Slovak Physics Olympiad Cat A common mistakes
Slovak Physics Olympiad Cat A · Understand the traps and how to avoid them.
When a problem involves a block on an incline, a pulley, or a body in a fluid, the candidate writes down only the weight and one applied force, omitting the normal force, tension, friction, buoyancy, or the reaction partner of a chosen force, then solves the resulting incomplete equation.
Candidates treat free-body diagrams as a formality and draw them from memory of a similar problem rather than from the actual situation described; they also confuse the reaction partner of a force with a force acting on the same body.
What to do instead
Before writing any equation, draw a separate diagram for each body, mark every contact and long-range interaction, and for each force name the other body exerting it. Then check that every drawn force appears in exactly one Newton equation and that forces internal to a chosen system cancel.
In a collision or explosion problem the candidate applies conservation of mechanical energy even though the collision is inelastic, or applies momentum conservation in a direction where an external impulse (e.g. friction, a hinge reaction) acts.
The candidate pattern-matches on 'collision' and reaches for the energy equation because it is algebraically easier, without checking whether kinetic energy is conserved or whether the net external impulse in a direction is zero.
What to do instead
State explicitly at the start which conserved quantity is being used and verify its condition: momentum only if net external impulse is zero along that axis, energy only if no non-conservative work occurs. For inelastic cases use momentum plus an energy-deficit term, and compute the impulse from hinges or friction if the axis is not free.
For a rigid body the candidate writes only the force balance and forgets the torque (moment) balance, or computes torques about a point that is not at rest and omits the pseudo-force term, giving a wrong reaction force or a wrong condition for tipping.
Candidates reduce every statics problem to 'sum of forces equals zero' and do not internalise that rotational equilibrium is an independent condition; they also pick a convenient pivot without checking whether it is inertial.
What to do instead
Always write both conditions: net force zero and net torque zero. Choose the pivot at the unknown reaction or at the contact point to eliminate unknowns, and if the body accelerates, use the centre of mass as pivot or add the inertial pseudo-force at the centre of mass before taking torques.
In thermodynamics the candidate applies pV=nRT or the first law to a process without identifying which quantity is held constant (isothermal, adiabatic, isochoric, isobaric), or uses the adiabatic relation pV^kappa=const for a process that is not adiabatic.
The candidate memorises formulas as a list and selects by keyword rather than by the physical constraint stated in the problem; the distinction between heat, work and internal energy is blurred.
What to do instead
Before computing, write a one-line process identification: which of p, V, T, Q is fixed or zero, and whether the process is reversible. Then choose the corresponding relation and verify with the first law that the signs of Q and W are consistent with the stated heating or cooling.
The candidate mixes Kelvin and Celsius in gas-law or efficiency calculations, or uses the molar heat capacity at constant pressure where the volume is fixed (or vice versa), producing answers off by a factor or a constant offset.
Temperatures are often given in Celsius in the problem statement and the candidate substitutes them directly into ratios or into expressions derived for absolute temperature; similarly the c_p versus c_V distinction is treated as interchangeable.
What to do instead
Convert every temperature to kelvin at the moment it is read from the statement and carry units through the algebra. When a heat capacity appears, check the process: c_V for fixed volume, c_p for fixed pressure, and for an ideal gas use c_p = c_V + R to cross-check.
In an AC circuit the candidate adds a resistor voltage and a capacitor or inductor voltage arithmetically, or uses the peak voltage where the RMS is required (or the reverse) in power calculations.
The candidate carries over DC habits where voltages add linearly, and does not connect the phase difference between voltages across R, L and C with the phasor or complex-impedance picture; RMS versus peak is treated as a cosmetic detail.
What to do instead
Draw the phasor (or impedance) diagram and add voltages as vectors; compute the impedance magnitude Z = sqrt(R^2 + (X_L - X_C)^2). State explicitly whether each given voltage is amplitude or RMS, and use P = U_rms I_rms cos(phi) with the power factor from the phase angle.
When applying Faraday's law or Ampere's law the candidate ignores the direction of the induced current or the sign of the flux change, and in induction problems forgets Lenz's law, so the direction of the current or the force on the loop comes out reversed.
The candidate treats the laws as magnitude formulas and skips the orientation step, and the right-hand rule is applied inconsistently because the normal to the surface or the sense of the path is never fixed.
What to do instead
Before computing, fix and write down the positive sense of the loop and the surface normal. Compute the flux with signs, then use the minus sign in Faraday's law to get the EMF direction, and confirm with Lenz's law by asking which way the induced current must flow to oppose the change.
In geometric optics the candidate applies the thin-lens or mirror equation with a sign convention chosen ad hoc, or draws a ray diagram with rays that do not obey the actual refraction or reflection at the surface, giving a virtual image where a real one is expected.
Sign conventions differ between textbooks and the candidate switches between them mid-problem; ray diagrams are drawn by intuition about where the image 'should' be rather than by tracing rays from the object through the optical element.
What to do instead
State the sign convention in one line at the start (e.g. real object distance positive, image distance positive for real images) and apply it to every quantity. Trace at least two principal rays using the actual surface, and check the result against the magnification sign and the lens equation.
In interference and diffraction the candidate uses the single-slit minima condition and the double-slit maxima condition interchangeably, or forgets the path difference in a thin film where a phase shift of pi occurs on reflection at one surface only.
The formulas look similar (d sin(theta) = k lambda versus a sin(theta) = k lambda) and the candidate matches on the word 'slit'; the reflection phase shift is an extra physical fact that is easily dropped.
What to do instead
Identify the setup first: two coherent sources give maxima at path difference k lambda; a single slit gives minima at a sin(theta) = k lambda. For thin films, add pi to the phase of the ray reflected from the optically denser medium, then set the total phase difference equal to 2 pi k for constructive interference.
In relativity or quantum problems the candidate applies classical formulas (e.g. kinetic energy = p^2/2m, or Galilean velocity addition) outside their validity range, or uses the non-relativistic de Broglie relation when the particle is relativistic.
The candidate does not check whether v is comparable to c or whether the photon/particle energy is comparable to its rest energy, and defaults to the familiar classical expression.
What to do instead
Before substituting, compute the ratio v/c or the ratio of kinetic to rest energy. If either is not small, use the relativistic energy-momentum relation E^2 = (pc)^2 + (mc^2)^2 and the relativistic velocity addition. For photons always use E = hc/lambda and p = h/lambda, never p^2/2m.
In the experimental task the candidate reports a result with more significant figures than the data justify, adds absolute and relative uncertainties incorrectly, or omits units and the uncertainty altogether, and does not propagate errors through a calculated quantity.
Candidates treat error analysis as an afterthought and are not fluent in combining uncertainties; they also equate 'more digits' with 'more precise', and the reporting conventions are not practised.
What to do instead
Carry uncertainties through each operation: add absolute uncertainties for sums and differences, add relative uncertainties in quadrature for products and quotients, and multiply the relative uncertainty by |n| for a power. Round the uncertainty to one significant figure and quote the result to the same decimal place, with units.