The gauge pressure in both tires of a bicycle is 720 kPa. If the bicycle and the rider have a combined mass of 87.0 kg, what is the area of contact of each tire with the ground? (Assume that each tire supports half the total weight of the bicycle.)

To find the area of contact of each tire with the ground, we need to use the given information and some physics concepts.

First, let's start by calculating the total weight of the bicycle and the rider. We are told that the combined mass is 87.0 kg. The weight can be calculated using the formula:

Weight = mass × gravitational acceleration

The gravitational acceleration is approximately 9.8 m/s^2. Therefore, the total weight is:

Weight = 87.0 kg × 9.8 m/s^2

Now, since each tire supports half the weight of the bicycle, we can calculate the weight supported by each tire:

Weight supported by each tire = Weight / 2

Now that we have the weight supported by each tire, we can use the concept of pressure to find the area of contact.

Pressure is defined as:

Pressure = Force / Area

In this case, the force is the weight supported by each tire, and the pressure is the given gauge pressure of 720 kPa. However, we need to convert this pressure from kilopascals to pascals since the SI unit of pressure is the pascal (Pa).

1 kPa = 1000 Pa

So, the given gauge pressure of 720 kPa is equal to 720,000 Pa.

Let's denote the area of contact of each tire as A. Rearranging the pressure formula, we get:

Area = Force / Pressure

Substituting the values we found earlier, we get:

A = (Weight supported by each tire) / Pressure

A = (Weight / 2) / (720,000 Pa)

Finally, we can substitute the value of the weight and solve for the area of contact:

A = [(87.0 kg × 9.8 m/s^2) / 2] / (720,000 Pa)

Calculating this expression will give us the area of contact of each tire with the ground.