfer into or out of a system or by conversion from one type to another within a system. It is measured in watts (W) , which is defined as \(\qty{1}{\watt} = \qty{1}{\joule\per\second}\). Other units used to measure power, especially in engineering practice in the United States, include horsepower (hp) and British thermal unit per hour (BTU/hr).
To help calibrate your understanding of power, the resistors you might have handled in electronics class are typically 1/8 or 1/4 watt. An old school incandescent lightbulb, of the sort no longer made, power might be 45 W or 60 W. Your microwave oven might be 1000 W. The propulsion power output of RMS Titanic was 46,000 shaft horsepower or 33.8 MW. A small reactor in a commercial nuclear power plant might be 1000 MW ( th ). The power output of the sun is 3.8 × 1026 W.
When you buy a computer charger that provides 30 W, it means it is able to supply 30 J of energy every second. A phone charger that supplies 15 W can only supply half the amount of energy per second as the 30 W charger, for example.
Average power
Average power is the amount of energy being transferred or converted, divided by the time it took for that transfer or conversion to occur. \[\begin{equation} P_{avg} = \dfrac{\Delta E}{\Delta t} \end{equation}\]
Because work is the change in energy of an object or system due to a force, average power is the total work done, divided by the time during which that work was done. \[\begin{equation} P_{avg} = \dfrac{dW}{dt} \end{equation}\]
Estimate the power
An electromagnetic aircraft launching system must supply 100 MJ to launch a single F-18. If it is desired to launch one F-18 per minute, what is the minimum power required? \[\begin{align} P &= \dfrac{\Delta W}{\Delta t} \\ &= \dfrac{\qty{100}{\mega\joule}}{\qty{60}{\second}} \\ &= \qty{1.7}{\mega\watt} \end{align}\]
Power, force, and velocity
Recall that work is the product of force and distance, so that \[\begin{align} \text{power} &= \dfrac{\Delta \text{work}}{\Delta \text{time}} \\ &= \dfrac{\Delta (\text{force} \cdot \text{distance})}{\Delta \text{time}} \\ &= \text{force} \dfrac{\Delta \text{distance}}{\Delta \text{time}} \\ &= \text{force} \cdot \text{velocity}\\ P &= F\cdot v. \end{align}\]
The instantaneous power delivered to an object by the component of a constant force parallel to the object’s velocity can be described with the derived equation \[\begin{equation} P_{avg} = F_{||} v = F v \cos{\theta} \end{equation}\]
Estimate the power
A small shipboard electric propulsion system generates 100000 N of thrust while traveling at 2.6 m s−1. Estimate the power. \[\begin{align} P &= F\cdot v \\ &= \qty{100000}{\newton}\cdot\qty{2.6}{\meter\per\second}\\ &= \qty{260}{\kilo\watt} \end{align}\]
See also
- list here
Comments
Power is commonly used in engineering to understand how big a system has to be; a system that has high power is generally larger than a system that has low power. For example, think about the size of a 100 W stereo compared to a 5 W stereo; or think about a 800 W computer power supply compared to a 15 W phone charger.
A small amount of power might be only a few mW. On the other hand, a large generating station might have a power rating of hundreds of MW or even GW.