AP Physics 1- 3.5 Power- Study Notes- New Syllabus

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. (3.5.A.1)

Average Power:

The amount of energy transferred or converted divided by the time interval:

\( P_\text{avg} = \dfrac{\Delta E}{\Delta t} \)

Because work is the change in energy due to a force, average power can also be expressed as: 

\( P_\text{avg} = \dfrac{W}{\Delta t} \)

Instantaneous Power:

The power delivered to an object by the component of a constant force parallel to the object’s velocity:

\( P = \vec{F} \cdot \vec{v} = F v \cos\theta \), where \( \theta \) is the angle between force and velocity vectors.

Power is a scalar quantity, even though it depends on vector quantities like force and velocity.

• The SI unit of power is the Watt (W): \( 1 \, \text{W} = 1 \, \text{J/s} \).

High power implies rapid energy transfer or conversion; low power implies slow transfer.

• For systems with variable forces or velocity, instantaneous power is more useful than average power.

Power can be positive or negative:

• • Positive power: Force and velocity components in the same direction → energy added to system.
  • Negative power: Force and velocity components in opposite directions → energy removed from system (e.g., braking).

In mechanical systems, the efficiency can be expressed in terms of power:

\( \text{Efficiency} = \dfrac{\text{useful power output}}{\text{total power input}} \times 100\% \)