The four tires of an automobile are inflated to a gauge pressure of 1.8 multiplied by 105 Pa. Each tire has an area of 0.025 m2 in contact with the ground. Determine the weight of the automobile.
No idea how to start, please help.
1 Pa = 1 N/m^2
[I think you meant 105kPa = 105000Pa]
(1.8)(105000Pa) = 189000 Pa = 189000 N/m^2
Total area of contact = (0.025 m2)(4) = 0.100 m^2
If you multiply the total pressure by the area of contact you will get the total weight in newtons.
Note: If you divide the weight in newtons by the gravitational acceleration, g = 9.8 N/kg, you will get the mass of the car in kilograms
To determine the weight of the automobile, we can use the concept of pressure and leverage it with the given information.
The formula for pressure is:
Pressure = Force / Area
In this case, the pressure is the gauge pressure in the tires, and the force is the weight of the automobile. The area is the contact area of each tire with the ground.
Therefore, we can rearrange the formula to solve for the force/weight:
Force = Pressure * Area
Let's calculate it step by step:
Given:
Gauge pressure (P) = 1.8 * 10^5 Pa
Area (A) = 0.025 m^2 per tire
Number of tires = 4
To find the total force (F), we need to calculate the force for each tire and then sum them up:
Force per tire = Pressure * Area
Force per tire = (1.8 * 10^5 Pa) * (0.025 m^2)
Force per tire = 4500 N
Total weight of the automobile = Force per tire * Number of tires
Total weight of the automobile = 4500 N * 4
Total weight of the automobile = 18,000 N
Therefore, the weight of the automobile is 18,000 Newtons.