If the small piston \( A_1 \) is slowly depressed a distance of \( y_1 = 0.400 \, \text{m} \), what distance \( y_2 \) will the large piston \( A_2 \) rise?\( y_2 = \) \_\_\_\_\_\_ mWhat is the magnitude \( W_1 \) of the work done when pushing down the small piston \( A_1 \)? What is the magnitude \( W_2 \) of the work done when pushing up the large piston \( A_2 \)?\( W_1 = \) \_\_\_\_\_\_ J \quad \( W_2 = \) \_\_\_\_\_\_ J **Hydraulic Lift Mechanics**Consider the hydraulic lift depicted in the figure:- The small piston has an area \( A_1 = 0.0330 \, \text{m}^2 \).- The large piston has an area \( A_2 = 4.00 \, \text{m}^2 \).**Objective:** Determine the force \( F_2 \) exerted by the large piston when a force \( F_1 = 14.0 \, \text{N} \) is applied to the small piston. Assume the fluid in the lift is incompressible.\[ F_2 = \_\_\_\_\_\_\_\_\_\_ \, \text{N} \]**Diagram Explanation:**The diagram shows a cross-section of the hydraulic lift system, consisting of two pistons:- **Small Piston \( A_1 \):** Positioned on the left, receiving the downward force \( F_1 \).- **Large Piston \( A_2 \):** Positioned on the right, experiencing the upward force \( F_2 \).- The system is filled with a fluid that transmits force from one piston to the other, highlighted by arrows indicating the direction of forces.**Calculating Piston Movement:**When the small piston \( A_1 \) is depressed by a distance \( y_1 = 0.400 \, \text{m} \), determine the resulting rise \( y_2 \) of the large piston \( A_2 \).> Use the principle of conservation of hydraulic fluid volume to find the relationship between the distances \( y_1 \) and \( y_2 \).---This task shows practical applications of Pascal's principle in hydraulic systems.

A) As per Pascal’s principle, Here, P1 and P2 are the pressures at the pistons of area A1 and A2, respectively. Substitute the relevant values.B) As per the energy conservation, the input work is equal to the output work in a hydraulic system. Substitute the relevant values.C) The work done by the force F1 in pushing the piston can be given as, Substitute the relevant values. The work done by the force F2 in pushing the piston can be given as, Substitute the relevant values.

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Consider the hydraulic lift shown in the figure. The small piston has an area Aj of 0.0330 m², and the large piston has an area A2 of 4.00 m². What force F2 will the large piston provide if the small piston is pushed down with a force F¡ of 14.0 N? Assume that the fluid used in the lift is incompressible.

Consider the hydraulic lift shown in the figure. The small piston has an area Aj of 0.0330 m², and the large piston has an area A2 of 4.00 m². What force F2 will the large piston provide if the small piston is pushed down with a force F¡ of 14.0 N? Assume that the fluid used in the lift is incompressible.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

If the small piston \( A_1 \) is slowly depressed a distance of \( y_1 = 0.400 \, \text{m} \), what distance \( y_2 \) will the large piston \( A_2 \) rise?

\( y_2 = \) \_\_\_\_\_\_ m

What is the magnitude \( W_1 \) of the work done when pushing down the small piston \( A_1 \)? What is the magnitude \( W_2 \) of the work done when pushing up the large piston \( A_2 \)?

\( W_1 = \) \_\_\_\_\_\_ J \quad \( W_2 = \) \_\_\_\_\_\_ J

**Hydraulic Lift Mechanics**

Consider the hydraulic lift depicted in the figure:

- The small piston has an area \( A_1 = 0.0330 \, \text{m}^2 \).
- The large piston has an area \( A_2 = 4.00 \, \text{m}^2 \).

**Objective:** Determine the force \( F_2 \) exerted by the large piston when a force \( F_1 = 14.0 \, \text{N} \) is applied to the small piston. Assume the fluid in the lift is incompressible.

\[ F_2 = \_\_\_\_\_\_\_\_\_\_ \, \text{N} \]

**Diagram Explanation:**

The diagram shows a cross-section of the hydraulic lift system, consisting of two pistons:

- **Small Piston \( A_1 \):** Positioned on the left, receiving the downward force \( F_1 \).
- **Large Piston \( A_2 \):** Positioned on the right, experiencing the upward force \( F_2 \).
- The system is filled with a fluid that transmits force from one piston to the other, highlighted by arrows indicating the direction of forces.

**Calculating Piston Movement:**

When the small piston \( A_1 \) is depressed by a distance \( y_1 = 0.400 \, \text{m} \), determine the resulting rise \( y_2 \) of the large piston \( A_2 \).

> Use the principle of conservation of hydraulic fluid volume to find the relationship between the distances \( y_1 \) and \( y_2 \).

---

This task shows practical applications of Pascal's principle in hydraulic systems.

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