3.5 Power

Learning objectives

3.5A—Describe the transfer of energy into, out of, or within a system in terms of powerDescribe the transfer of energy into, out of, or within a system in terms of power.• 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.• Average power is the amount of energy being transferred or converted, divided by the time it took for that transfer or conversion to occur. Relevant 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. Relevant equation:• 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. TOPIC 4.1 Linear Momentum

Read power as a rate

Power is the rate at which energy is transferred into or out of a system, or converted from one form to another within it. The SI unit is the watt: $1\,\text{W}=1\,\text{J/s}$ .

$P_{\text{avg}}=\frac{\Delta E}{\Delta t}=\frac{W}{\Delta t}$

Calculate an interval average

Worked example: A force transfers $600\,\text{J}$ of energy to a system in $3.0\,\text{s}$ .

$P_{\text{avg}}=\dfrac{600\,\text{J}}{3.0\,\text{s}}=200\,\text{W}$ .

On average, energy entered the system at $200\,\text{J}$ each second during that interval.

Connect force and velocity

At one instant, a constant force delivers power according to

$P_{\text{inst}}=F_{\parallel}v=Fv\cos\theta,$

where $\theta$ is the angle between force and velocity. A perpendicular force has $F_{\parallel}=0$ and delivers zero instantaneous power, even if it changes the direction of motion.

Separate power from energy

Power and energy are not interchangeable. A high-power transfer can move a given amount of energy in less time; it does not necessarily transfer more total energy unless the time interval is also known. Average power describes an interval, while instantaneous power describes one moment.

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—AP Physics 1Read