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Topic 2.5: Practice Sheet — Newton's Second Law, Part 1

Name: _______________________________ Date: _______________ Period: ______

Directions: For every problem, write the Newton's-second-law equation ($\Sigma F = ma$) in symbols FIRST, with correct signs, then solve symbolically, THEN substitute numbers. Use $g = 10\text{ m/s}^2$ unless told otherwise.

Warm-Up Level (straightforward, one-step)

  1. A 50 kg person stands on a scale in an elevator accelerating upward at 1 m/s². Find the scale's reading (the normal force).
  2. A block slides down a frictionless incline at 20° to the horizontal. Write the expression for its acceleration down the ramp (do not calculate a number).

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

  1. A 70 kg person stands on a scale in an elevator accelerating downward at 3 m/s². Find the scale's reading.
  2. A car's brakes are applied, and its acceleration magnitude increases linearly with time as $a = Ct$, where $C$ is a positive constant and the car's mass $m$ stays constant. Write an expression for the net force on the car as a function of time, and describe the shape of its graph.
  3. A block of mass $m$ is pushed up a frictionless ramp (angle $\theta$ to horizontal) by a horizontal force $F_p$ (not along the ramp's surface). Write the expression for the block's acceleration along the ramp, in terms of $F_p$, $m$, $\theta$, and $g$.

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

  1. A 60 kg person rides in an elevator. At time $t_1$, the elevator accelerates downward with magnitude 3 m/s². At time $t_2$, it accelerates upward with magnitude 1 m/s². a) Find the scale reading (normal force) at $t_1$ and at $t_2$. b) Find the ratio of the normal force at $t_1$ to the normal force at $t_2$.
  2. A spacecraft in deep space fires a thruster that exerts a constant force on it. The spacecraft's total mass decreases at a constant rate as fuel burns. a) Using $a = F_{net}/m$, explain whether the spacecraft's acceleration increases, decreases, or stays the same over time. b) Explain why the relationship between acceleration and mass here is not a linear one, even though the force is constant.

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

  1. A 90 kg person stands on a scale in an elevator. The scale reads 1100 N. (Use $g = 10\text{ m/s}^2$, so the person's weight is 900 N.) Which of the following is a valid claim about the elevator's motion? (A) The elevator must be moving upward (B) The elevator must be moving downward and slowing down (C) The elevator could possibly be moving upward and speeding up, or moving downward and slowing down (D) The elevator must be at rest

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

  1. A person stands on a scale in an elevator that is moving upward with increasing speed. Consider four forces: the force of the person on the scale, the force of the scale on the person, the force of the person on Earth (gravitational), and the force of Earth on the person (gravitational). a) Identify which two of these four forces are a genuine Newton's-third-law pair with each other, and which other two are also a genuine pair. b) Rank all four forces from smallest to largest magnitude, and justify your ranking using $F_{net}=ma$ for the person.
  2. A 10 kg block is connected to both ends of a rope that passes over a frictionless, massless pulley; the entire pulley-and-block assembly is fixed inside an elevator accelerating upward at 2 m/s². Find the tension in the rope.
  3. A truck moves down a ramp while braking, so the truck (and a box sitting in its bed) are slowing down together, with the box staying at rest relative to the truck bed (no slipping). Draw a correct FBD for the box, including gravity, the normal force from the truck bed, and friction. a) Explain why the normal force is NOT necessarily equal in magnitude to gravity here. b) Explain which direction the friction force must point, given that the box's acceleration matches the truck's deceleration.

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