A 1200kg car has its tyres inlated to a gauge pressure of 180kpa.How large an area for each tyre is in contact with the ground
4*P*A = M*g
P is the tire gauge pressure. This assumes there are 4 tires with equal load and area per tire.
Solve for A
To find the area of each tire in contact with the ground, we need to use the formula for pressure:
Pressure = Force / Area
In this case, the force is the weight of the car, and we need to convert it to newtons. The weight of the car can be found by multiplying the mass (1200 kg) by the acceleration due to gravity (9.8 m/s^2):
Weight = Mass * Gravity
Weight = 1200 kg * 9.8 m/s^2
Next, we need to convert the gauge pressure from kilopascals to pascals. Since 1 kPa = 1000 Pa:
Pressure = 180 kPa * 1000 Pa/kPa
Now we have all the necessary values to calculate the area:
Pressure = Force / Area
Area = Force / Pressure
Area = (Weight) / Pressure
Plug in the values:
Area = (1200 kg * 9.8 m/s^2) / (180 kPa * 1000 Pa/kPa)
Now we can solve for the area:
Area = (1200 kg * 9.8 m/s^2) / (180,000 Pa)
Calculating the values:
Area = 11760 kg*m/s^2 / 180000 Pa
Area = 0.065333... m^2
Therefore, each tire has an area of approximately 0.0653 m^2 in contact with the ground.