An automobile has four tires, each one inflated to a gauge pressure of 176,357 Pa. Each tire is slightly flattened by its contact witht he ground, so that the area of contact is 21.9 cm by 17.9 cm. What is the weight of the automobile?
total contact area = 4 * .217 * .179
= .155 meters^2
total force = gage pressure * area
= 176357*.155 = 27,401 Newtons weight
It might be interesting to also find the mass in kilograms assuming this all happens on earth
27,401/9.81 = 2793 Kg mass (heavy car)
To find the weight of the automobile, we need to use the concept of pressure and area. The weight of an object can be calculated by multiplying its pressure and the area over which the pressure is applied.
Given:
- Gauge pressure (P) = 176,357 Pa
- Area of contact (A) = 21.9 cm * 17.9 cm
Before calculating the weight, we need to convert the area from square centimeters (cm²) to square meters (m²), since pressure is given in pascals (Pa), which is the SI unit for pressure.
The conversion factor is 1 m² = 10,000 cm².
Converting the area:
A = 21.9 cm * 17.9 cm
A = (21.9 cm * 17.9 cm) / (1 m² / 10,000 cm²)
A = 0.0219 m * 0.0179 m
A = 0.00039261 m²
Now, we can calculate the weight (W):
W = P * A
Substituting the given values:
W = 176,357 Pa * 0.00039261 m²
Calculating the weight:
W = 69.1731 kg * 9.81 m/s²
Finally, we can solve for the weight:
W ≈ 678.336 N
Therefore, the weight of the automobile is approximately 678.336 N.