A friend asks you how much pressure is in your car tires. You know that the tire manufacturer recommends 30 psi, but it’s been a while since you’ve checked. You can’t find a tire gauge in the car, but you just finished taking physics and so you tell your friend, "I don’t know, but I can figure it out." From the owner’s manual you find that the car’s mass is 1700 kg . It It seems reasonable to assume that each tire supports one-fourth of the weight. Using a ruler, you find that the tires are 16 cm wide and the flattened bottom segment of the tire is 15 cm long. Your observation of the tire tread pattern suggests that two-thirds of this segment is in actual contact with the road.
What answer—in psi—will you give your friend?

To calculate the pressure in the car tires, we can use the equation $P = \frac{F}{A}$, where $P$ is the pressure, $F$ is the force acting on the area, and $A$ is the area over which the force is applied. In this case, the force acting on the tire is the weight of the car, and the area is the portion of the tire that is in contact with the road.

First, we need to calculate the weight of the car. The weight of the car is given by the equation $W = mg$, where $m$ is the mass of the car and $g$ is the acceleration due to gravity. We are given that the mass of the car is 1700 kg, so the weight is $W = 1700 \text{ kg} \times 9.8 \text{ m/s}^2 = 16786 \text{ N}$.

Next, we need to calculate the force acting on each tire. Since the weight of the car is distributed evenly among the four tires, each tire supports one-fourth of the total weight, or $F = \frac{1}{4} \times 16786 \text{ N} = 4196.5 \text{ N}$.

Now we need to calculate the area of the tire that is in contact with the road. The width of the tire is 16 cm, and we are given that two-thirds of the flattened bottom segment is in contact with the road.

This means that the length of the segment in contact with the road is $\frac{2}{3} \times 15 \text{ cm} = 10 \text{ cm}$. The area of the tire in contact with the road is therefore $A = 16 \text{ cm} \times 10 \text{ cm} = 160 \text{ cm}^2$.

Finally, we can use the equation $P = \frac{F}{A}$ to calculate the pressure in the tires. Plugging in the values for the force and the area, we get

$P = \frac{F}{A} = \frac{4196.5 \text{ N}}{160 \text{ cm}^2} = 26.2 \text{ Pa}$

Since 1 psi is equivalent to 6894.757 Pa, the pressure in the tires is approximately

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