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3.5 Power

Section 1 of 2

Power

Interactive Content
Note: All content in this lesson is interactive. Hover over the glowing blue terms to learn more about a Vocabulary term. Hover over the icons to learn more about a Key Formula or Graph. Hover over any line, point, or curve on any graph or diagram to learn more about it.

Power is the rate at which work is done or energy is transferred. Power tells us how quickly energy is used or work is completed. Power is a scalar, measured in units of Watts (W), and represented with the variable P.

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

  • Pavg{P_{avg}}
    represents the average power exerted on a system,
  • Δt{\Delta t}
    is the duration of time over which the power was exerted,
  • W{W}
    is the work done onto the system, and
  • ΔE{\Delta E}
    is the change in energy of the system



For example, if 50 J of work is done in a window of 2 s, the power exerted will be 25 W. This also means that the object that the work was done on has gained 50 J in the 2 s.

To find the instantaneous power, you can change manipulate the average power equation to find that

P=FdcosθΔt{P = \frac{Fdcos\theta}{\Delta t}}
. At an instantaneous moment,
dΔt{\frac{d}{\Delta t}}
is the velocity of the object.

Simplifying it all, we get the below equation. It is important to note that this equation only works to find the power exerted at a single moment.
P_{inst} = Fvcos\theta

  • Pinst{P_{inst}}
    represents the instantaneous power exerted on a system,
  • F{F}
    is the force exerted onto the system,
  • v{v}
    is the velocity of the system
  • θ{\theta}
    is the angle between the force and velocity vectors



It is important to note that this equation only works to find the power exerted at an instantaneous moment or to find the power exerted on an object that is moving at a constant velocity.

MCQ Reading Checkpoint

Which object exerts the most power?

Choose the best option:
A

A car moving at a constant speed on the highway (ignoring friction)

B

An electron being accelerated to double its initial velocity

C

A horse running at a constant speed (friction included)

D

A crane lifting a very heavy block at a constant speed upward
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