2023 Ap Physics C Mechanics Frq

Introduction

The 2023 AP Physics C: Mechanics Free‑Response Questions (FRQ) represent the portion of the exam where students must demonstrate not only factual recall but also the ability to apply calculus‑based reasoning to novel, multi‑step problems. Unlike the multiple‑choice section, the FRQs require a clear, logical derivation of equations, proper labeling of diagrams, and careful attention to units and significant figures. Success on these questions hinges on a deep understanding of Newtonian mechanics, proficiency with integration and differentiation, and the habit of showing every step of work. In this article we will unpack the structure of the 2023 FRQ set, walk through a step‑by‑step approach to each problem, illustrate the concepts with real‑world‑style examples, examine the underlying theory, highlight common pitfalls, and answer frequently asked questions to help you prepare effectively.

Detailed Explanation

The AP Physics C: Mechanics exam consists of 35 multiple‑choice questions and 3 free‑response questions. The FRQ section accounts for 50 % of the total exam score, with each question worth 7 points (for a total of 21 points). The 2023 FRQ set covered the full breadth of the mechanics curriculum, including:

• Kinematics – one‑dimensional and two‑dimensional motion, projectile motion, relative velocity.
• Newton’s Laws – force diagrams, friction, tension, normal force, systems of objects.
• Work, Energy, and Power – work‑energy theorem, conservation of mechanical energy, power, non‑conservative forces (e.g., friction).
• Linear Momentum and Impulse – conservation of momentum, collisions (elastic and inelastic), impulse‑momentum theorem.
• Rotation – rotational kinematics, torque, moment of inertia, angular momentum, rotational energy. * Oscillations – simple harmonic motion, springs, pendulums, energy in SHM.
• Gravitation – Newton’s law of universal gravitation, orbital motion, energy in gravitational fields.

Because the course is calculus‑based, students are expected to set up integrals (e.g., for work done by a variable force) and differentiate (e.g., to find acceleration from a velocity function). The FRQs often combine two or more of these topics in a single scenario, forcing the test‑taker to identify which principle applies at each stage of the problem. ---

Step‑by‑Step or Concept Breakdown

Below is a concise roadmap for tackling each of the three 2023 FRQs. The actual wording of the questions is reproduced in spirit (no copyrighted text), but the logical flow mirrors what appeared on the exam.

FRQ 1 – Combined Translation and Rotation

Scenario (paraphrased): A uniform solid cylinder of mass M and radius R rolls without slipping down an inclined plane that makes an angle θ with the horizontal. A light string is wrapped around the cylinder and attached to a hanging mass m that passes over a frictionless pulley at the top of the incline. The system is released from rest.

What it tests: Newton’s second law for translation and rotation, the rolling‑without‑slipping condition (a = αR), and the relationship between linear and angular acceleration.

Step‑by‑step solution outline:

1. Draw free‑body diagrams for the cylinder (weight Mg, normal N, friction f, tension T) and the hanging mass (weight mg, tension T).
2. Write translational equations:
   • For the cylinder along the incline: Mg sinθ − T − f = Ma (positive down the plane).
   • For the hanging mass: mg − T = ma (positive upward). 3. Write rotational equation for the cylinder about its center: τ = Iα. The only torque comes from friction: fR = Iα. For a solid cylinder, I = ½ MR².
3. Apply rolling condition: a = αR → α = a/R. Substitute into the torque equation: fR = (½ MR²)(a/R) → f = ½ Ma.
4. Combine equations to eliminate T and f. Solve the two translational equations together with the friction expression to obtain a in terms of M, m, g, and θ.
5. Find tension T by plugging a back into either translational equation.
6. Check limits: If m = 0 the expression reduces to the acceleration of a rolling cylinder down an incline (a = (2/3)g sinθ); if the incline is frictionless (f = 0) the cylinder would slip, showing the necessity of the friction term.

FRQ 2 – Work‑Energy with a Variable Force

Scenario (paraphrased): A block of mass m slides on a horizontal surface with a coefficient of kinetic friction μₖ. It is attached to a spring of spring constant k that is initially compressed a distance x₀ from its natural length. The block is released and moves until the spring reaches its natural length, after which it continues to slide until it comes to rest due to friction.

What it tests: Work‑energy theorem, integration of a variable spring force, work done by friction (a non‑conservative force), and the ability to split the motion into segments