Comparing Kinetic Energy of Two Airplanes with Different Speeds and Weights

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Homework Help Overview

The discussion revolves around comparing the kinetic energy of two airplanes, one traveling at the speed of sound and the other with half the weight of the first but traveling at twice the speed of sound. The subject area includes concepts of kinetic energy and the effects of mass and velocity on it.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between mass and velocity in the kinetic energy formula, questioning how changes in these variables affect the overall kinetic energy. Some participants attempt calculations to compare the two scenarios, while others express uncertainty about their reasoning.

Discussion Status

The discussion is active, with participants providing calculations and insights into the effects of speed and mass on kinetic energy. There is a recognition that speed has a significant impact, and some participants suggest that plane two may have higher kinetic energy, although this is not universally agreed upon.

Contextual Notes

Participants are working within the constraints of a homework assignment, which may limit the information available for a comprehensive analysis. There is also a focus on understanding the implications of the kinetic energy formula without reaching a definitive conclusion.

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Homework Statement


Which has a higher kinetic energy?
An airplane traveling at the speed of sound or an airplane with half the weight of plane one and traveling at 2 times the speed of sound?

Homework Equations


KE = 1/2 mv^2
v=gt

The Attempt at a Solution


I think I am just get mixed up on words. If they were the same weight the plane going twice as fast would have 4 times the kinetic energy. (v=2^2=4).
I think I am going the wrong direction. Would their kinetic energy be the same? Since plane two weight is half but double the speed. Help
 
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E1 = (1/2)(m)(v^2)

E2 =(1/2)(0.5m)(2v^2)
E2 =(.5)(2^2)(1/2*m*v^2)
E2 =(.5)(2^2)(E1)
E2 = 2E1

I think you multiplied the final 2 by the half that is in the equation for kinetic energy.
 
Since the kinetic energy depends on the speed _squared_, doubling the speed will have more effect than doubling the mass. Try calculating both KE's.
 
I think I have it. Plane two will have the higher KE since KE is quadrupled with increase in speed. The weight is a factor but not as much as speed. Thanks
 

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