Kinetic and potential energy: motion and position
Energy is the ability to do stuff — lift, heat, move, glow. Physicists sort it into two big bins. Kinetic energy (KE) is energy of motion: anything moving has it. Potential energy (PE) is stored energy of position or condition: a stretched rubber band, a book on a high shelf, a sandwich (chemical PE).
The formulas: KE = ½mv² (mass times speed squared, halved) and gravitational PE = mgh (mass times g times height). Notice that speed is squared in KE — double your speed and your energy quadruples, which is why highway crashes are so much worse than parking-lot ones.
- KE = ½mv² — energy of motion, in joules
- PE = mgh — stored energy from height above the ground
- Speed is squared in KE: 2× speed = 4× energy
- Types of PE: gravitational (height), elastic (stretch), chemical (food, fuel)
- Energy unit: the joule (J)
Conservation of energy: the universe's budget
The law of conservation of energy says energy is never created or destroyed — only transformed. A falling book trades PE for KE: at the top it has maximum PE and zero KE; mid-fall it has some of each; just before impact, nearly all PE has become KE. The total stays constant the whole way down.
A roller coaster is conservation in action: the first hill charges the car with PE, and every later hill, loop and valley is that energy switching between PE and KE. Friction and air resistance skim off a little as heat and sound — which is why the second hill is always shorter than the first.
- Energy transforms; it never disappears
- Falling: PE → KE · being thrown upward: KE → PE
- Friction converts mechanical energy into heat
- Total energy before = total energy after (counting heat)
Drop a 1 kg ball from 20 m (use g ≈ 9.8 m/s²). PE at the top = mgh = 1 × 9.8 × 20 = 196 J. Just before impact all of that is KE, so 196 = ½(1)v² → v² = 392 → v ≈ 19.8 m/s. You found the speed without touching the motion equations.
Work and power: getting things done
In physics, work is force applied over a distance: W = Fd. Push a box with 50 N across 3 m and you do 150 J of work. Two rules keep it honest: the object has to actually move, and pushing at right angles to the motion does zero work. Holding a heavy box perfectly still is exhausting, but it does no physics work — no distance, no work.
Power is how fast you do work: P = W/t, measured in watts (1 watt = 1 joule per second). Sprinting up the stairs takes more power than strolling, even though the work is identical — same energy, less time.
- Work = force × distance (W = Fd), in joules
- No movement → no work, no matter how tired you feel
- Power = work ÷ time (P = W/t), in watts
- 1 watt = 1 joule per second
- Same job done faster = more power
You lift a 50 N box 2 m in 4 seconds. Work = Fd = 50 × 2 = 100 J. Power = W/t = 100 ÷ 4 = 25 W. Lift it in 2 seconds instead and the work is still 100 J, but the power doubles to 50 W.
Key concepts to memorize
🎯 Study tips for this topic
- Memorize the four formulas as a family: KE = ½mv², PE = mgh, W = Fd, P = W/t.
- For conservation problems, write 'energy at start = energy at end' before plugging in anything.
- Trace one full energy story out loud (toaster: electrical → heat; s'mores optional).
- Keep g as a letter until the last step — it makes canceling visible.
- Do one numeric problem per formula per day for a week and the whole chapter stops being scary.
