A car tire makes contact with the ground on a rectangular area of 12cm by 18cm and the pressure exerted on the ground by the car is 1.05 x 10^5 Pa . the car mass is ..........
the answer is 925 but i need the steps
1.05*10^5 * .12*.18 = ---- kilograms
now it is not clear if that is one of four tires
if so then multiply by 4
I wonder because around 2,000 kg is reasonable for a car and four times that is pretty heavy.
To find the mass of the car, we need to use the given information about the pressure exerted by the car and the area of contact between the tire and the ground. We can use the formula:
Pressure = Force / Area
Given:
Pressure = 1.05 x 10^5 Pa
Area = 12 cm x 18 cm
First, let's convert the area from cm to m:
1 cm = 0.01 m
So, the area = 12 cm x 18 cm = (12 x 0.01 m) x (18 x 0.01 m) = 0.12 m x 0.18 m = 0.0216 m²
Now, rearrange the formula to solve for the force:
Force = Pressure x Area
Substituting the values:
Force = (1.05 x 10^5 Pa) x (0.0216 m²)
Force = 2268 N
Now, we can use the formula:
Force = mass x acceleration
Since the car is not accelerating vertically, the acceleration is the acceleration due to gravity, which is approximately 9.8 m/s².
Rearranging the formula to solve for mass:
mass = Force / acceleration
Substituting the values:
mass = 2268 N / 9.8 m/s²
mass ≈ 231.43 kg
Therefore, the mass of the car is approximately 231.43 kg.
To find the mass of the car, we need to use the formula for pressure:
Pressure = Force / Area
The force exerted by the car on the ground can be calculated as:
Force = Pressure x Area
Given:
Pressure = 1.05 x 10^5 Pa
Area = 12 cm x 18 cm = 216 cm^2 = 0.0216 m^2 (converting cm^2 to m^2 by dividing by 10000)
Substituting the values into the formula, we get:
Force = (1.05 x 10^5 Pa) x (0.0216 m^2)
Now, the force exerted by the car is equal to the weight of the car (mass x acceleration due to gravity, g).
Force = mass x g
Rearranging the equation, we can find the mass of the car:
mass = Force / g
The acceleration due to gravity, g, is approximately 9.8 m/s^2.
mass = (1.05 x 10^5 Pa x 0.0216 m^2) / 9.8 m/s^2
Calculating the above expression:
mass ≈ 226.08 kg
Therefore, the mass of the car is approximately 226.08 kg.