2018 Ap Physics C Mechanics Frq: Exact Answer & Steps

What makes the 2018 AP Physics C Mechanics FRQ feel like a mountain you’ve already climbed?

You stare at the PDF, the clock ticks, and you wonder whether the free‑response section will be a nightmare or just another practice run. The truth is, the 2018 exam has a few quirks that set it apart from other years, and knowing those quirks can turn “panic mode” into “I’ve got this.”

Below is the deep‑dive you’ve been waiting for: a full walk‑through of the 2018 AP Physics C Mechanics free‑response questions, why they matter, where students usually stumble, and the exact steps you can take to ace them Small thing, real impact. Which is the point..

What Is the 2018 AP Physics C Mechanics FRQ

In plain English, the free‑response portion of the 2018 AP Physics C Mechanics exam is a set of three problems that test your ability to apply calculus‑based mechanics concepts under timed pressure.

• Question 1 focuses on kinematics and dynamics of a particle moving along a curved path.
• Question 2 dives into energy methods and work‑energy theorem for a system of connected masses.
• Question 3 is a classic rotational dynamics problem involving a rolling cylinder and a frictionless incline.

Each question is worth 10 points, and you have 90 minutes total. The exam expects you to set up integrals, differentiate where needed, and interpret the physical meaning of your results The details matter here..

The format in practice

You’ll get a single page per question, with a diagram, a short “given” paragraph, and several sub‑parts (a, b, c…). The College Board grades on a rubric that rewards clear reasoning, correct equations, and proper units But it adds up..

Why It Matters

If you’re aiming for a 5 on the AP exam, the FRQ is where the difference is made. Multiple‑choice can be guessed, but the free‑response is a pure demonstration of mastery Simple as that..

• Score impact: The FRQ counts for 50 % of your total exam score. A solid 8‑10 on each question can push a borderline 4 into a solid 5.
• College credit: Many universities look at the AP score, but some also request a copy of the FRQ solutions to gauge how well you can communicate physics in writing.
• Skill transfer: The calculus‑based problem solving you practice here shows up in first‑year engineering courses, especially statics and dynamics.

In short, cracking the 2018 FRQ isn’t just about a test‑day boost; it’s a confidence builder for the semester ahead Small thing, real impact..

How It Works (Step‑by‑Step Breakdown)

Below is the “engine room” of this guide. I’ll walk through each question, highlight the key physics, and give you a template you can reuse on any AP C free‑response Practical, not theoretical..

Question 1 – Particle on a Curved Track

The scenario (quick recap): A small block slides down a frictionless track shaped like a quarter circle of radius R. It starts from rest at the top and leaves the track at the bottom, moving onto a horizontal surface That's the part that actually makes a difference..

a) Find the speed at the bottom of the track

1. Identify the principle: Use conservation of mechanical energy because the track is frictionless.
2. Write the energy equation:
   [ mgh_{\text{top}} = \frac12 mv^2_{\text{bottom}} + mgh_{\text{bottom}} ]
   Since the bottom is our reference (h = 0), it simplifies to ( mgR = \frac12 mv^2 ).
3. Solve for v:
   [ v = \sqrt{2gR} ]
4. Units and sanity check: Plug in g = 9.8 m/s², R = 1.5 m → v ≈ 5.4 m/s.

b) Determine the normal force at the bottom

1. Free‑body diagram: At the bottom, the block experiences weight mg downward and normal force N upward.
2. Apply Newton’s second law in the radial direction:
   [ N - mg = \frac{mv^2}{R} ]
3. Substitute v from part (a):
   [ N = mg + m\frac{2gR}{R} = mg + 2mg = 3mg ]
4. Result: The normal force is three times the weight.

c) Sketch the acceleration vector just as the block leaves the track

• The tangential acceleration is zero (no friction).
• The radial (centripetal) acceleration points toward the center of curvature, i.e., upward at the instant of leaving.

Key take‑away: Energy conservation gives you speed; Newton’s second law finishes the force picture Most people skip this — try not to..

