Ch. 13 - Fluids

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 13 - Fluids

Problem 84a

Chapter 13, Problem 84a

A hydraulic lift is used to jack a 960-kg car 52 cm off the floor. The diameter of the output piston is 18 cm, and the input force is 380 N. What is the area of the input piston?

Verified step by step guidance

Step 1: Recall the formula for the area of a circle, which is given by \( A = \pi r^2 \), where \( r \) is the radius of the circle.

Step 2: The diameter of the input piston is not provided directly in the problem, so we need to calculate it. Use the relationship between the diameters of the pistons and the forces applied in a hydraulic system to determine the input piston's diameter.

Step 3: Once the diameter of the input piston is known, calculate the radius by dividing the diameter by 2. \( r = \frac{d}{2} \).

Step 4: Substitute the radius of the input piston into the area formula \( A = \pi r^2 \) to calculate the area of the input piston.

Step 5: Ensure that the units are consistent throughout the calculation (e.g., convert cm to meters if necessary) and simplify the expression to find the area in square meters.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Area of a Circle

The area of a circle is calculated using the formula A = πr², where r is the radius. In the context of hydraulic systems, understanding how to calculate the area of the pistons is crucial, as it directly affects the force transmission and mechanical advantage of the lift.

Hydraulic Systems

Hydraulic systems operate based on Pascal's principle, which states that pressure applied to a confined fluid is transmitted undiminished in all directions. This principle allows a small input force applied to a smaller piston to generate a larger output force at a larger piston, enabling heavy objects to be lifted with relatively little effort.

Mechanical Advantage

Mechanical advantage is the factor by which a machine multiplies the force put into it. In hydraulic lifts, the mechanical advantage can be determined by the ratio of the areas of the output and input pistons. This concept is essential for understanding how a hydraulic lift can lift heavy loads with a smaller input force.

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