Power (OCR AS Physics): Revision Note

Power

• Power is defined as:

The rate of energy transfer

• Since work done is equal to the energy transferred, power can also be defined as:

Work done per unit time

• Power can be calculated using the following equations:

$P=\frac{E}{t}=\frac{W}{t}$

• Where:

  • P = power in watts (W)

  • E = energy in joules (J)

  • W = work done in joules (J) or newton metres (N m)

  • t = time in seconds (s)

• Power is also used in electricity, with labels on lightbulbs which indicate their power, such as 60 W or 100 W

  • These indicate the amount of energy transferred by an electrical current rather than by a force doing work

The Watt

• The watt (W) is the unit for power (and radiant flux)

  • It is defined as 1 W = 1 J s^-1

• In SI base units, the watt is kg m² s^–3

• One watt is defined as:

A transfer of energy of 1 J in 1 s

Power & Force

• If an object is moving at constant velocity with a constant force, the power can be calculated by:

$P=Fv$

• Where:

  • $F$ = force (N)

  • $v$ = velocity (m s^–1)

• This equation is only relevant where a constant force moves a body at constant velocity

• Power is required in order to produce an acceleration

• The force must be in the direction of the velocity

  • Otherwise, the component of the force in the direction of the velocity must be used instead

Derivation of P = Fv

• Power is the rate of doing work

$P=\frac{W}{t}$

• Work is done when a force moves an object over a distance

$W=Fs$

• At a constant velocity, the distance moved by the object can be described as:

$d=vt$

• Substituting this into the work done equation gives:

$W=Fvt$

• And substituting this into the power equation gives:

$P=\frac{Fv\bcancel{t}}{\bcancel{t}}$

$P=Fv$