AP Physics 1 Unit 2 FRQ Practice: Force and Translational Dynamics Free Response

Free-Response Question · Unit 2

Scenario: A block of mass m = 4 kg is released from rest at the top of a ramp tilted at an angle of 30° above horizontal. The coefficient of kinetic friction between the block and the ramp is μ_k = 0.20. The block slides down the incline. Use g = 10 m/s², sin 30° = 0.50, and cos 30° ≈ 0.87.

— AP Physics 1 style problem · Topics 2.2, 2.5, & 2.7

Draw a free-body diagram of the block as it slides down the incline. Describe each force, including its direction. (In a written response, list each force and its direction.)

✓ Model answer (earns the points)

Three forces act on the block:

1. Gravity (F_g = mg) — straight down (toward the center of the Earth). Magnitude = 4 · 10 = 40 N.

2. Normal force (F_N) — perpendicular to the incline surface, pointing away from the surface (up and away from the incline).

3. Kinetic friction (F_k) — parallel to the incline surface, pointing UP the incline (opposite to the block's motion down the incline).

Tip: For incline problems, tilt your coordinate axes so one axis (x) is parallel to the incline and the other (y) is perpendicular. Then resolve gravity into components: F_g,x = mg·sin(θ) down the incline, and F_g,y = mg·cos(θ) into the incline.

Why it scores: Identifies all three forces (gravity, normal, friction) with correct directions. Note that friction points UP the incline because the block is sliding DOWN. Listing only "gravity" or omitting friction would lose points.

Calculate the magnitude of the block's acceleration as it slides down the incline.

✓ Model answer (earns the points)

Use tilted axes: x parallel to the incline (positive down the incline), y perpendicular to the incline.

Perpendicular direction (y): The block doesn't accelerate into or out of the surface, so ΣF_y = 0.

F_N − mg·cos(θ) = 0 → F_N = mg·cos(θ) = 4 · 10 · 0.87 = 34.8 N

Friction: F_k = μ_k · F_N = 0.20 · 34.8 = 6.96 N (pointing up the incline)

Parallel direction (x): Apply Newton's second law down the incline:

mg·sin(θ) − F_k = ma

4 · 10 · 0.50 − 6.96 = 4a

20 − 6.96 = 4a → a = 13.04 / 4 ≈ 3.26 m/s²

Answer: a ≈ 3.3 m/s² down the incline.

Why it scores: (1) Correctly resolves gravity into components parallel and perpendicular to the incline. (2) Sets ΣF_⊥ = 0 to find the normal force (NOT mg). (3) Uses F_k = μ_k·F_N with the correct normal force. (4) Applies Newton's second law along the incline. (5) Reports answer with units.

A student claims: "If the incline angle is increased from 30° to 60°, the block's acceleration down the incline will double, because sin 60° / sin 30° = √3 ≈ 1.73, and at steeper angles, gravity pulls harder along the surface." Is the student's claim correct? Justify with a calculation.

✓ Model answer (earns the points)

The student is partially correct but missing important details. They're right that sin(θ) increases at steeper angles (gravity's pull along the surface gets larger), but they ignored that the NORMAL FORCE — and therefore friction — DECREASES as the angle increases.

Calculate at θ = 60°: sin 60° ≈ 0.87, cos 60° = 0.50.

F_N = mg·cos(60°) = 4 · 10 · 0.50 = 20 N

F_k = μ_k · F_N = 0.20 · 20 = 4 N

a = g·sin(60°) − μ_k·g·cos(60°) = 10·0.87 − 0.20·10·0.50 = 8.7 − 1.0 = 7.7 m/s²

Compare to part B: a at 30° ≈ 3.3 m/s². At 60°, a ≈ 7.7 m/s². That's a ratio of 7.7/3.3 ≈ 2.3, not 2.0. So acceleration MORE than doubles — the student's reasoning was incomplete but underestimated the effect.

The reason: friction shrinks as cos(θ) decreases, so two effects amplify the acceleration at steeper angles.

Why it scores: (1) Evaluates whether the claim is correct (gives a clear yes/no/partial). (2) Computes the acceleration at the new angle with correct work. (3) Compares numerically to the original. (4) Identifies the missing physics (friction also changes with angle). Even just saying "incorrect" with a calculation that proves it earns most points.

How to score points on AP Physics 1 FRQs

Always start with a free-body diagram. Even when not asked, sketch one to organize your thinking. Many graders give partial credit for a correct FBD even when the algebra goes sideways.
Tilt your axes on incline problems. Choose one axis parallel to the surface, one perpendicular. This makes the math cleaner because the acceleration only has one component.
Resolve gravity into components. On an incline tilted by θ: parallel component = mg·sin(θ), perpendicular = mg·cos(θ).
Write Newton's second law in symbols first. Then substitute numbers. This shows you know the physics, not just arithmetic.
State your sign convention. Pick one direction as positive and stick with it.
Don't assume F_N = mg. On inclines, in elevators, when something pushes down — F_N changes. Always derive it from ΣF_⊥ = 0.
Units matter. An answer of "3.3" doesn't earn full credit; "3.3 m/s²" does.