the car on the hydraulic lift in figure 22-2 has a weight of 16,170 N. Piston B has a surface area of 5,005 centimeters cubed; Piston A has an area of 65 centimeters cubed. What force must be applied to Piston A to lift the call?
I tried to do 16,170 by 5,005 but I don't think its right :/.
Help?
And can you explain the work if u can?
To find the force that must be applied to Piston A to lift the car, you can use Pascal's principle, which states that the pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and the walls of its container.
First, let's convert the piston areas to square meters to ensure consistent units:
Piston A area = 65 cm^2 = 65/10,000 m^2 = 0.0065 m^2
Piston B area = 5005 cm^2 = 5005/10,000 m^2 = 0.5005 m^2
Next, we need to find the pressure exerted on Piston B by the weight of the car. Pressure is defined as force per unit area. Therefore, the pressure on Piston B is given by:
Pressure on Piston B = Force on the car / Area of Piston B
= 16,170 N / 0.5005 m^2
Now, with Pascal's principle, we know that the pressure is transmitted undiminished throughout the fluid. So if the pressure on Piston B is the same as the pressure on Piston A, we can use the same equation to find the force on Piston A:
Force on Piston A = Pressure on Piston A x Area of Piston A
= Pressure on Piston B x Area of Piston A
So, the force that must be applied to Piston A to lift the car can be calculated as follows:
Force on Piston A = (16,170 N / 0.5005 m^2) × 0.0065 m^2
Now, let's calculate the answer:
Force on Piston A = (16,170 N / 0.5005 m^2) × 0.0065 m^2
= 209.259 N
Therefore, a force of approximately 209.259 N must be applied to Piston A to lift the car.