O-Level Pressure: worked solution

Question

A solid rubber bicycle tyre rests on the ground. The bicycle plus rider has a mass of 60 kg, the tyre-road contact area totals 2.4 × 10^-3 m², and g = 10 N/kg. (a)(ii) Work out the pressure on the road, showing your working.

Principle: pressure is the normal force per unit area, p = F/A, and when the answer is wanted in pascals every quantity must be in SI units, because 1 Pa is defined as 1 N/m². Step 1 - turn the mass into a force. The force pressing on the road is the weight of the bicycle and rider, and weight = mass × gravitational field strength: W = mg W = 60 kg × 10 N/kg W = 600 N. (Mass in kilograms is not a force; it must be converted before it can go into p = F/A.) Step 2 - the area. The contact area is given as the total for the tyre against the road, already in SI units: A = 2.4 × 10⁻³ m² = 0.0024 m². Step 3 - divide. p = F/A p = 600 N / 0.0024 m² p = 250 000 N/m² p = 250 000 Pa. Step 4 - convert to a tidier unit. Since 1 kPa = 1000 Pa, divide by 1000: p = 250 000 / 1000 p = 250 kPa.