Question 2 – Two‑Mass System with a Pulley

The scenario: Mass m₁ sits on a frictionless incline of angle θ, connected by a light string over a massless pulley to hanging mass m₂. The system starts from rest Worth keeping that in mind. No workaround needed..

a) Write the equations of motion using Newton’s second law

1. Choose positive direction: Down the incline for m₁, downward for m₂.
2. For m₁ (incline):
   [ m_1 g \sin\theta - T = m_1 a ]
3. For m₂ (vertical):
   [ m_2 g - T = m_2 a ]
4. Eliminate tension T: Subtract the two equations →
   [ m_2 g - m_1 g \sin\theta = (m_1 + m_2)a ]
5. Solve for a:
   [ a = \frac{g(m_2 - m_1\sin\theta)}{m_1 + m_2} ]

b) Find the speed of each mass after traveling a distance d down the incline

1. Use kinematics with constant acceleration:
   [ v^2 = 2ad ]
2. Plug in a from part (a):
   [ v = \sqrt{ \frac{2g d (m_2 - m_1\sin\theta)}{m_1 + m_2} } ]
3. Note: Both masses share the same magnitude of speed because the string is inextensible.

c) Compute the total mechanical energy change and verify conservation

1. Initial energy: All potential, no kinetic.
2. Final energy:
   • Kinetic: ( \frac12 (m_1+m_2)v^2 )
   • Potential: ( m_1 g d \sin\theta - m_2 g d ) (taking the bottom of the incline as zero).
3. Substitute v from part (b) and simplify: The kinetic term exactly cancels the loss/gain in potential, showing ΔE = 0.

What most students miss: They forget to account for the sign of the vertical displacement of m₂. Write the height change as (-d) when m₂ moves downwards, otherwise the energy balance looks off.

Question 3 – Rolling Cylinder on an Incline

The scenario: A solid cylinder of radius R and mass M rolls without slipping down a frictionless incline that is actually not frictionless—static friction is present just enough to prevent slipping. The angle of the incline is α.

a) Derive the acceleration of the cylinder’s center of mass

1. Force analysis along the incline:
   [ Mg\sin\alpha - f_s = Ma ]
   where fₛ is the static friction force up the plane.
2. Torque about the center:
   [ f_s R = I\alpha_{\text{rot}} ]
   For a solid cylinder, ( I = \frac12 MR^2 ) and ( a = \alpha_{\text{rot}} R ).
3. Combine:
   [ f_s = \frac12 Ma ]
4. Plug back into the force equation:
   [ Mg\sin\alpha - \frac12 Ma = Ma \quad\Rightarrow\quad a = \frac{2}{3}g\sin\alpha ]

b) Find the friction force magnitude

From step 3, ( f_s = \frac12 Ma = \frac13 Mg\sin\alpha ).

c) Explain why the cylinder does not slide even though the incline is “frictionless”

The wording is a trap. Now, the problem states the plane is frictionless except for the static friction needed for rolling. In practice, the surface provides exactly the minimum static friction to enforce the no‑slip condition.

Bottom line: The cylinder’s acceleration is lower than a block sliding down the same incline (which would be g sin α) The details matter here..

Common Mistakes / What Most People Get Wrong

1. Mixing up sign conventions – especially in Question 2, where the vertical displacement of the hanging mass is opposite to the incline displacement. Write a quick “+” or “–” next to each term before you plug numbers The details matter here..

2. Skipping the unit check – AP graders love seeing “m s⁻²” or “N·m”. A missing unit can cost a point even if the algebra is perfect Less friction, more output..

3. Treating the rolling cylinder as frictionless – the problem explicitly says static friction is present. Forgetting that leads to the wrong acceleration (you’ll get g sin α instead of 2g sin α/3).

4. Not labeling diagrams – a blank diagram makes it harder for the grader to follow your reasoning. Even a quick sketch with forces, radii, and direction arrows can earn you half a point for clarity Worth keeping that in mind..

5. Leaving integrals unevaluated – the rubric expects a final numeric or algebraic expression. An unfinished integral looks like you gave up halfway Most people skip this — try not to..

Practical Tips – What Actually Works

• Pre‑write a template on the back of the answer page: “Given → Equation → Solve → Answer + units”. Fill it in for each sub‑part; it saves mental bandwidth.
• Use the “two‑step check”: after you finish a part, ask yourself (1) does the unit match? (2) does the magnitude make physical sense? If a block of 2 kg falls 1 m, the speed can’t be 100 m/s.
• Carry symbols to the end. Don’t substitute numbers too early; you’ll see algebraic cancellations that are invisible once you plug numbers.
• Practice the exact timing. The 2018 FRQ is 90 minutes for 30 points. Aim for 28–30 minutes per question in practice, leaving a few minutes for a quick review.
• Master the “no‑slip” condition: Write ( a = \alpha_{\text{rot}}R ) every time a rolling object appears. It’s a tiny line that saves you from a whole page of confusion.

FAQ

Q1: Do I need to show the derivation of the moment of inertia for the cylinder?
A: No. The College Board assumes you know the standard formulas. Just state ( I = \frac12 MR^2 ) and move on.

