Energy in Fields
How fields store energy
Do Now: You lift a book onto a high shelf. You did work on it, but the book isn’t moving. Where did the energy go?
It’s stored in the gravitational field between the book and Earth, as gravitational potential energy. Knock the book off and the field turns that energy into kinetic energy.
A. Fields Store Energy
When two objects that attract are pulled apart, you do work against the field. That energy is stored in the field as potential energy.
When they are let go, the field pulls them together and the stored energy becomes kinetic energy.
The potential energy belongs to the system (Earth + book), not to the book alone.
B. Near Earth’s Surface
A 2.0-kg book is lifted 1.5 m. How much energy is stored in the field? If it falls back down, how fast is it moving just before it lands?
m = 2.0 kg, g = 9.81 N/kg, Δh = 1.5 m
ΔPE = (2.0)(9.81)(1.5) = 29 J stored
Falling: KE = 29 J = ½(2.0)v2 → v = 5.4 m/s
C. The Same Idea Everywhere
| Situation | Field | Energy Stored When… |
|---|---|---|
| Roller coaster lift hill | Gravitational | the cars are pulled up, away from Earth |
| Water behind a dam | Gravitational | water is held high above the river |
| Opposite charges | Electric | they are pulled apart |
| Like charges | Electric | they are pushed together |
| Two magnets (N to S) | Magnetic | they are pulled apart |
Energy is stored whenever you push objects against the direction the field wants them to move.
D. Practice
How much potential energy is stored when a 60.-kg student climbs 4.0 m of stairs?
ΔPE = (60.)(9.81)(4.0) = 2,350 J (about 2.4 × 103 J)
Two positive charges are pushed closer together. Does the energy stored in their field go up or down? Why?
Up. Like charges repel, so pushing them together works against the field and stores energy. Let go and they fly apart.
Where does the kinetic energy of a falling apple come from?
From the gravitational field between the apple and Earth. Stored potential energy becomes kinetic energy as the field pulls them together.
Check Your Understanding
5 quick questions — pick an answer to see if you’re right.
1. When you lift a box, the energy you add is stored
2. Two objects that attract are pulled farther apart. Their stored potential energy
3. Two like charges are pushed closer together. Their stored energy
4. A 3.0-kg object is lifted 2.0 m. About how much energy is stored?
5. A dropped ball speeds up because