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Topic 3.4: Nonconservative Forces and Energy Transfer

Name: _______________________________ Date: _______________ Period: _______

Before We Start: Yesterday's Recap

A block slides down a rough ramp and still speeds up. A student says, "It speeds up, so kinetic energy increased, so energy is conserved." Is the student right? Say why or why not.

Today's New Concepts

AP CED Alignment: Unit 3, Topic 3.4

Friction Turns Mechanical Energy Into Internal Energy

  • Friction and air resistance convert mechanical energy into internal (thermal) energy: $E_f=E_i-E_{dis}$, with $E_{dis}=f,d$ for a constant friction force $f$ over sliding distance $d$
  • Mechanical energy of the system decreases; the total energy including internal energy is conserved
  • An object can speed up (or stay at constant speed) and still be losing mechanical energy

Worked Example: A $1.0\text{ kg}$ block slides down a rough ramp ($h=1.0\text{ m}$, length $2.0\text{ m}$) and reaches the bottom with $v^2=12\text{ m}^2/\text{s}^2$. $E_i=10\text{ J}$, $E_f=\tfrac12(1.0)(12)=6\text{ J}$, $E_{dis}=4\text{ J}$, $f=4/2.0=2.0\text{ N}$.

External Work: $W_{ext}=\Delta E_{sys}$

  • Energy enters or leaves a system when an external force does work: $W_{ext}=\Delta K+\Delta U+\Delta E_{internal}$
  • Lifting a book at constant speed: system book–Earth $\Rightarrow$ $W_{person}=\Delta U_g$, $\Delta K=0$. System book alone $\Rightarrow$ net work $=0$ (person $+$, gravity $-$)

Worked Example: A $2.0\text{ kg}$ book is lifted $1.5\text{ m}$ at constant speed. Book–Earth: $W_{person}=\Delta U_g=30\text{ J}$. Book alone: $+30\text{ J}+(-30\text{ J})=0$.

The Conservation Checklist

  1. What is the system?
  2. Does any external force do work on it (push, pull, drag, outside friction)?
  3. Is energy being converted to internal energy?
  • If 2 and 3 are both "no," mechanical energy is conserved; otherwise it isn't. "Because energy is always conserved" is not a valid justification — it confuses total energy with mechanical energy

Worked Example: A $70\text{ kg}$ skydiver falls $100\text{ m}$ at constant speed. $\Delta K=0$, $\Delta U_g=-70{,}000\text{ J}$, so $E_{mech}$ decreases by $70{,}000\text{ J}$ — dissipated by air drag as internal energy.