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Topic 3.4: Practice Sheet — Nonconservative Forces and Energy Transfer

Name: _______________________________ Date: _______________ Period: ______

Directions: Name the system first. Use $E_f=E_i-E_{dis}$ and $E_{dis}=f,d$ where friction acts, and $g=10\text{ m/s}^2$. For "explain" items, write the three checklist answers (system, external work, internal energy). Show every step.

Warm-Up Level (straightforward, one-step)

  1. A $2.0\text{ kg}$ box is released from rest $1.5\text{ m}$ above the bottom of a rough ramp and reaches the bottom at $4.0\text{ m/s}$. Find its initial mechanical energy, its final kinetic energy, and the energy dissipated.
  2. The ramp in Problem 1 is $3.0\text{ m}$ long. Find the average friction force.

Standard Level (multi-step, matches typical AP Classroom depth)

  1. A $0.20\text{ kg}$ rock slides up a rough ramp starting at $5.0\text{ m/s}$ and stops after sliding $1.5\text{ m}$ along the ramp, at a vertical height of $0.50\text{ m}$. Find the energy dissipated and the friction force.
  2. A person pushes a $20\text{ kg}$ crate $5.0\text{ m}$ across a rough floor at constant speed with a horizontal $40\text{ N}$ force. Find the work done by the person, $\Delta K$ of the crate, and where the energy goes.
  3. An $80\text{ kg}$ skydiver with an open parachute falls $50\text{ m}$ at constant speed. Find $\Delta K$, $\Delta PE_g$, and the change in mechanical energy of the skydiver–Earth system.
  4. A $3.0\text{ kg}$ block is lifted at constant speed $2.0\text{ m}$. (a) System = block–Earth: find $W_{person}$, $\Delta PE_g$, $\Delta K$. (b) System = block alone: find the net work.

AP-Level (multi-part: calculate + justify/represent/predict-a-change)

  1. A rock of mass $m$ slides up a rough ramp starting at speed $v_0$ and stops after sliding a distance $d$ along the ramp, at vertical height $h$. a) Write $E_f=E_i-E_{dis}$ for the rock–Earth system. b) Show that the friction force is $f=\dfrac{m(v_0^2-2gh)}{2d}$. c) Evaluate $f$ for $m=0.30\text{ kg}$, $v_0=4.0\text{ m/s}$, $h=0.40\text{ m}$, $d=1.0\text{ m}$.
  2. A block is released from rest on a rough ramp and slides down, speeding up. Take the system to be block–Earth. a) Is mechanical energy conserved? Answer the three checklist questions. b) Now take the system to be block–Earth–ramp. Is the total energy conserved? Explain.
  3. A skydiver with an open parachute falls at constant speed. Sketch (or describe) how $K$, $PE_g$, and $E_{mech}$ of the skydiver–Earth system change with time, and identify the force that changes $E_{mech}$.

Progress Check Style (evaluate the method — AP Classroom format)

  1. A block is released from rest at the top of a rough ramp. There's significant friction, but the block's speed still increases as it slides down. Which correctly states whether the total mechanical energy of the block–Earth system decreases or stays the same, with a valid justification? (A) Decreases, because a force external to the system is dissipating energy. (B) Decreases, because the gravitational potential energy of the system decreases. (C) Stays the same, because energy is always conserved. (D) Stays the same, because gravitational potential energy is converted into kinetic energy.
  2. A skydiver with an open parachute falls at constant speed. Is the mechanical energy of the skydiver–Earth system constant? Why or why not? (A) Yes, because the kinetic energy remains constant. (B) Yes, because the net force on the skydiver–Earth system is zero. (C) No, because the potential energy decreases while the kinetic energy remains constant. (D) No, because the kinetic energy increases while the potential energy remains constant.

Keep this sheet — it's part of your semester study materials, same as your Concept Sheets.