Question

. A hydraulic lift office chair has its seat

attached to a piston with an area of 11.2
cm2. The chair is raised by exerting force on
another piston, with an area of 4.12 cm2. If
a person sitting on the chair exerts a
downward force of 219 N, what force needs
to be exerted on the small piston to lift the
seat?

Answer 1

To lift a chair with a hydraulic system, the force applied to the smaller piston can be calculated using Pascal's Principle which equates the ratios of force to area between two pistons. For a force of 219 N on a piston with an area of 11.2 cm², a force of approximately 80.52 N is required on a piston with an area of 4.12 cm².

Step-by-step explanation:

The subject matter of this question pertains to Physics, specifically the topic of hydraulic systems and Pascal's Principle. Given the area of the piston attached to the chair and the area of the piston to which force is applied, we need to calculate the force necessary to lift the chair when a downward force of 219 N is exerted by an individual sitting on it.

The force required on the small piston to lift the seat can be calculated using the relationship established by Pascal’s Principle, which states that pressure applied to a confined fluid is transmitted undiminished throughout the fluid. Therefore, the ratio of the forces is equal to the ratio of the areas of the two pistons.

The equation for Pascal's Principle in this context is:

F1/A1 = F2/A2, where:

• F1 is the unknown force applied to the small piston,
• A1 is the area of the small piston (4.12 cm2),
• F2 is the downward force exerted by the person (219 N),
• A2 is the area of the piston attached to the seat (11.2 cm2).

To find F1, we rearrange the equation to:

F1 = (F2 * A1) / A2

Substituting the given values:

F1 = (219 N * 4.12 cm2) / 11.2 cm2 = 80.52 N

Therefore, a force of approximately 80.52 N needs to be exerted on the small piston to lift the chair.

Answer 2

To solve this problem, we can use Pascal's principle, which states that a change in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container.

First, we need to calculate the pressure applied by the person's downward force on the large piston:

Pressure = Force / Area

The area of the large piston (A1) is 11.2 cm², and the person exerts a downward force (F1) of 219 N. Let's convert the area to square meters for consistency:

A1 = 11.2 cm² = 11.2 / 10000 m² = 0.00112 m²
F1 = 219 N

Pressure on the large piston:
P1 = F1 / A1
P1 = 219 N / 0.00112 m²
P1 ≈ 195133.93 N/m² (Pascals)

According to Pascal's principle, this pressure is transmitted undiminished to the small piston. Now we need to calculate the force exerted on the small piston (F2) using the pressure and the area of the small piston (A2), which is 4.12 cm²:

A2 = 4.12 cm² = 4.12 / 10000 m² = 0.000412 m²

Pressure on the small piston (P2) = P1
F2 = P2 * A2
F2 = 195133.93 N/m² * 0.000412 m²
F2 ≈ 80.42 N

Therefore, a force of approximately 80.42 N needs to be exerted on the small piston to lift the seat with a person exerting a downward force of 219 N on the chair.