Conservation of Energy - AP Physics C: Mechanics

$E_{\text{initial}} = E_{\text{final}}$. States that initial total energy equals final total energy in isolated systems.

$PE = mgh$. Energy due to position in gravitational field, proportional to height.

Joule (J). Standard unit for all forms of energy in physics.

Kinetic and potential energy. Mechanical energy is the sum of these two energy types.

Total mechanical energy remains constant if only conservative forces act. No energy is lost when only conservative forces do work.

Maximum potential energy. At maximum height, all energy is potential with zero velocity.

Decreases. Kinetic energy is proportional to velocity squared.

$9 \text{ J}$. Using $KE = \frac{1}{2}mv^2 = \frac{1}{2}(2)(3)^2 = 9$ J.

$490 \text{ J}$. Using $PE = mgh = (5)(9.8)(10) = 490$ J.

$2 \text{ m/s}$. Solving $8 = \frac{1}{2}(2)v^2$ gives $v = 2$ m/s.

$1 \text{ kg}$. Solving $50 = m(10)(5)$ gives $m = 1$ kg.

No energy loss to friction. Energy conservation requires no dissipative forces like friction.

Sum of kinetic and potential energy. Total mechanical energy equals $KE + PE$.

Joule (J). Standard unit for all forms of energy in physics.

$0 \text{ J}$. No motion means no kinetic energy present.

Potential to kinetic energy. Elastic potential energy converts to kinetic energy when spring extends.

Potential to kinetic energy. Gravitational potential energy converts to kinetic energy during fall.

Gravitational force. Conservative forces allow energy to be recovered completely.

Potential to kinetic energy. Gravitational potential energy converts to kinetic energy as object falls.

Potential to kinetic energy. Gravitational potential energy converts to kinetic energy during fall.

Gravitational force. Conservative forces allow energy to be recovered completely.

$500 \text{ J}$. Using $PE = mgh = (10)(10)(5) = 500$ J.

Sum of kinetic and potential energy. Total mechanical energy equals $KE + PE$.

No energy loss to friction. Energy conservation requires no dissipative forces like friction.

Kinetic energy. Energy possessed by objects due to their motion or velocity.

Decreases. Potential energy converts to kinetic energy during free fall.

$0 \text{ J}$. Zero velocity means zero kinetic energy by definition.

$25 \text{ J}$. Total mechanical energy is the sum of kinetic and potential energies.

$0 \text{ J}$. Reference level for gravitational potential energy is typically ground level.