in a car, compressed air exerts a force F1 on a small piston having a radius of 5cm. this pressure is transmitted to a second piston of radius 15cm.if the mass of car to be lifted is 1350kg ,what is the force F1 necessary to accomplish this task?
the pressure on each piston is the same:
Pressure=force/area
force2/area2=force1/area1
force1=1350*9.8N * (5/15)^2
5.8 × 10^5
To find the force F1 necessary to lift the car, you can use the principle of Pascal's Law, which states that when pressure is applied to a fluid in a sealed container, it is transmitted equally in all directions.
Step 1: Find the pressure exerted by the compressed air on the first piston.
Pressure (P1) = Force (F1) / Area (A1)
Since the radius of the first piston is given as 5cm, the area can be calculated as:
A1 = π * r1^2 = π * (0.05m)^2 = 0.00785m^2
Step 2: Calculate the pressure transmitted to the second piston from the first piston.
Since the pressure is transmitted equally in all directions, the pressure exerted on the second piston (P2) will be equal to P1.
P2 = P1 = Force (F2) / Area (A2)
Since the radius of the second piston is given as 15cm, the area can be calculated as:
A2 = π * r2^2 = π * (0.15m)^2 = 0.0707m^2
Step 3: Calculate the force exerted on the second piston.
F2 = P2 * A2
F2 = P1 * A2
Step 4: Find the force required to lift the car (F1).
Since the force exerted on the second piston (F2) is equal to the force needed to lift the car, we have:
F1 = F2
Let's substitute the values and calculate F1:
F2 = P1 * A2
F1 = P1 * A2
Now we need to find P1. To find the pressure, we need some additional information, such as the volume of the compressed air or any other data related to the air compression process. Without that information, it is not possible to calculate the force F1 in this scenario.