Forms of Energy
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 6 practice questions.
Energy comes in forms you can calculate: kinetic K = ½mv² (motion), gravitational potential Ug = mgh (height), and spring potential Us = ½kx² (stretch or compression). All are measured in joules, and a system’s mechanical energy is their sum.
1. The three forms
You choose where h = 0: the floor, the table, the ground. Only changes in potential energy matter, so any choice works as long as you stick with it.
Kinetic energy depends on v², so doubling the speed quadruples the kinetic energy. That’s why stopping distances grow so fast with speed.
2. Energy changing form
A 1 kg ball dropped from 5 m starts with Ug = (1)(10)(5) = 50 J and no kinetic energy.
Halfway down, half of that has become kinetic energy. Just before it lands, all 50 J is kinetic.
Bar charts like these are a fast way to track energy, and they show up on AP free-response questions.
3. Example, then try it
A 1200 kg car moves at 20 m/s. What is its kinetic energy? What if it goes 40 m/s?
K = ½(1200)(20)² = 240,000 J.
At 40 m/s: K = ½(1200)(40)² = 960,000 J, four times as much for twice the speed.
A 2.0 kg ball is dropped from 5.0 m above the ground. How fast is it moving when it is 2.0 m above the ground? (Ignore air resistance; g = 10 N/kg.)
Start: Ug = mgh = (2.0)(10)(5.0) = 100 J; K = 0. Total = 100 J.
At 2.0 m: Ug = (2.0)(10)(2.0) = 40 J.
Kinetic energy there: K = 100 − 40 = 60 J.
Speed: ½(2.0)v² = 60 → v² = 60 → v ≈ 7.7 m/s.
Answer: about 7.7 m/s. (Check with kinematics: v² = 2gΔy = 2(10)(3.0) = 60. ✓)
4. Common mistakes
Cars A and B have the same mass. Car A moves three times as fast as car B. How does A’s kinetic energy compare with B’s?
K = ½mv². With the same mass, tripling v multiplies v² by 3² = 9, so A has 9 times the kinetic energy.
Ready to practice?
6 questions on Forms of Energy, each with a hint and an explanation for every wrong answer.