Energy
High-Yield Summary
- Energy is the capacity to do work or produce heat, and is conserved — never created or destroyed, only converted between forms.
- Kinetic energy (KE = ½mv²) depends on speed, scales with the square of speed, and is measured in Joules.
- Potential energy is stored energy due to position/composition — gravitational (U = mgh), elastic (U = ½kx²), nuclear, chemical.
- Total mechanical energy (E = U + K) is conserved in closed systems governed only by conservative forces: ΔE = ΔU + ΔK = 0.
- Conservative forces (gravity, springs) are path-independent and don't dissipate energy; non-conservative forces (friction, drag) are path-dependent and convert mechanical energy into other forms like heat.
Kinetic vs. Potential Energy
| Kinetic Energy | Potential Energy |
|---|---|
| Energy due to motion | Energy due to position or composition |
| KE = ½mv² | Gravitational: U = mgh; Elastic: U = ½kx² |
| Motion, sound, thermal, electrical | Gravitational, elastic, nuclear, chemical |
Kinetic and Potential Energy
KE = ½mv² | U = mgh | U = ½kx²
- m = Mass
- v = Speed
- g = Acceleration due to gravity, ≈ 9.81 m/s²
- h = Height above the reference datum
- k = Spring constant
- x = Displacement from equilibrium
Conservative vs. Non-Conservative Forces
| Conservative (gravity, springs) | Non-Conservative (friction, air resistance, drag) |
|---|---|
| Path-independent | Path-dependent |
| Total mechanical energy conserved | Net loss of mechanical energy (converted to heat, etc.) |
Common MCAT Trap
- "Lost" mechanical energy from friction doesn't violate the First Law of Thermodynamics — it converts to a non-mechanical form (usually heat), it doesn't vanish.
- Kinetic energy scales with v², not v — doubling speed quadruples KE, not doubles it.
Quick Recall
What happens to kinetic energy if speed doubles?
Why does mechanical energy 'decrease' when friction acts on a system?