A HYDRAULIC LIFT OFFICE CHAIR HAS ITS SEAT ATTACHED TO A PISTON WITH AN AREA OF 11.2CM2. THE CHAIR IS RAISED BY EXERTING FORCE ON ANOTHER PISTON, WITH AN AREA OF 4.12CM2. IF A PERSON SITTING ON THE CHAIR EXERTS A DOWNWARD FORCE OF 219 N, WHAT FORCE NEEDS TO BE EXERTED ON A THE SMALL PISTON TO LIFT THE SEAT?
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219 * (4.12/11.2)
To determine the force needed to be exerted on the small piston to lift the seat, we can use the principle of Pascal's law. Pascal's law states that when pressure is applied to an enclosed fluid, the pressure is transmitted equally in all directions. In this case, the enclosed fluid is the hydraulic system of the chair.
First, convert the given areas to square meters since the force will be in Newtons, which is the SI unit of force.
1 cm^2 = 0.0001 m^2
The area of the large piston is 11.2 cm^2. Converting it to square meters:
11.2 cm^2 * 0.0001 m^2/cm^2 = 0.00112 m^2
The area of the small piston is 4.12 cm^2. Converting it to square meters:
4.12 cm^2 * 0.0001 m^2/cm^2 = 0.000412 m^2
According to Pascal's law, the pressure exerted by the fluid is the same throughout the system.
Therefore, the pressure exerted by the person on the seat is equal to the pressure exerted on the small piston.
Pressure = Force / Area
The pressure exerted by the person on the seat can be found as:
Pressure = 219 N / 0.00112 m^2
Now, to lift the seat, we need to calculate the force that needs to be exerted on the small piston.
Force = Pressure * Area
Force = (Pressure exerted by person) * (Area of small piston)
Substituting the values:
Force = (219 N / 0.00112 m^2) * 0.000412 m^2
Simplifying:
Force = 1911.60714 N
Therefore, a force of approximately 1911.61 N needs to be exerted on the small piston to lift the seat.