The law of conservation of energy states that energy cannot be created or destroyed - it can only change form. A roller coaster converts gravitational potential energy into kinetic energy on the way down, and back to potential on the way up. Friction converts mechanical energy into thermal energy.
In every case, the total energy of a closed system remains constant.
Energy bar charts (also called LOL diagrams) are a visual tool for tracking these transformations. Each bar represents a type of energy before and after an event. The bars must balance: whatever disappears from one category must appear in another.
This accounting view makes it easy to spot when you've forgotten an energy form or made a calculation error.
Understanding Conservation of Energy
A conservation problem starts by choosing the system. The system might be one cart, the cart plus Earth, or a whole track setup. This choice decides which energy transfers are internal and which count as energy entering or leaving.
If a person pushes a skateboard, chemical energy in the person is transferred through work to the board. If the person is outside the chosen system, that transfer must be included.
If the person and board are both inside, it is an internal change. Clear system boundaries prevent many mistakes in energy questions.
Gravitational potential energy depends on a chosen zero height. The floor, the bottom of a ramp, or a tabletop can all serve as the reference level. A different choice changes the numerical value of potential energy, but it does not change the energy difference between two positions.
This is why an object can have negative gravitational potential energy in some calculations. Negative does not mean the object has no energy or behaves strangely.
It only means the object is below the selected reference level. Students should label the reference level before substituting heights into a calculation.
Thermal energy deserves careful attention because it is often hidden. On a rough surface, tiny bumps on two materials push, bend, and vibrate as the surfaces slide. Ordered motion of an object becomes random microscopic motion in the materials.
The object slows down, while the track, wheels, brakes, and nearby air become slightly warmer. The temperature rise may be too small to feel, yet the energy transfer is real. A bouncing ball shows a similar effect.
Each impact produces sound, deformation, and heating, so the ball returns to a lower height after each bounce. Mechanical energy is not missing. It has spread into forms that are hard to collect again.
Energy methods are useful when forces or motion are complicated. A cyclist descending a hill gains speed even when the path curves. A dropped phone converts energy during a very short collision, when acceleration is difficult to describe in detail.
In these cases, compare the initial and final states, then account for transfers such as friction, air resistance, motor work, or a spring. Keep units consistent in joules and remember that speed has a strong effect on kinetic energy. Doubling speed makes kinetic energy four times as large for the same mass.
Check whether the final speed or height is physically sensible. A negative value under a square root, or a result that exceeds the available energy, usually signals a missing transfer or an incorrect system choice.
Key Facts
- Kinetic energy: (depends on speed squared)
- Gravitational potential energy: (h measured from a reference level)
- Conservation law: (for no friction)
- Work-energy theorem: Net work done on an object equals its change in kinetic energy.
- When friction is present, some mechanical energy converts to thermal energy (heat).
- Energy is measured in joules (J); .
Vocabulary
- Kinetic energy
- Energy associated with an object's motion. KE = ½mv².
- Potential energy
- Energy stored based on an object's position or state; gravitational .
- Mechanical energy
- The sum of kinetic and potential energy in a system.
- Thermal energy
- Energy associated with the random motion of atoms and molecules; produced by friction.
- Work
- Energy transferred to an object by a force over a displacement. .
Common Mistakes to Avoid
- Setting the reference level for height incorrectly. Choose a consistent reference and stick with it - the absolute height doesn't matter, only the difference matters.
- Using conservation of energy when non-conservative forces (friction, air resistance) are present without accounting for energy lost to heat.
- Confusing power (rate of energy transfer, in watts) with energy (in joules). More time at lower power can transfer the same energy as less time at higher power.
- Squaring velocity incorrectly in . A 2x increase in speed means a 4x increase in kinetic energy.
Practice Questions
- 1 A 2 kg ball is dropped from 5 m. What is its speed just before hitting the ground? (ignore air resistance)
- 2 A roller coaster car of mass 500 kg starts from rest at a height of 30 m. What is its speed at a height of 10 m?
- 3 A 1 kg block slides down a 3 m ramp with 4 J of energy lost to friction. If it starts from rest, what is its speed at the bottom?