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Topic 2.3: Practice Sheet — Newton's Third Law

Name: _______________________________ Date: _______________ Period: ______

Directions: Show your work for every problem — a correct answer with no work shown earns partial credit at best. For "is this a genuine pair" questions, explain using the two-different-objects test, not just "yes/no."

Warm-Up Level (straightforward, one-step)

  1. A person leans against a wall. Is the force the person exerts on the wall equal in magnitude to the force the wall exerts on the person? Explain using Newton's third law.
  2. A book rests on a table. Gravity and the normal force on the book are equal in magnitude. Is this a Newton's-third-law pair? Explain why or why not.

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

  1. A student pushes a filing cabinet with force $F$. The cabinet pushes back on the student with force $F$ as well. The student then pushes three times as hard, applying $3F$. What force does the cabinet now exert on the student?
  2. A heavy, uniform chain hangs from the ceiling, not touching the floor. The tension at the very top is $F_{top}$. Find an expression for the tension exactly one-third of the way down from the top, in terms of $F_{top}$.
  3. Two ice skaters of very different mass stand facing each other and push off. Are the push forces they exert on each other equal in magnitude? If one skater ends up moving much faster than the other, does that contradict your answer? Explain.

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

  1. A rope pulls a block of mass $3m$ to the right, which is in contact with and pushing a second block of mass $m$ ahead of it, both accelerating together across a frictionless floor. a) Is the force the $3m$ block exerts on the $m$ block equal in magnitude to the force the $m$ block exerts on the $3m$ block? Justify using Newton's third law. b) A classmate claims the $3m$ block must push harder on the $m$ block "because it's heavier and pushing it." Explain what's wrong with this reasoning.
  2. Two boxes of unequal mass are connected by an ideal (massless) string and pulled straight upward at constant speed by a second string above them. a) Explain why the tension in the connecting string between the two boxes is the same at both the point where it attaches to the upper box and the point where it attaches to the lower box. b) Would your answer to part a) change if the connecting string had significant mass of its own? Explain why or why not.

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

  1. A box is pulled to the right at constant speed across a rough floor. Four forces act on the box: tension (forward), friction (backward), gravity (down), and normal force (up). Which pair of these four forces represents a genuine Newton's-third-law interaction pair? (A) Tension and friction (B) Gravity and normal force (C) None of these four forces form a Newton's-third-law pair, because all four act on the same object (D) All four forces form third-law pairs with each other

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

  1. A bucket holding a rock is lifted upward by a rope, and the rope, bucket, and rock all accelerate upward together. Consider the force the rock exerts on the bucket and the force the bucket exerts on the rock. a) Are these two forces a genuine Newton's-third-law pair? Justify using the two-different-objects test. b) Is the force the rope exerts on the bucket equal to the combined weight of the rock and bucket in this situation? Explain why or why not, given that the system is accelerating.
  2. A rover attached by a cord to a parachute descends at constant speed near the surface of Mars. Let $F_g$ be the gravitational force Mars exerts on the rover, and $F_T$ be the tension force the cord exerts on the rover. a) Are $F_g$ and $F_T$ equal in magnitude? Explain using the rover's motion. b) Are $F_g$ and $F_T$ a genuine Newton's-third-law pair? Justify your answer using the two-different-objects test — be specific about which two objects are involved in each force.

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