Understanding Air Resistance: Explaining the Math Behind Reduced Force

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Homework Help Overview

The discussion revolves around understanding the mathematical implications of air resistance on an object's motion, particularly when the force of air resistance is altered. The subject area includes concepts from dynamics and forces, specifically relating to constant velocity and the effects of changing forces.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the relationship between air resistance and gravitational force when an object is moving at constant velocity. Questions arise regarding the net force acting on the object when air resistance is reduced and how this affects acceleration.

Discussion Status

The discussion is active, with participants attempting to clarify their understanding of the forces involved. Some offer insights into how reducing air resistance affects the net force, while others seek further explanation of the mathematical reasoning behind the fractions involved.

Contextual Notes

There is a focus on the implications of reducing air resistance by a factor of four, and participants are questioning the assumptions regarding the balance of forces at constant velocity. The original poster expresses confusion about the mathematical reasoning leading to the conclusion regarding acceleration.

brake4country
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Can someone please explain the math of this problem?

-If F is the force of air resistance on an object with mass m moving at a constant velocity, which of the following best describes the acceleration of the object when the force of air resistance is reduced by a factor of 4?
(a) F/m
(b) 1/2 F/m
(c) 1/4 F/m
(d) 3/4 F/m

The answer is d but I do not understand how to get it. Thanks in advance!
 
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If it is moving at a constant velocity, what force is required in order to maintain that velocity in the initial case (with full air resistance)?

If the Air resistance is reduced by a factor of four, but the same force is assumed to be acting on the object, how does the object react?
 
I am assuming that when velocity is constant, then the F(air) must cancel out the F of (mg). Therefore, when I drew this out on paper, I made the F(mg) component longer and the F(air) shorter since F(air) is reduced.

How do the fraction come into play? How is the answer 3/4 F/m? Thanks in advance
 
brake4country said:
I am assuming that when velocity is constant, then the F(air) must cancel out the F of (mg). Therefore, when I drew this out on paper, I made the F(mg) component longer and the F(air) shorter since F(air) is reduced.

How do the fraction come into play? How is the answer 3/4 F/m? Thanks in advance

What is the net force remaining when you reduce the air resistance by a factor of 4?
 
I get it. Reducing by a factor of 4 requires one to think in terms of fractions (1/4). Therefore, the net F remaining is 3/4. Thanks again!
 

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