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Topic 3.3: Practice Sheet — Gravitational Potential Energy

Name: _______________________________ Date: _______________ Period: ______

Directions: For every problem, write the expression for $PE$ (or $\Delta PE$) before substituting numbers, and include signs. Use $g=10\text{ m/s}^2$ near Earth's surface. Show every step.

Warm-Up Level (straightforward, one-step)

  1. A $0.50\text{ kg}$ book is lifted $2.0\text{ m}$ from the floor to a shelf. Find $\Delta PE_g$ of the book–Earth system.
  2. The same book sits on a shelf $2.0\text{ m}$ above the floor. A table is $0.75\text{ m}$ above the floor. (a) Find $PE_g$ of the book on the shelf with the zero line at the floor. (b) Find $PE_g$ with the zero line at the table top. (c) The book is moved from the shelf to the table top. Find $\Delta PE_g$ using each zero line, and comment.

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

  1. Two $2.0\text{ kg}$ spheres touch a ceiling $3.0\text{ m}$ above the floor. Sphere 1 has radius $0.10\text{ m}$, Sphere 2 has radius $0.40\text{ m}$. Each is lowered to the floor. Find $|\Delta PE_g|$ for each, and state which is larger and why.
  2. At time $t_1$ a moon of mass $m$ is a distance $d$ from a planet's center (planet mass $M$). At $t_2$ it is $2d$ away. Find the ratio $PE_{t_1}:PE_{t_2}$. Did the system's potential energy increase or decrease from $t_1$ to $t_2$?
  3. Planet A (mass $m_0$) orbits a star of mass $M$ at radius $r_0$. Planet B (mass $4m_0$) orbits it at radius $2r_0$. Find $PE_A:PE_B$.
  4. A satellite of mass $m$ is a distance $D$ from an asteroid of mass $M$. It moves to $2D$ and its mass becomes $\tfrac{m}{2}$. Find $\Delta PE_g$ of the system.

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

  1. A probe of mass $m$ is a distance $R$ from the center of a planet of mass $M$. It moves to a distance $3R$, and by then its mass has changed to $3m$ (assume nothing else changes). a) Find $PE$ at $R$ and at $3R$ in terms of $G$, $M$, $m$, $R$. b) Find $\Delta PE_g$. c) Explain, in one sentence, how mass and distance combined to give this result.
  2. A satellite in circular orbit is moved to a slightly larger orbit radius. a) Does the gravitational potential energy of the satellite–Earth system increase or decrease? Justify using $PE=-Gm_1m_2/r$. b) Sketch $PE$ vs. $r$ (r on the horizontal axis) and mark the two orbits on it.

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

  1. An object is released from rest near Earth's surface and speeds up, then reaches terminal velocity before landing. Air resistance acts on it. Which claim about the gravitational potential energy of the object–Earth system is true? (A) It stays constant while accelerating, then decreases at terminal velocity. (B) It decreases while accelerating, then stays constant at terminal velocity. (C) It stays constant the whole time. (D) It decreases while accelerating and continues to decrease at terminal velocity.

Progress-Check-Aligned Practice (extra depth — same style as your unit test)

  1. A student says, "The boulder at the top of the cliff has $5000\text{ J}$ of gravitational potential energy, and that number belongs to the boulder." Explain two things wrong or incomplete with this statement.
  2. A satellite of mass $m$ orbits Earth (mass $M$) at radius $R$. It is moved to $3R$. (a) Find $\Delta PE_g$. (b) A student says the satellite "lost" potential energy because the distance got larger. Identify the mistake in the student's reasoning.

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