In a simple system, you track how much energy is in each store at the start and at the end, then show where any difference went. The total energy is conserved: it never disappears, it moves between stores.
This lesson builds on calculating work along a displacement, because doing work is one way energy moves from store to store. It also supports power and energy resources.
How do I follow energy through a system?
Use a simple four-step routine.
- List the stores at the start. For a ball held high, this is gravitational potential energy.
- List the stores at the end. For the ball just before landing, this is mainly kinetic.
- Name the transfer. Falling is a mechanical transfer by the force of gravity.
- Check for any extra store. With air resistance, some energy also goes to the thermal store.
The two formulas you need are:
- Change in gravitational potential energy = mgh (mass in kg, g = 10 N/kg, height change in m).
- Kinetic energy = ½mv² (mass in kg, speed in m/s).
Worked example
A ball of mass 0.50 kg is dropped from a height of 3.0 m. Take g = 10 N/kg and ignore air resistance. Find its speed just before it lands. (Invented example data.)
Step 1, gravitational potential energy lost. mgh = 0.50 × 10 × 3.0 = 15 J.
Step 2, apply conservation. With no air resistance, all 15 J becomes kinetic energy, so KE = 15 J.
Step 3, use KE = ½mv². 15 = ½ × 0.50 × v², so 15 = 0.25 × v².
Step 4, solve. v² = 15 ÷ 0.25 = 60, and v = √60 = 7.7 m/s (2 significant figures).
Step 5, check. ½ × 0.50 × 7.75² ≈ 15.0 J, which matches.
Now suppose a measurement shows the ball lands with 12 J of kinetic energy. The missing 3 J went to the thermal store of the air and ball, and some to sound. The total is still 15 J.
What mistake should I watch for?
A very common slip is to forget to square the speed or to forget the ½.
Mistaken answer: The KE of a 2.0 kg trolley at 3.0 m/s is ½ × 2.0 × 3.0 = 3.0 J.
The student multiplied by the speed but never squared it.
The correction: KE = ½ × 2.0 × 3.0² = ½ × 2.0 × 9.0 = 9.0 J. Squaring comes before multiplying by ½m. A quick sanity check is that doubling the speed should quadruple the kinetic energy.
Check yourself
Try these without a calculator, then open each answer. Use g = 10 N/kg.
1. A pendulum bob is released from its highest point. Name the main energy store at the highest point, at the lowest point, and where the small energy loss goes.
Show answer
Top: gravitational potential (and momentarily no kinetic). Lowest point: mainly kinetic. The small loss goes to the thermal store of the air and pivot.
2. Find the kinetic energy of a 2.0 kg trolley moving at 4.0 m/s.
Show answer
KE = ½ × 2.0 × 4.0² = ½ × 2.0 × 16 = 16 J.
3. A 0.20 kg stone is thrown straight up at 10 m/s. Ignoring air resistance, what is its maximum height?
Show answer
KE at start = ½ × 0.20 × 10² = 10 J. At the highest point, all of it is gravitational potential energy: 0.20 × 10 × h = 10, so h = 5.0 m.
Where this leads next
With energy tracked between stores, you can ask how much of it is useful. Calculate efficiency with consistent quantities does exactly that. The mistake log and retest queue is useful when you want to keep a record of which store or formula you keep mixing up.
If you can do each step but the setup of a new system still feels uncertain, our teachers in online one-to-one Physics tuition can build fresh systems with you until the routine is automatic.