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Topic 2.4: Practice Sheet — Newton's First Law

Name: _______________________________ Date: _______________ Period: ______

Directions: For every calculation, write the equilibrium equation ($\Sigma F_x = 0$ or $\Sigma F_y = 0$) in symbols FIRST, then solve symbolically, THEN substitute numbers if given. Show every step.

Warm-Up Level (straightforward, one-step)

  1. A ball is thrown straight up. At the exact peak of its path, is the ball in equilibrium? Explain why or why not.
  2. A box hangs motionless from a single vertical string. The box's weight is 12 N. What is the tension in the string? Write the equilibrium equation first.

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

  1. A box hangs at rest, suspended by a string above and resting on a scale below. The scale reads a normal force $F_N$ of 4 N, and the box's weight is 10 N. Find the tension in the string above (write $\Sigma F_y = 0$ symbolically first, then substitute).
  2. A hockey puck slides across frictionless ice at a constant nonzero speed. Is the puck in equilibrium? Are there forces acting on it? Explain both answers.
  3. Two forces act on a box moving at constant velocity across a frictionless floor: $F_1$ at angle $\theta_1$ above horizontal, $F_2$ at angle $\theta_2$ above horizontal, on opposite sides. Using only the horizontal balance, find an expression for $F_1$ in terms of $F_2$, $\theta_1$, and $\theta_2$.

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

  1. A box moves at constant velocity to the right across a frictionless floor. Two applied forces act on it: one at a fixed angle above the horizontal on the right, and one that starts purely horizontal on the left, with both magnitudes constant. The angle of the right-side force is slowly decreased toward zero. a) Write the horizontal equilibrium equation symbolically for the original setup. b) Explain what happens to the box's motion as the angle decreases, and why.
  2. A skydiver-parachute system of mass $m$ falls and reaches a constant terminal speed $v_T$, where air resistance follows $F_{air} = Av^2$. a) Write the equilibrium equation for the system at terminal speed. b) Solve symbolically for $v_T$ in terms of $m$, $g$, and $A$ — do not substitute any numbers.

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

  1. A person of mass $m$ stands on a scale inside an elevator, motionless relative to the scale. The scale reads a normal force $F_N$ that is LESS than the person's weight $mg$. Which of the following is a valid claim about the elevator's motion? (A) The elevator must be moving downward (B) The elevator could possibly be moving downward and speeding up, or moving upward and slowing down (C) The elevator must be at rest (D) The elevator must be moving upward

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

  1. A rope pulls a crate at a fixed angle above horizontal across a rough floor at a constant speed. While the crate is moving, the coefficient of kinetic friction between the crate and floor increases, but the crate's speed stays exactly constant. Using $\Sigma F_x = 0$ and $\Sigma F_y = 0$, explain what must be true about the friction force as the coefficient increases, and explain whether the tension in the rope must also change to keep the crate in equilibrium.
  2. A textbook is pushed against a rough vertical wall by an applied force directed up and to the right, at an angle to the horizontal, and the book remains completely at rest. Draw a complete FBD for the textbook, labeling all forces acting on it. Then write $\Sigma F_x = 0$ and $\Sigma F_y = 0$ symbolically, and explain which force must balance gravity in this scenario.
  3. For each of the following situations, state whether the object is in translational equilibrium, and justify your answer using the definition $\Sigma F = 0$: a) An object undergoing projectile motion with no air resistance b) A car turning a corner on level pavement at constant speed c) A sled sliding down a hill at constant velocity d) A ball being swung in a vertical circle at constant speed

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