Final answer:
To lift the chair, a force of approximately 76.52 N needs to be exerted on the smaller piston of the hydraulic system, as determined by Pascal's Principle which equates the pressure (force per unit area) across the system.
Step-by-step explanation:
The question pertains to the operation of a hydraulic lift office chair, which is a common application of Pascal's Principle in physics. The principle states that when an external pressure is applied to a confined fluid, the pressure change is transmitted undiminished to every portion of the fluid and to the walls of its container. This means that in a hydraulic system, the pressure across the system must remain constant. Given that a person is exerting a downward force of 210 N on the chair's piston with an area of 11.5 cm², we can calculate the required force to exert on the smaller piston (4.20 cm²) to lift the chair. By Pascal's Principle, the pressure (force divided by area) applied to both pistons must be the same, which gives us:
Pressure = Force ÷ Area
Thus, the pressure on the larger piston is 210 N ÷ 11.5 cm², and this pressure must be equal to the pressure exerted on the smaller piston. Solving for the force required on the smaller piston gives:
Force on small piston = Pressure × Area of small piston
We find that Force on small piston = (210 N ÷ 11.5 cm²) × 4.20 cm². Calculating this, we find that the force required is approximately 76.52 N.