The 2016 Physics Bowl favored short stems and clean numbers, with mechanics chains and circuit analysis as the main line and friendly thermodynamics and geometric optics; 40 questions in 45 minutes with separate Division awards. Scan for the full paper and answer key.
The 25 online practice questions start instantly; the full past-paper & answers PDF is available free from an advisor via the QR code — it is not a direct download on this page.2016 Physics Bowl paper overview and exam highlights.
The 2016 paper was known for short stems and quick calculations. Mechanics was again the largest block, dominated by kinematics and energy-conversion chains, with circular motion and celestial orbits arriving in the second half. Electromagnetism carried a solid share, with dense classic models such as circuit simplification and the ideal transformer. Thermodynamics and geometric optics were friendly enough to be done first to bank time.
The format matched previous years: 40 multiple-choice questions in 45 minutes, points for correct answers with no penalty for wrong ones, calculators allowed, all in English. Division 1 (for first-year students and beginners, no calculus) and Division 2 (for second-year and AP Physics C students) are ranked and awarded separately and cannot both be entered. Registration and contest dates follow the official AAPT announcement each year; the contest is typically held in spring, around late March to early April.
For this style, training should focus on modeling speed and unit discipline: upon reading a question, write the formula and units immediately and avoid mid-stream conversions. The 25 original practice questions on this page cover the five sections across basic, medium and hard tiers. After finishing, scan for the 2016 paper and answer key to check your work item by item.
2016 Physics Bowl main topic areas, weights and emphasis.
Kinematics ratios and energy-conversion chains dominate, with circular motion and orbits in the second half
Circuit simplification and the ideal transformer are high-frequency models, with basic induction closing the set
Optical models such as lens imaging and thin-film interference rise in share, geometric optics prominent
Fixed patterns of thermal expansion, conduction and gas laws, all in the low-to-mid difficulty zone
Nuclear structure and half-life calculations appear steadily, quantum concepts kept light
2016 Physics Bowl-style mock questions (Basic · Medium · Hard) — submit to grade and view step-by-step solutions.
A sports car accelerates steadily from 20 m/s to 60 m/s in 4.0 s. What is its acceleration during this interval?
Correct answer: B
Acceleration a = Δv/Δt = (60 − 20)/4.0 = 40/4.0 = 10 m/s2. Answer B. Core: acceleration = change in velocity divided by time.A spring scale stretches 4.0 cm when a 200 g mass is hung on it (g = 10 m/s2). What is the spring constant?
Correct answer: D
The force F = mg = 0.200×10 = 2.0 N, so k = F/x = 2.0/0.040 = 50 N/m. Answer D. Core: Hooke law k = F/x, with centimeters converted to meters.A climber of mass 60 kg ascends a vertical 10 m rock wall at constant speed in 20 s (g = 10 m/s2). What is her average power output against gravity?
Correct answer: A
Work against gravity W = mgh = 60×10×10 = 6000 J; average power P = W/t = 6000/20 = 300 W. Answer A. Core: power = work divided by time; compute the work first.An electric heater has a resistance of 50 Ω and carries a current of 2.0 A. What power does the heater consume?
Correct answer: C
With current and resistance known, P = I2R = 2.02×50 = 200 W. Answer C. Core: P = I2R fits whenever current and resistance are given.A drone controller has a 6 Ω resistor and a 3 Ω resistor in parallel. What is the equivalent resistance of that part of the circuit?
Correct answer: E
Parallel combination Req = (6×3)/(6+3) = 18/9 = 2.0 Ω. Answer E. Core: two parallel resistors use product over sum, and the equivalent is smaller than either branch.A 2.0 μF capacitor and a 6.0 μF capacitor are connected in parallel across a 3.0 V source. What total charge do the parallel capacitors store?
Correct answer: C
Parallel capacitances add: C = 2.0 + 6.0 = 8.0 μF; total charge Q = CU = 8.0×3.0 = 24 μC. Answer C. Core: capacitances in parallel add (opposite to resistors), and Q = CU.A 2.0 m steel rail rises in temperature by 50 ℃; the linear expansion coefficient of steel is α = 2.0×10-5 /℃. By how much does the rail lengthen?
Correct answer: D
Linear expansion ΔL = αL0ΔT = 2.0×10-5×2.0×50 = 2.0×10-3 m = 2.0 mm. Answer D. Core: expansion = coefficient × original length × temperature rise.An ocean buoy measures a swell with period 8.0 s and wavelength 40 m. What is the propagation speed of the swell?
