BPhO challenge toolkit

They are balanced

HintSteady speed means no change in motion — so what must the resultant force be?

The whyBalanced forces do not mean "not moving"; they mean "not changing". A steady speed in a straight line is exactly what you get when the upward drag equals the downward weight, so the resultant is zero. Only an unbalanced force can speed something up, slow it down or bend its path — which is why a challenge question that says "constant velocity" is quietly telling you the forces cancel.

40

HintAverage speed is the whole journey divided by the whole clock reading, so find how long each leg lasts before you go near a mean.

The whyAverage speed is total distance ÷ total time, never the mean of the two speeds. The fast half takes 30 ÷ 60 = 0.5 h and the slow half takes 30 ÷ 30 = 1 h, so the car covers 60 km in 1.5 h and averages 40 km/h. The slower leg lasts twice as long, so it drags the average below the midpoint of 45 — and no amount of speeding up on the first half could ever lift the average to 60, because that would need the second half to take no time at all. Challenge papers set this trap most years, and the defence never changes: add the distances, add the times, divide once.

Weight

HintThe one of the pair that changes when you travel to the Moon.

The whyWeight is a force, so it takes the unit of force, the newton. Mass is the amount of matter and is measured in kilograms; it does not change when you travel. Take a 60 kg astronaut to the Moon and they are still 60 kg, but the pull on them drops from about 600 N to about 100 N because the Moon pulls roughly one sixth as hard. Bathroom scales measure a push and label it in kilograms — a shortcut that only works on Earth.

10

HintA round number; the precise value is a whisker under it.

The whyWeight = mass × g. On Earth g is about 9.8 N/kg, but challenge questions nearly always let you round to 10. Always write the unit: 3 kg is a mass, 30 N is a force, and a bare 30 is only half an answer.

100 J

HintEnergy transferred = force × distance moved. Work out the upward pull needed to raise the ball before you multiply by anything.

The whyTwo steps, and the first is the one most pupils skip. Weight = mass × g = 2 × 10 = 20 N, so raising the ball needs a 20 N upward force; energy transferred = force × distance = 20 × 5 = 100 J, and a joule is simply a newton-metre. Let the ball fall back off the shelf and that same 100 J moves into its kinetic store, so ½ × 2 × v² = 100 gives v² = 100 and a landing speed of 10 m/s — the store picture and a number, joined up. In reality air resistance shaves a little off, warming the surroundings instead.

2000

HintTurn the kilowatts into watts first — the prefix kilo- means a thousand of them.

The why2 kW is 2000 W, and a watt is a joule every second, so the kettle transfers 2000 J of energy in every second it is on. The prefixes are the same in every unit: kilo- ×1000, mega- ×1 000 000, centi- ÷100, milli- ÷1000. Challenge questions love to hand you a mixture of km, m and cm in one sentence; converting everything to one unit before calculating is the step that saves the mark.

ammeter

HintIt sits in series with the component, and its name says what it counts.

The whyAn ammeter reads current in amperes (A) and must be placed in series, so the current passes through it. A voltmeter reads potential difference in volts (V) and is connected in parallel, across the two ends of the component. In a series loop the current is the same at every point, so it does not matter where in the loop the ammeter goes — the reading is identical.

A parallel circuit

HintThink of the lights in a house — one bulb blowing does not black out the lot.

The whyIn a series circuit there is a single loop, the current is the same everywhere, and one break stops everything. In a parallel circuit each branch has its own path back to the cell, so each branch gets the full voltage of the supply and a break in one branch leaves the others working. Two identical bulbs in parallel are each as bright as a single bulb on its own; in series they share the voltage and are dimmer.

Nothing

HintA vibration has to be passed on from particle to particle — so remove the particles.

The whySound is a vibration carried by particles bumping into their neighbours, so it needs a medium: a solid, a liquid or a gas. Pump the air out and there is nothing left to carry it, though you can still see the hammer striking — light needs no medium at all. That is why space is silent, and why sound travels faster through water and faster still through steel, where the particles are held together more strongly and pass the vibration on more quickly.

340

HintRoughly a million times slower than light — count the seconds from flash to bang and divide by three for kilometres.

The whyThe speed of sound in air is about 340 m/s — UK textbooks quote 330, 340 or 343 depending on the temperature assumed, and a quiz will accept any of them or tell you which to use. Light travels at about 300 000 km/s, close enough to instant over any distance on Earth, so the flash arrives at once and the sound trails behind at roughly a third of a kilometre per second. The same fact runs echo questions: a clap that returns after 2 s has travelled to the cliff and back, so the cliff is about 340 m away, not 680.

The wood

HintSame volume, different mass. Which block squeezes fewer grams into each cubic centimetre?

The whyDensity = mass ÷ volume, and water is the yardstick at 1 g/cm³ (1000 kg/m³). Wood at roughly 0.7 g/cm³ floats; iron at about 7.9 g/cm³ sinks. Size is a distraction — a huge log floats and a tiny nail sinks. What matters is whether the object is less dense or more dense than the water it pushes aside, because that displaced water is what provides the upthrust holding it up.

force; area; pascal

HintThe same push over a smaller patch is a bigger squeeze; the unit honours a French scientist.

The whyOne pascal (Pa) is one newton spread over one square metre, so it can also be written N/m². Halving the area doubles the pressure, which is why a person on one foot exerts twice the pressure on the floor as on two, why a drawing pin goes in point-first, and why snowshoes stop you sinking. The unit is named after Blaise Pascal.