Conservation of Energy

Kinetic, Potential, and Thermal Energy

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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.

Key Facts

Kinetic energy: $KE = \frac{1}{2}mv^2$ (depends on speed squared)
Gravitational potential energy: $GPE = mgh$ (h measured from a reference level)
Conservation law: $KE_i + GPE_i = KE_f + GPE_f$ (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); $1 \text{ J} = 1 \text{ kg} \cdot \text{m}^2/\text{s}^2$ .

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 $PE = mgh$ .
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. $W = F \cdot d \cdot \cos \theta$ .

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 $KE = \frac{1}{2}mv^2$ . 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?

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