The piston of hydraulic automobile lift is 0.30 m in diameter. Calculate the gauge pressure required to lift a car with a mass 1000 kg in,
A) Pascals
B) Atm
Hint:
pressure=force/area
To calculate the gauge pressure required to lift a car using a hydraulic automobile lift, we need to use the following formula:
Pressure (P) = Force (F) / Area (A)
The force required to lift the car can be found using the formula:
Force (F) = mass (m) * acceleration due to gravity (g)
where:
mass (m) = 1000 kg (given)
acceleration due to gravity (g) = 9.8 m/s^2
Let's calculate the area (A) of the piston first.
A) Pascals:
The area of a circular piston can be calculated using the formula:
Area (A) = π * (radius)^2
where:
radius = diameter / 2
Given:
diameter = 0.30 m
Calculating the radius:
radius = 0.30 m / 2 = 0.15 m
Now we can calculate the area (A):
Area (A) = π * (0.15 m)^2
Next, we can calculate the force (F) using the mass of the car and acceleration due to gravity:
Force (F) = 1000 kg * 9.8 m/s^2
Finally, we can calculate the pressure (P) using the formula:
Pressure (P) = Force (F) / Area (A)
Plug in the calculated values for force and area to find pressure in Pascals.
B) Atm:
To convert pressure from Pascals to atm, we need to divide the pressure in Pascals by the value of 1 atm, which is approximately 101325 Pascals.
To summarize:
A) Pascals:
1. Calculate the area (A) = π * (0.15 m)^2
2. Calculate the force (F) = 1000 kg * 9.8 m/s^2
3. Calculate the pressure (P) = F / A
B) Atm:
4. Convert the pressure from Pascals to atm by dividing the pressure in Pascals by approximately 101325.