The pressure in each of your car tires is 2.30X10^5 Pa. The mass of your car is 1640 kg. Assuming that each of your tires bears one-quarter of the total load, what is the contact area of each tire with the road?
To find the contact area of each tire with the road, we can use the formula:
Pressure = Force / Area
In this case, the force is equal to the weight bearing on each tire, and the pressure given is the pressure exerted by each tire on the road surface. Since each tire bears one-quarter of the total load, we need to calculate the force borne by one tire.
First, let's calculate the weight of the car:
Weight = mass * gravity
where mass = 1640 kg and gravity ≈ 9.8 m/s^2
Weight = 1640 kg * 9.8 m/s^2 = 16072 N (Newtons)
Now, let's calculate the force borne by one tire:
Force = Weight / 4
Force = 16072 N / 4 = 4018 N
Next, we can rearrange the formula to solve for the contact area:
Area = Force / Pressure
Area = 4018 N / 2.30 × 10^5 Pa
Now, let's calculate the contact area: