solve problems using P = W / t

Energy Conservation ⚡

In physics, energy conservation means that the total energy in a closed system remains constant. Think of a water tank: the amount of water stays the same unless you add or remove it. Similarly, energy can change form (from kinetic to potential, from chemical to electrical), but the total amount stays the same.

Power – The Rate of Energy Transfer

Power tells us how fast energy is being used or transferred. The basic formula is:

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

  • \$P\$ = Power (watts, W)

  • \$W\$ = Work or Energy (joules, J)

  • \$t\$ = Time (seconds, s)

If you do 100 J of work in 5 s, the power is:

  1. Identify \$W = 100\$ J and \$t = 5\$ s.

  2. Apply the formula: \$P = \dfrac{100}{5} = 20\$ W.

That means you’re using energy at a rate of 20 joules every second – like a lightbulb that consumes 20 watts of power.

Step‑by‑Step Problem Solving

  1. Read the problem carefully and pick out the values for \$W\$ and \$t\$.

  2. Check the units – they must be joules for \$W\$ and seconds for \$t\$.

  3. Plug the numbers into \$P = W/t\$.

  4. Perform the division and write the answer with the correct unit (W).

Example Problems

ProblemGivenPower \$P\$
A 60 W lightbulb runs for 2 h.\$W = 60\,\text{J/s} \times 7200\,\text{s}\$\$P = 60\$ W (constant)
A car does 5 MJ of work in 300 s.\$W = 5\times10^6\$ J, \$t = 300\$ s\$P = \dfrac{5\times10^6}{300} \approx 16667\$ W
A battery supplies 200 J of energy in 10 s.\$W = 200\$ J, \$t = 10\$ s\$P = 20\$ W

Practice Problem

A cyclist uses 120 kJ of energy to climb a hill in 15 minutes. What is the average power output of the cyclist? 🚴‍♂️

Solution

  1. Convert time to seconds: \$15\,\text{min} = 900\,\text{s}\$.

  2. Use \$P = W/t\$: \$P = \dfrac{120\,000}{900} \approx 133.3\$ W.

  3. Answer: The cyclist’s average power is about \$133\$ W.

Great job! Remember, power is just how fast you’re using energy. Keep practicing and you’ll master energy conservation in no time. 🌟