Correct answer: E
Wave speed v = λ/T = 40/8.0 = 5.0 m/s. Answer E. Core: wave speed = wavelength divided by period (equivalent to v = fλ).A carbon-14 nucleus has charge number 6 and mass number 14. How many neutrons does the nucleus contain?
Correct answer: A
Mass number A = proton number Z + neutron number N, so N = 14 − 6 = 8. Answer A. Core: neutrons = mass number minus charge number.A window pane is 4.0 mm thick with area 0.50 m2 and thermal conductivity k = 0.8 W/(m·K); the temperature difference across it is 40 ℃. What is the rate of heat conduction through the glass?
Correct answer: C
Conduction P = kAΔT/L = 0.8×0.50×40/0.0040 = 4000 W = 4.0 kW. Answer C. Core: conduction scales with area and temperature difference, inversely with thickness.A race car takes a horizontal curve of radius 80 m at a constant 20 m/s. What is its centripetal acceleration?
Correct answer: E
Centripetal acceleration a = v2/r = 202/80 = 400/80 = 5.0 m/s2. Answer E. Core: uniform circular motion accelerates toward the center with magnitude v2/r.A skateboarder starts from rest at the edge of a 1.25 m half-pipe and slides to the bottom. Ignoring friction (g = 10 m/s2), what is the speed at the bottom?
Correct answer: B
Energy conservation mgh = ½mv2 gives v = √(2gh) = √(2×10×1.25) = √25 = 5.0 m/s. Answer B. Core: the drop height fixes the speed via v = √(2gh), independent of path.An 80 kg astronaut at rest outside a space station throws a 2.0 kg wrench at 6.0 m/s in one direction. What is her recoil speed afterward?
Correct answer: D
Total momentum starts at zero: 80v = 2.0×6.0 = 12, so v = 0.15 m/s, opposite to the wrench. Answer D. Core: the thrown object and the recoiling astronaut carry equal and opposite momenta.A 0.50 kg mass hangs from a light vertical spring of stiffness 200 N/m and undergoes small-amplitude simple harmonic motion. What is the period of the oscillation?
Correct answer: E
Spring oscillator period T = 2π√(m/k) = 2π√(0.50/200) = 2π×0.050 ≈ 0.31 s. Answer E. Core: the vertical spring oscillator uses the same period formula as a horizontal one.A 12 V source feeds R1 = 2 Ω followed by a parallel pair R2 = 4 Ω and R3 = 4 Ω. What current flows through R2?
Correct answer: C
Parallel part 4∥4 = 2 Ω; total 4 Ω; main current I = 12/4 = 3 A; parallel section voltage = 3×2 = 6 V, so I2 = 6/4 = 1.5 A. Answer C. Core: find the main current first, then split it using the parallel voltage.An ideal transformer has 2000 primary turns connected to 240 V AC and 100 secondary turns. What is the secondary output voltage?
Correct answer: B
Ideal transformer U1/U2 = N1/N2: U2 = 240×100/2000 = 12 V. Answer B. Core: voltage scales with turns; a step-down transformer has fewer turns and lower voltage.An object sits 30 cm in front of a converging lens of focal length 10 cm. How far from the lens optical center is the image?
Correct answer: E
Lens equation 1/v = 1/f − 1/u = 1/10 − 1/30 = 2/30, so v = 15 cm, an inverted reduced real image. Answer E. Core: with 1/f = 1/u + 1/v, an object beyond twice the focal length images between f and 2f.White light strikes a soap film of refractive index n = 1.25 at normal incidence. Only the reflection at the top surface of the film undergoes a half-cycle phase flip. What is the minimum film thickness for constructive reflection of light of wavelength 500 nm in air?
Correct answer: D
With one half-wave flip, constructive reflection requires 2nt = (m + ½)λ; taking m = 0 gives tmin = λ/4n = 500/(4×1.25) = 100 nm. Answer D. Core: thin-film constructive reflection makes 2nt an odd multiple of half wavelengths, with minimum λ/4n.A deep-sea bubble has a volume of 2.0 cm3 at a pressure of 300 kPa. It rises at constant temperature to the surface, where the pressure is 100 kPa. What is its volume there?
Correct answer: C
Isothermal, so Boyle law P1V1 = P2V2: V2 = 300×2.0/100 = 6.0 cm3. Answer C. Core: at constant temperature, pressure and volume are inversely proportional.A nucleus X has charge number 88 and mass number 226. It first undergoes one alpha decay and then one beta-minus decay. What are the charge number Z and mass number A of the final nucleus?
