Pancyprian Physics common mistakes
Pancyprian Physics · Understand the traps and how to avoid them.
When solving projectile or free-fall problems, students plug g = +9.8 m/s² into every equation regardless of the chosen positive direction, then report a negative time or a height with the wrong sign and simply drop the sign instead of interpreting it.
Textbooks often write the constant as g = 9.8 m/s² and the student memorises it as a positive number, treating the sign convention as a formality rather than a decision made once per problem. Because the Pancyprian paper mixes upward-positive and downward-positive setups across questions, the student never fixes a convention explicitly and the algebra silently produces contradictions (e.g. t < 0) that get 'fixed' by deleting a minus sign.
What to do instead
Before writing any equation, draw the axis and write 'upward positive, so a = −g' (or the reverse) in the margin. Substitute the signed value, and when a negative root appears, state in words what it means (the object was earlier at that position) rather than discarding it. Check the final sign against the physical picture before writing the answer.
On inclined-plane and connected-body problems, students draw the weight straight down the slope, or omit the normal force's role in friction, so the acceleration comes out as g sinθ plus a spurious extra g, and the tension in a two-mass system is set equal to one of the weights.
The free-body diagram is treated as a labelling exercise after the equations are already written, so components are resolved from memory. Students also carry the intuition that 'the heavy block pulls with its weight', which is only true in equilibrium, not when the system accelerates. The result is a diagram that does not match the equations, and no consistency check is performed.
What to do instead
Force the discipline of diagram-first: draw each body separately, mark only real forces (weight, normal, tension, friction), then resolve along and perpendicular to the acceleration direction. For connected bodies, write one equation per body and eliminate the tension; verify that T ≠ m₁g whenever a ≠ 0 and that T is the same magnitude at both ends of an ideal string.
In momentum and collision questions, students apply conservation of kinetic energy to any collision, or use conservation of momentum only when the collision is elastic, and they forget that momentum is a vector when the bodies move at an angle.
Momentum and energy are taught in adjacent chapters and both are 'conserved quantities', so the conditions attached to each get blurred. Students also default to scalar arithmetic because most textbook collisions are head-on, and the angled case exposes the missing vector treatment only in the exam.
What to do instead
Write the rule pair explicitly at the top of every collision solution: momentum is conserved in all isolated collisions (vector, so resolve into x and y); kinetic energy is conserved only if the collision is elastic. For two-dimensional cases, set up p_x and p_y conservation separately and check the total KE before and after to classify the collision.
For simple harmonic motion, students use ω = 2πf and T = 2π/ω interchangeably with the pendulum and spring formulas without checking which system they have, and they state that acceleration is maximum at the equilibrium position or that velocity is zero at maximum displacement and also at equilibrium.
The SHM formulas look similar and are memorised as a list rather than derived from a = −ω²x. Because the defining relation a ∝ −x is not internalised, the phase relationship between displacement, velocity and acceleration is guessed, and the student cannot self-check a graph of x(t), v(t), a(t).
What to do instead
Anchor everything on a = −ω²x: acceleration is zero at equilibrium and maximum at the extremes; velocity is maximum at equilibrium and zero at the extremes; v leads x by a quarter cycle. For springs use T = 2π√(m/k) and for a simple pendulum T = 2π√(l/g), and state which restoring force justifies each before substituting numbers.
In wave and sound problems, students add frequencies or wavelengths when two waves superpose, confuse the observed frequency in the Doppler effect with the source frequency, and treat a phase difference of π as a path difference of one wavelength instead of half a wavelength.
Superposition is described verbally as 'waves adding', which suggests adding their parameters rather than their displacements at a point. The Doppler formula is memorised as a single fraction without the sign logic for approaching versus receding, and the phase–path relation Δφ = 2πΔx/λ is recalled incompletely.
What to do instead
Superpose displacements, never frequencies or wavelengths. Write the Doppler relation with an explicit sign table (approaching raises f, receding lowers it) and check the limiting case v_source = 0. For interference, always convert through Δφ = 2πΔx/λ, so Δφ = π corresponds to Δx = λ/2 and gives destructive interference.
In DC circuit problems, students treat the terminal voltage of a real battery as equal to its EMF while current flows, ignore the internal resistance when computing the total current, and add parallel resistors by direct summation.
Ideal-battery problems dominate early practice, so the internal resistance r is bolted on as an afterthought and dropped under exam pressure. The parallel rule is confused with the series rule because both are 'combining resistors', and the reciprocal in 1/R = 1/R₁ + 1/R₂ is a frequent arithmetic slip.
What to do instead
Always redraw the circuit with r drawn as a resistor in series with the ideal EMF. Use ε = I(R + r) and V_terminal = ε − Ir, and sanity-check that V_terminal < ε whenever I > 0. For parallel branches, compute the equivalent resistance from the reciprocal sum and verify it is smaller than the smallest branch resistance.
