The weight of an airplane varies with the cube of the plane’s length. The lift generated by an airplane’s wings varies with the square of the plane’s length. Will a different airplane with the same constants be able to fly if it is 75 feet long?

The weight of an airplane varies with the cube of the plane’s length. The lift generated by an airplane’s wings varies with the square of the plane’s length. Will a different airplane with the same constants be able to fly if it is 75 feet long?

Refrigeration and Air Conditioning Technology (MindTap Course List)

8th Edition

ISBN:9781305578296

Author:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill Johnson

Publisher:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill Johnson

Chapter2: Matter And Energy

Section: Chapter Questions

Problem 10RQ: Why does an object weigh less on the moon than on earth?

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Concept explainers

Basic Terminology in Mechanics

The area of science and mathematics concerned the motion of the objects, the relation between the force matter, and motion if specified. Forces exerted over the objects result in displacements or changes in the position of an object concerning its environment. This branch of physics keeps its roots in Ancient Greece in the form of the scripts of Aristotle and Archimedes.

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The weight of an airplane varies with the cube of the plane’s length. The lift generated by an airplane’s
wings varies with the square of the plane’s length. Will a different airplane with the same constants be able to fly if it is 75 feet long?

Expert Solution

Step 1

Given:

Weight of an airplane varies with the cube of the plane's length:

W $\propto$ L³

W = k $\times$ L³

Lift generated by an airplane's wings varies with the square of the plane's length:

H $\propto$ L²

H = a $\times$ L²

where, k and a are some constants.

To find:

if a different airplane with the same constants will be able to fly if it is 75 feet long?

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