Correct answer: A
Alpha decay lowers A by 4 and Z by 2 (giving Z = 86, A = 222); beta-minus decay keeps A and raises Z by 1, ending at Z = 87, A = 222. Answer A. Core: alpha decay is (A−4, Z−2) and beta-minus is (A, Z+1).A satellite moves in a circular orbit of radius r = 2.0×107 m around a planet of mass M = 6.0×1024 kg (gravitational constant G = 6.7×10-11 N·m2/kg2). What is the orbital speed of the satellite?
Correct answer: D
Gravity supplies the centripetal force, GMm/r2 = mv2/r, so v = √(GM/r) = √(6.7×10-11×6.0×1024/2.0×107) = √(2.0×107) ≈ 4.5×103 m/s = 4.5 km/s. Answer D. Core: orbital speed v = √(GM/r), independent of the satellite mass.A 2.0 kg block slides from rest down a frictionless track from a height of 1.25 m (g = 10 m/s2), then crosses a 0.50 m rough horizontal patch (friction coefficient μ = 0.50) before hitting a horizontal spring of stiffness 160 N/m. What is the maximum compression of the spring?
Correct answer: A
Initial mechanical energy mgh = 25 J; friction dissipates μmgd = 0.50×2.0×10×0.50 = 5 J; the remaining 20 J goes into the spring: ½×160×x2 = 20, so x2 = 0.25 and x = 0.50 m. Answer A. Core: keep a full energy ledger — potential energy minus friction heat equals spring energy.A rectangular coil of N = 100 turns and area 0.020 m2 rotates at angular speed ω = 50 rad/s about an axis perpendicular to a uniform 0.10 T magnetic field. What is the maximum induced emf in the coil?
Correct answer: B
Generator peak emf εmax = NBAω = 100×0.020×0.10×50 = 10 V. Answer B. Core: a coil spinning in a uniform field gives εmax = N×B×A×ω.Two speakers in phase emit 170 Hz sound; the speed of sound in air is 340 m/s. A point lies 12.0 m from one speaker and 15.0 m from the other. Is the sound at that point constructive or destructive?
Correct answer: C
Wavelength λ = v/f = 340/170 = 2.0 m; path difference Δ = 15.0 − 12.0 = 3.0 m = 1.5λ, an odd multiple of half a wavelength, so the waves arrive out of phase. Answer C. Core: in-phase sources interfere destructively when the path difference is an odd multiple of half a wavelength.A radioactive sample starts at 640 g and 80 g remains after 18 days. What is the half-life of the nuclide?
Correct answer: E
640 → 320 → 160 → 80 covers 3 half-lives in 18 days, so the half-life = 18/3 = 6 days. Answer E. Core: the number of half-lives = total time divided by the half-life, with mass halving as ½n.Unified Physics Bowl specs, consistent across years.
Division 1 is for first-year physics students (no calculus); Division 2 is for second-year and AP Physics C students. The two divisions are ranked and awarded separately — students must choose one and cannot take both. Pick based on your level; our advisor can help.
Four steps · Overview / Topics / Practice / Prep
Read the 2016 Physics Bowl overview and format specs to grasp the year’s style.
Review the key topics and weights, and locate your weak areas.
Complete the 25 mock questions; submit for auto-grading and right/wrong marks.
Open the step-by-step solutions, learn from mistakes, and scan for full papers to push for national and global rankings.
Prep tips and score-boosting advice for the 2016 Physics Bowl.
The 2016 paper has short stems and clean data; after reading, write the formula with units before substituting. Do ten timed single questions a day to compress reading-to-equation time under 20 seconds.
Series-parallel simplification, branch current sharing and transformer turn ratios are high-frequency models this year. Drill until equivalent resistors are mental math and transformer voltage ratios take one step.
Master 1/f = 1/u + 1/v with sign rules for lenses, and for thin films focus on the half-wave flip and the 2nt condition. These two models cover most of the optics in this paper.
Orbital speed √(GM/r), half-life arithmetic and balancing Z and A in decay equations are late-paper scoring points. Write the conservation relation before substituting to avoid blind formula errors.
Before the contest, run a full 45-minute set every two weeks, logging accuracy and time by section. Afterward scan for the 2016 paper and answer key and check whether the weak sections have truly closed.
Frequent questions about the 2016 Physics Bowl papers and answers.
Scan to add the advisor for 2016 Physics Bowl past papers, answer keys and solutions, plus a custom prep plan.
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