A 1,200kg car has its tyres inflated to a gauge pressure of 180kPa.How large an area for each tyre is in contact with the ground?
Assume 4 tyres and mass evenly distributed.
Then use pressure= force/area
1 Pa = 1 N m^-2
force = mass x acceleration
I would assume that g= 9.8 m s^-2
To find the area of each tire in contact with the ground, we need to consider the weight of the car and the pressure of the tires. Here's how you can calculate it step by step:
Step 1: Convert the car's weight from kilograms (kg) to Newtons (N).
The weight of the car can be calculated using the formula:
Weight = mass × gravitational acceleration
Given: mass of the car = 1,200 kg and gravitational acceleration = 9.8 m/s^2
Weight = 1,200 kg × 9.8 m/s^2 = 11,760 N
Step 2: Calculate the force exerted on each tire.
Since there are four tires evenly supporting the weight of the car, we divide the total weight by the number of tires. So, the force exerted on each tire is:
Force = Weight ÷ Number of tires
Given: Number of tires = 4
Force = 11,760 N ÷ 4 = 2,940 N
Step 3: Convert the gauge pressure from kilopascals (kPa) to Pascals (Pa).
1 kPa = 1,000 Pa
Given: gauge pressure = 180 kPa
Gauge Pressure = 180 kPa × 1,000 Pa/kPa = 180,000 Pa
Step 4: Calculate the area of each tire.
The area of each tire can be calculated using the formula:
Area = Force ÷ Pressure
Given: force = 2,940 N and gauge pressure = 180,000 Pa
Area = 2,940 N ÷ 180,000 Pa = 0.01633 m^2
Therefore, each tire has an area of approximately 0.01633 square meters in contact with the ground.