Energy, work and power
Energy never disappears
- At the top of a roller-coaster hill the car is slow but high; at the bottom it is fast but low.
- The energy did not vanish — it just moved from one store to another.
- This is the big idea of this lesson: energy is stored, transferred, and always conserved.
Energy stores and transfers
- Energy can be stored as: kinetic, gravitational potential, chemical, elastic (strain), nuclear, electrostatic, and internal (thermal).
- It is transferred between stores by: forces (mechanical work), electric currents, heating, and waves (such as light and sound).
- "Using energy" really means moving it from one store to another.
Select all of these that are energy stores.
Kinetic, chemical and gravitational potential are energy stores. "Loud" and "fast" describe things, but they are not energy stores.
Kinetic and potential energy
- Kinetic energy is the energy of a moving object:
- Lifting a mass by a height $\Delta h$ changes its gravitational potential energy:
- A falling object turns gravitational PE into kinetic energy.
A $2.0\ \text{kg}$ ball moves at $3.0\ \text{m/s}$. What is its kinetic energy, in J?
$E_k = \tfrac{1}{2}mv^2 = \tfrac{1}{2} \times 2.0 \times 3.0^2 = 9.0\ \text{J}$.
Conservation of energy
- The principle of conservation of energy: energy is never made or destroyed — it only moves between stores.
- Some energy is always wasted — usually spread out as heat to the surroundings.
- A Sankey diagram shows the input energy splitting into useful energy and wasted energy.
When a machine wastes energy, where does the wasted energy usually go?
Energy is conserved — it is never destroyed. Wasted energy is usually spread out as heat, which is hard to use again.
Work
- Work done equals the energy transferred. When a force moves an object along its direction:
- The unit of work and energy is the joule (J).
- Lifting a heavier load, or moving it further, does more work.
A force of $50\ \text{N}$ pushes a box $4.0\ \text{m}$ along the floor. How much work is done, in J?
$W = Fd = 50 \times 4.0 = 200\ \text{J}$.
Power and efficiency
- Power is the work done (energy transferred) each second:
- The unit is the watt (W); $1\ \text{W} = 1\ \text{J/s}$.
- Efficiency is how much of the input energy becomes useful:
- It is always less than $100\%$ because some energy is always wasted.
A motor does $200\ \text{J}$ of work in $10\ \text{s}$. What is its power, in W?
$P = \dfrac{W}{t} = \dfrac{200}{10} = 20\ \text{W}$.
A lamp takes in $50\ \text{J}$ of electrical energy and gives out $30\ \text{J}$ of useful light. What is its efficiency, in %?
efficiency $= \dfrac{\text{useful}}{\text{total}} \times 100\% = \dfrac{30}{50} \times 100\% = 60\%$.
You've got it
- $E_k = \tfrac{1}{2}mv^2$ · $\Delta E_p = mg\,\Delta h$
- energy is conserved — wasted energy usually ends up as heat
- work $W = Fd$ (joule); power $P = \dfrac{W}{t}$ (watt)
- efficiency $= \dfrac{\text{useful}}{\text{total}} \times 100\%$, always below $100\%$