Bicycle Braking Distances on a Wet Court
During a road-safety unit, students measure the braking distance of a bicycle on the school court, first when dry and again after the caretaker hoses it down. The same rider (mass 55 kg) uses the same bicycle (mass 12 kg), tyre pressure is checked before every run, and the brakes are adjusted before each session. Each test is repeated three times and the mean is recorded. Speed 10 km/h: 2.1 m dry, 3.0 m wet. Speed 15 km/h: 4.6 m dry, 6.7 m wet. Speed 20 km/h: 8.0 m dry, 12.5 m wet. Speed 25 km/h: 12.9 m dry, 20.4 m wet. After seeing the results, one student says the wet distances are longer because "the water makes the bike heavier, so it takes more force to stop". Another student suggests the class should also test a loaded bike to see if mass matters.
1. Describe the relationship between speed and braking distance shown by the dry data, and explain it using energy.
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The distance does not rise in step with speed - it rises much faster. Doubling speed from 10 to 20 km/h multiplies the dry distance by about 3.8 (2.1 m to 8.0 m), close to a factor of four, and doubling from 12.5 to 25 km/h would give a similar jump. So doubling speed roughly quadruples braking distance.
The reason is that the energy the brakes must remove is kinetic energy, E = ½mv², which depends on the square of speed. At twice the speed the bicycle carries four times the kinetic energy, so at the same braking force it needs four times the distance. The braking force itself is roughly constant (set by friction between tyre and road), and work done = force × distance, so four times the energy needs four times the distance.
This is why the difference between 20 and 25 km/h looks small on the speedometer but adds nearly 5 m of dry stopping distance.
2. Evaluate the claim that water makes the bike heavier, and state what the wet results actually show.
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The claim does not survive scrutiny. A wetted tyre and frame pick up at most a few grams of water spread over the whole bike and rider, which is negligible against 67 kg - it cannot explain a 55–60 % increase in distance at every speed. If mass really were the cause, the dry and wet runs at the same speed and the same mass would be identical, and they are not.
What the wet data show is a reduction in the friction available between the tyre and the road. Water acts as a lubricant and partly separates the rubber from the surface, so the maximum braking force before skidding is lower. With less force, the same kinetic energy takes a longer distance to remove. Heavy rain also reduces visibility and the rider's reaction time, which adds to total stopping distance beyond what this experiment measures.
The mass question is worth testing, but it must be tested with a genuinely different mass - a loaded pannier of 20 kg - on the same surface, not inferred from a wet tyre.
3. At 20 km/h the wet braking distance is 12.5 m. A rider approaching a car park entrance sees a vehicle at the 10 m mark and brakes. Use the data to judge whether the rider stops in time, stating any assumption.
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From the data alone, the rider needs 12.5 m to stop on the wet court, which is already more than the 10 m available - so on braking distance alone the answer is no.
The real situation is worse, because 12.5 m is only the braking distance. The rider must first react: at 20 km/h the speed is 20 ÷ 3.6 = 5.6 m/s, and a typical reaction time of 0.7 s adds 5.6 × 0.7 ≈ 3.9 m before the brakes even bite. Total stopping distance is therefore about 16.4 m, well beyond 10 m.
Assumptions to state: the court surface has similar grip to the car park (wet asphalt may be worse), the rider is alert and braking at maximum without skidding, and the 0.7 s reaction time is typical rather than measured. A cautious conclusion is that the rider would strike the vehicle at roughly 15–20 km/h, which is why the wet-distance data matter for setting speed limits near entrances.