When applying Faraday's and Lenz's laws, students compute the induced EMF magnitude but assign the current direction by guessing, or they claim an induced current appears in a coil that moves through a uniform magnetic field without any change in flux.
Lenz's law is stated as 'opposes the change', which is easy to recite and hard to apply, so the direction step is skipped. The flux condition Φ = BA cosθ is remembered as 'field present' rather than 'flux changing', so uniform-field translation is mistakenly treated as inducing a current.
What to do instead
Apply a fixed three-step routine: (1) identify the area and the field, (2) decide whether Φ is increasing or decreasing, (3) choose the current direction whose own field opposes that change. State explicitly that EMF requires a changing flux, so motion parallel to a uniform field or motion that keeps the flux constant gives zero EMF.
In thermodynamics and kinetic theory, students apply the ideal-gas law with temperatures in degrees Celsius, mix up heat Q = mcΔT with internal energy change, and assert that in an isothermal process no heat is exchanged.
The gas law is practised with 'nice' numbers where the temperature unit is not stressed, and the words 'isothermal' and 'adiabatic' are both associated with 'no change', so they collapse into one idea. The first law is memorised as a formula rather than as an energy balance, so Q and ΔU are used as synonyms.
What to do instead
Convert to kelvin at the start of every gas calculation and write the conversion in the working. Keep the first law as ΔU = Q − W and classify each process by which quantity is zero: isothermal means ΔU = 0 (so Q = W), adiabatic means Q = 0 (so ΔU = −W), isochoric means W = 0. Use Q = mcΔT only for sensible heat with no phase change, and add mL for latent heat.
In geometric optics, students place the image on the same side as the object for a converging lens, or use the mirror equation with the wrong sign for a virtual image, and they draw ray diagrams that do not actually intersect at the computed image position.
The thin-lens and mirror equations are memorised as 1/f = 1/u + 1/v without a sign convention, and the real-is-positive rule is applied inconsistently between lenses and mirrors. Because the diagram and the algebra are done as separate tasks, a mismatch between them is never noticed.
What to do instead
Adopt one sign convention and write it at the top of the page (for example, real object distance positive, real image distance positive, f positive for converging). After computing v, check its sign against the ray diagram: a negative v must correspond to a virtual image on the object side of a lens. Use the magnification m = −v/u (or the mirror equivalent) to confirm orientation and size.
In modern physics and nuclear questions, students use the photoelectric equation with the photon frequency and the threshold frequency swapped, or they balance a nuclear equation by mass number only and leave the atomic number unbalanced.
The photoelectric equation is recalled as 'hf = work function plus something' without the physical meaning of each term, so the threshold frequency is inserted where the incident frequency belongs. Nuclear equations are treated as arithmetic on the top number only, because the element symbol is copied rather than derived from Z.
What to do instead
Write the photoelectric equation as hf = φ + K_max and label each symbol in words (incident photon energy, work function, maximum kinetic energy), then check that K_max = 0 exactly at f = f₀. For nuclear equations, balance both A and Z explicitly and identify the daughter element from Z using the periodic table, not from the symbol given in the question.
In fluid and elasticity questions, students apply Archimedes' principle using the volume of the object rather than the submerged volume, and they use the full weight instead of the apparent weight when a body floats, so a floating block is reported to displace its entire volume.
The buoyancy formula F = ρgV is learned with V described loosely as 'the volume', and the distinction between total and displaced volume is lost. Floating and submerged cases are not separated conceptually, so the equilibrium condition weight equals buoyant force is not used to find the submerged fraction.
What to do instead
State the rule before substituting: the buoyant force equals the weight of displaced fluid, so V is the submerged volume. For a floating body, set ρ_object V_total = ρ_fluid V_submerged and solve for the submerged fraction; for a fully submerged body, use V_total and compare buoyant force with weight to decide whether it sinks or rises.
In laboratory and error-analysis questions, students quote a final result to more significant figures than the data justify, add percentage uncertainties arithmetically when quantities are multiplied or divided, and read a vernier or micrometer scale without applying the zero error.
Calculator output is copied verbatim because the significant-figure rule is treated as presentation rather than physics, and the uncertainty rules for sums versus products are memorised as one rule. Zero error is skipped because the instrument is assumed correct, even though the question deliberately supplies a non-zero reading.
What to do instead
Round the final answer to the least number of significant figures in the data and state the absolute uncertainty with one significant figure. Use absolute uncertainties added for sums and differences, and percentage uncertainties added for products and quotients. For vernier and micrometer readings, record the zero error first and subtract it with its sign before quoting the measurement.