Physics / Unit 5: Work, Energy and Power
5.4 Conservation of Energy
Notes
The law of conservation of energy: energy cannot be created or destroyed, only changed from one form to another.
- Mechanical energy $ME = KE + PE$. With no friction or air resistance, $ME$ stays constant: $KE_i + PE_i = KE_f + PE_f$.
- With friction, some mechanical energy becomes thermal energy (heat), but the total energy is still conserved.
- Speed after falling a height $h$ from rest (no friction): $\displaystyle v = \sqrt{2gh}$, independent of mass.
- Example: a ball dropped from 5 m hits the ground at $\displaystyle v = \sqrt{2(9.8)(5)} \approx 9.9 \text{ m/s}$.
Practice
A roller coaster car starts from rest at the top of a 20 m hill. Ignoring friction, how fast is it moving at the bottom?
$\displaystyle v = \sqrt{2(9.8)(20)} = \sqrt{392} \approx 19.8 \text{ m/s}$.
A pendulum swings from its highest point to its lowest point. What energy change happens?
The bob loses height and gains speed.
A 3 kg ball slides down a ramp from 2 m high, starting at rest, and reaches the bottom with 50 J of kinetic energy. How much energy was changed to heat by friction?
Starting $PE = 3 \times 9.8 \times 2 = 58.8 \text{ J}$; $58.8 - 50 = 8.8 \text{ J}$.
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