Just Physics

← Unit 3 Handouts

Topic 3.4: Practice Sheet — Conservation of Mechanical Energy

Name: _______________________________ Date: _______________ Period: ______

Directions: For each problem, first write System: ___. Then write $K_i+PE_i=K_f+PE_f$ before substituting. Use $g=10\text{ m/s}^2$ and assume no friction unless told otherwise. Show every step.

Warm-Up Level (straightforward, one-step)

  1. A ball is dropped from rest from $20\text{ m}$ above the ground. Find its speed just before landing, using energy.
  2. A frictionless ramp has height $h$. A block slides down from rest. (a) Write its speed at the bottom in terms of $g$ and $h$. (b) Does the answer depend on the block's mass? On the ramp's angle?

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

  1. A sled slides on flat ice at $6.0\text{ m/s}$ and climbs a frictionless hill to a flat top $1.0\text{ m}$ higher. Find its speed at the top.
  2. A $0.20\text{ kg}$ block is pressed against a spring ($k=100\text{ N/m}$), compressing it $0.20\text{ m}$, then released on a frictionless horizontal surface. Find the block's speed when the spring reaches its relaxed length.
  3. A $0.40\text{ kg}$ block is launched by a spring ($k=400\text{ N/m}$, compressed $0.10\text{ m}$) up a frictionless incline. Assuming all the spring's energy becomes gravitational potential energy at the highest point, find the maximum height the block reaches above its starting position.
  4. A $2.0\text{ kg}$ ball is released from rest at Position A, $5.0\text{ m}$ above the bottom of a frictionless track (Position B). Position C is $3.0\text{ m}$ above B. Find the ball's total mechanical energy, its kinetic energy at C, and its speeds at B and C.

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

  1. A block is at rest on a vertical spring, in equilibrium. a) List the types of energy in the block–spring–Earth system. b) List the types of energy in the block–spring system. c) Explain why the two lists differ, using the definition of "system."
  2. An asteroid moves directly toward a planet (the planet's velocity change is negligible). a) For the asteroid–planet system, state whether $\Delta E_{tot}$ is positive, negative, or zero, and justify. b) State the sign of $\Delta K$ for the asteroid and $\Delta PE_g$ for the system, and explain how they're connected.
  3. A student says: "If I double the sled's mass, the sled's final speed at the top of the frictionless hill will be smaller, because there's more mass to lift." Evaluate the claim using the energy equation.

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

  1. A sled is traveling with speed $v_i$ along flat, frictionless ground and reaches a hill. It moves up to a flat section at height $h$ with speed $v_f$. What is $v_f$? (A) $\sqrt{2gh}$ (B) $\sqrt{v_i^2-2gh}$ (C) $\sqrt{v_i^2+2gh}$ (D) $\sqrt{2gh-v_i^2}$
  2. At time $t_0$ a block is held at rest against a compressed horizontal spring at the top of a frictionless track. The total mechanical energy of the block–spring–Earth system is $E_0$. The block is released, slides down the track, and at $t_1$ is on a flat section. Friction is negligible. Which is true of $E_1$ and $E_0$? (A) $E_1<E_0$ (B) $E_1=E_0$ (C) $E_1>E_0$ with $E_0=0$ (D) $E_1>E_0>0$

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