Power (Cambridge International A-Level Physics)

Defining 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)

• You may be familiar with power ratings on household appliances, such as 60 W or 1000 W

• These power ratings tell you the amount of energy transferred electrically from the mains supply per second

Solving Problems Involving Power

• Since power describes the energy transferred or the work done per unit time, power calculations commonly include energy or work calculations, which can also include efficiency

Worked Example A car engine exerts a force of 500 N for 1.0 km over 200 s.

What is the average power developed by the engine?

Answer:

Step 1: List the known quantities and convert to SI units

• Force, F = 500 N
• Displacement, s = 1.0×10³ m
• Time, t = 200 s

Step 2: Substitute the work done equation into the power equation

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

$W=Fs$

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

Step 3: Substitute the known values to calculate

$P = \frac{500 \times ( 1.0 \times 10^{3} )}{200}$

$P=2500W$

Exam Hint Think of power as “energy per second”. Thinking of it this way will help you to remember the relationship between power and energy: “Watt is the unit of power?”