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Physics interview
Estimate, model and check dimensions using basic principles and justified approximations.
One thinking framework
Use the same five steps for the exercises below. Familiarise yourself once, then focus on explaining your reasoning.
Five steps for your reasoning
1
Define variables, assumptions and a model
State what you are studying and what you will temporarily ignore.
2
Explain your choice of method
Connect your formula, theorem or comparison to the problem.
3
Explain each step as you calculate
Explain relationships, substitutions and intermediate conclusions.
4
Check units, scale and plausibility
Check signs, ranges, dimensions and possible sources of error.
5
Adapt to hints and changes
Identify which assumption changes and revise your approach.
1
Estimate: roughly how much electrical energy is consumed in the UK in a year for boiling water to make tea?
2
A block of ice with a small air bubble embedded in it is floating in a glass of water. When the ice has completely melted, will the water level rise, fall or stay the same?
3
Two small balls of the same material fall slowly in the same viscous liquid, and the radius of one is 2 times that of the other. Assuming the drag satisfies the Stokes form , by what factor do their terminal velocities differ? Derive it from the force balance and the scaling relations.
Scale derivation and validity of the model12–15 minutesForce equilibriumDimensional analysisAssumption checksModel comparison
4
A satellite orbits a planet of mass in a circular orbit of radius . Using only Newtonian gravitation and circular motion, derive the orbital speed and period, and determine by what factor each changes when the orbital radius becomes 4 times as large.
First-principles derivation and physical explanation12–16 minutesEquation modellingAlgebraic derivationOrder-of-magnitude judgementConcept clarification
5
A train starts horizontally with constant acceleration , and a small ball suspended from the ceiling of a carriage eventually comes to rest relative to the carriage, deflected from the vertical. Find the angle between the string and the vertical, and explain what “effective gravity” should be used when the ball makes small oscillations near this position.
Force diagrams and approximations in non-inertial frames15–18 minutesFree-body diagramChoice of reference frameVector additionSmall-oscillation approximation
6
A uniform small boat of length and mass is at rest on a frictionless water surface. A person of mass walks from the left end of the boat to the right end. How far does the boat move relative to the shore? State clearly the coordinate system and positive direction you choose.
Conservation of centre of mass and analysis of reference frames12–15 minutesSystem boundaryConservation of centre of massRelative displacementSign check