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Topic 2.1: Practice Sheet — Systems and Center of Mass

Name: _______________________________ Date: _______________ Period: ______

Directions: For reasoning questions, write full sentences. For calculations, show your work. Circle or box final numeric answers.

Warm-Up Level (straightforward, one-step)

  1. A plain wooden meter stick, uniform all the way through, is 100 cm long. Where is its center of mass, and how do you know without calculating anything?
  2. A 2 kg block sits at 0 m and a 2 kg block sits at 8 m. Without calculating, where is the center of mass? Explain why the "don't just average" warning doesn't matter here.

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

  1. A 1 kg ball is at the 0 cm mark on a track. A 3 kg ball is at the 20 cm mark. Find the center of mass of the two-ball system.
  2. A bowling pin has uniform density. Based on its symmetry, describe (in words, no diagram needed) where its center of mass must be located along its height.
  3. Two blocks, 4 kg and 2 kg, sit on a track 12 m apart, with the 4 kg block at the 0 m mark. A student calculates the center of mass and gets 6 m. Explain what mistake this student made, and find the correct answer.

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

  1. Three drones hover in a line above a field. Drone A (mass 2 kg) is at the 5 m mark, Drone B (mass 3 kg) is at the 15 m mark, and Drone C (mass 5 kg) is at the 35 m mark. a) Find the center of mass of the three-drone system. b) A classmate says "the center of mass should be close to 18 m, since that's roughly the middle of the three positions." Explain why this reasoning is wrong, and state what the classmate forgot to do.
  2. A 10 kg sphere and a 2 kg sphere are separated by 3.0 m. a) Without calculating, is the center of mass closer to the 10 kg sphere or the 2 kg sphere? Explain why. b) Now calculate the exact distance from the 10 kg sphere's center to the system's center of mass.

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

  1. A 40 g block is at the 0 cm mark and a 20 g block is at the 60 cm mark on a track. Which of the following is the center of mass of the two-block system? (A) 20 cm (B) 30 cm (C) 40 cm (D) 60 cm

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