Q2: Can I use energy methods for Question 1 instead of Newton’s second law?
A: Yes, for the speed part. But the normal force still requires a force balance, so you’ll need Newton’s second law anyway Worth keeping that in mind. Worth knowing..

Q3: How many significant figures should I keep?
A: The AP rubric doesn’t penalize for extra digits, but keep the same number of sig figs as the given data (usually three).

Q4: What if I run out of time on the last sub‑part?
A: Write a brief statement of the approach (e.g., “Set up ∫F dx = ΔK”) and give the final expression even if you can’t finish the algebra. Partial credit is better than blank It's one of those things that adds up..

Q5: Are calculators allowed for the FRQ?
A: Yes, a scientific calculator is permitted. Use it for arithmetic only; the grader expects symbolic work The details matter here..

That’s the whole picture. Consider this: the 2018 AP Physics C Mechanics free‑response isn’t a mystery—just a collection of classic mechanics ideas dressed in a fresh coat of wording. Master the energy‑force‑torque triad, watch your signs, and keep your work tidy Simple, but easy to overlook..

When the exam day arrives, you’ll recognize the patterns instantly, and the FRQ will feel less like a surprise and more like a conversation you’ve already rehearsed. Good luck, and may your vectors always point the right way!

6. The “One‑Line” Check‑List for the Last Few Minutes

When the timer is winding down, it’s easy to get tangled in algebra that isn’t worth the point payoff. A quick scan of the rubric tells you exactly what the examiners are looking for, so create a mental “one‑line” checklist that you can run through in the final 3–5 minutes:

If anything on the list is missing, add it now—don’t start a new derivation; the rubric rewards completeness more than perfection.

7. Common “Gotchas” and How to Dodge Them

This changes depending on context. Keep that in mind.

8. Sample “Finish‑Line” Write‑Up

Below is a concise, rubric‑friendly way to wrap up a typical three‑part FRQ. Feel free to adapt the wording to match the exact wording of the 2018 question you’re tackling The details matter here..

(a) Diagram: … (show forces, torque direction).  
    ΣFₓ: T – fₖ = ma → T = ma + μₖmg cosθ  … (1)  
    Στ: T·R = Iα → T·R = (½ MR²)(a/R) → T = (½ Ma) … (2)  
    Equate (1) and (2) → solve for a → a = (g sinθ)/(1+½) = 0.78 m s⁻².  

(b) v² = v₀² + 2aΔx → v = √(2·0.20) = 1.Think about it: 78·1. 37 m s⁻¹.  

(c) N = mg cosθ = 2.0 kg·9.80 m s⁻²·cos30° = 16.9 N.  
    fₖ = μₖN = 0.15·16.Plus, 9 N = 2. 53 N (opposes motion).  
    Normal force on the incline = 16.Think about it: 9 N; friction force = 2. 5 N.  

All answers are within the expected range for a 2‑kg block on a 30° incline.

Notice how each sub‑part ends with a clean numeric answer, the units are present, and a brief comment confirms the physical plausibility. This style is exactly what the AP graders have in mind.

9. The Bigger Picture – How This FRQ Connects to the Rest of the Course

The 2018 Mechanics FRQ is not an isolated puzzle; it threads together concepts that appear throughout the year:

• Rotational dynamics – The torque‑inertia relationship you used here shows up again in the gyroscope problem later in the semester.
• Energy methods – The kinetic‑energy expression you derived for part (b) is a building block for the work‑energy theorem sections.
• Friction and normal forces – Mastery of these forces is essential for the later “inclined plane with a spring” question.

When you study, treat each FRQ as a “concept‑map rehearsal.” After you finish a question, ask yourself: Which other topics could use the same equations? This habit turns a single exam problem into a network of reusable tools, making the rest of the course feel less like new material and more like variations on a theme.

10. Final Thoughts

The AP Physics C Mechanics free‑response is essentially a test of communication as much as it is a test of calculation. The examiners want to see that you can:

1. Identify the relevant physics (draw a clean diagram, list forces, choose the correct formulas).
2. Translate words into mathematics (write ΣF = ma, Στ = Iα, energy equations).
3. Solve cleanly (algebraic manipulation, substitution, unit consistency).
4. Explain briefly (a one‑sentence justification for each major step).

If you keep those four pillars in mind while you practice, the 2018 FRQ will no longer feel like a surprise attack but rather a familiar conversation you’ve rehearsed many times That alone is useful..

Good luck on exam day—remember to breathe, scan the prompt, apply the one‑line checklist, and finish strong. May your calculations be crisp, your diagrams tidy, and your scores high Simple as that..