power
Summary
Power is the rate at which work is done or energy is transferred, measured in watts (1 W = 1 J/s). The most testable point is that power depends on time as well as work: the same work done faster takes more power.
Detail
Meaning: Power is the rate of doing work or transferring energy. Two machines can do the same work, but the one that finishes in less time has the greater power. Average power is total work divided by elapsed time. For a force acting on a moving object, power depends on the part of the force along the motion, so a force perpendicular to the velocity delivers no power.
Equation: P = W/t = ΔE/t = Fv cosθ. P is power (watt, W = J/s), W is work (joule, J), ΔE is energy transferred (J), t is time (s), F is force (N), v is speed (m/s), θ is the angle between the force and the velocity. In circuits, P = IV = I²R = V²/R, where I is current (A), V is potential difference (V) and R is resistance (Ω).
On the MCAT: Expect the power needed to lift a load at constant speed (P = mgv), the power output of a person climbing stairs, or the power dissipated by a resistor. For a resistor, choose the form that matches what is held constant. With fixed voltage, doubling R halves P. With fixed current, doubling R doubles P.
Common confusion: Power and energy are different quantities. The kilowatt-hour on an electric bill is a unit of energy (3.6 × 10⁶ J), not power. More work does not mean more power unless the time is the same or shorter.
Sources
- Physics (Giancoli)
- Fundamentals of Physics (Halliday, Resnick, Walker)
- College Physics (Knight, Jones, Field)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.