Step-by-Step Solution

1. Calculate the total force due to weight:

The force exerted by the cyclist and bike due to gravity is: \[ F = m \times g \] where:

• \( m = 90 \, \text{kg} \) is the total mass
• \( g = 9.8 \, \text{m/s}^2 \) is the acceleration due to gravity

Therefore, the force is: \[ F = 90 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 882 \, \text{N} \]

2. Determine the total contact area of the tires:

The area of one tire's contact patch is \( 0.0005 \, \text{m}^2 \). Since both tires equally share the load, the total contact area is: \[ A = 2 \times 0.0005 \, \text{m}^2 = 0.001 \, \text{m}^2 \]

3. Calculate the required pressure:

We use the pressure formula: \[ P = \frac{F}{A} \] Substituting the values for \( F \) and \( A \): \[ P = \frac{882 \, \text{N}}{0.001 \, \text{m}^2} = 882,000 \, \text{N/m}^2 = 882 \, \text{kPa} \]

4. Convert to psi:

To convert from kilopascals (kPa) to pounds per square inch (psi), we use the conversion: \[ 1 \, \text{kPa} = 0.145 \, \text{psi} \] Therefore: \[ 882 \, \text{kPa} \times 0.145 = 127.89 \, \text{psi} \]