Now that we have a general understanding of pressure, let’s dive into Pascal’s Principle. Essentially, when you apply pressure to one part of a fluid in a confined space, that pressure is transmitted undiminished to all other parts of the fluid. In technical terms, in a confined fluid, an external pressure applied to the fluid is distributed evenly throughout the fluid.

The foundational equation for this principle is:
\[ P_1 = P_2 \]
This implies:
\[ \frac{F_1}{A_1} = \frac{F_2}{A_2} \]

Relationship between Force and Area

While understanding the equation is important, it’s often more crucial to grasp the proportionality, especially for MCAT-style questions. So, let’s break down the relationship between force and area on the same side of a system.

Let’s consider two sides of a system, like in a hydraulic press. If one side (Side A) has a larger area than the other (Side B), and you apply the same pressure to both sides, the larger side (Side A) will experience a larger force. Why? Because for pressure to remain constant across both sides, the force has to change in proportion to the area.

Imagine doubling the area of Side A compared to Side B. To keep the pressure constant, the force on Side A has to be double that of Side B. In essence:
\[ F_A = 2 \times F_B \]
when:
\[ A_A = 2 \times A_B \]

This doesn’t just apply to doubling though it applies to all sorts of factor changes. So if you half the area you would half the force and if you triple the area you got it you triple the force.

This principle is what makes hydraulic systems so powerful and useful. By adjusting the areas in a system, we can amplify forces, enabling us to do things like lifting cars with hydraulic jacks or operating heavy machinery.

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A researcher applies a force to a syringe, causing a small, incompressible volume of liquid to exert pressure on the system. If the pressure is increased at one point in the liquid, which of the following best describes what happens according to Pascal’s Law?

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Question 2 of 5

2. Question

A hydraulic lift is used to raise a car in a garage. The surface area of the small piston is 0.015 square meters, and the surface area of the large piston is 0.93 square meters. If a force of 150 Newtons is applied to the small piston, what is the force exerted by the large piston?

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Question 3 of 5

3. Question

A hydraulic press has two connected pistons with different surface areas. The smaller piston has an area of 2 cm², and the larger piston has an area of 10 cm². If a force is applied to the smaller piston, the force exerted by the larger piston will:

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Question 4 of 5

4. Question

In a hydraulic system within a piece of medical equipment, the output piston has an area that is quadruple the area of the input piston. If a constant force is applied to the input piston, what is the effect on the force exerted by the output piston?

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Question 5 of 5

5. Question

A hydraulic lift is used to elevate a car in an auto shop. The original setup has an input piston area of 1.5 cm² and requires a force of 300 N to lift the car. If the input piston area is doubled and the force applied is halved, what is the effect on the output force?