Ugo watches traffic from a bridge: a 1000 kg car at 10 m/s, a 2000 kg van at 10 m/s, and later the same van at 20 m/s.
Three movers, three kinetic energies. Can they be put in order without computing a single joule?
Compare two at a time, letting only one factor change per comparison.
The car and the van at 10 m/s: same speed, double the mass. The van carries more kinetic energy.
The van at 10 m/s and the same van at 20 m/s: same mass, double the speed. The faster van carries more kinetic energy, four times as much.
Chain the two comparisons: the car has the least, then the van at 10 m/s, then the van at 20 m/s.
A loaded freight car and an empty freight car roll along a siding at the same speed. Which carries more kinetic energy?
Two identical delivery vans leave a depot, one at 8 m/s and one at 16 m/s. Which carries more kinetic energy?
One warning. If two movers differ in both mass and speed in opposite directions, a heavier-but-slower against a lighter-but-faster, no single-factor step settles it: that comparison needs the calculation.
So scan the list first: as long as each neighboring comparison changes one factor, the whole order chains together for free.
Three travelers wheel suitcases through a train station at the same speed: a 10 kg case, a 20 kg case, and a 30 kg case. Rank their kinetic energies from least to greatest.
All three move at the same speed, so each comparison changes mass only.
More mass at the same speed means more kinetic energy.
Least to greatest: the 10 kg case, the 20 kg case, the 30 kg case.
A 700 kg race kart laps at 25 m/s. An identical 700 kg kart laps at 35 m/s, and a third identical kart carries ballast, with more mass, at 35 m/s. Rank the three kinetic energies from least to greatest.
First comparison: same mass, 25 m/s against 35 m/s. The faster kart carries more kinetic energy.
Second comparison: same 35 m/s, more mass. The ballasted kart carries more still.
Each comparison changed one factor, so the chain holds.
Least to greatest: the 25 m/s kart, the plain 35 m/s kart, the ballasted 35 m/s kart.
Talia says: 'Of two identical paddleboards, the faster one always carries more kinetic energy.' Is Talia correct?
Three baggage carts roll through an airport: an empty cart at 3 m/s, a loaded cart of twice the empty cart's mass at 3 m/s, and an identical loaded cart at 6 m/s. Which order ranks them from least kinetic energy to greatest?
Four rowboats cross a lake: an empty boat at 2 m/s, an empty boat at 4 m/s, a loaded boat at 4 m/s, and a loaded boat at 2 m/s. The loaded boats are identical to the empty ones apart from their passengers. Which rowboat carries the least kinetic energy?
Which pair of movers cannot be ranked by kinetic energy using single-factor comparisons alone?