Net Force & Kinetic Energy: Does More Work Occur?

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Homework Help Overview

The problem involves a particle whose speed doubles twice due to the action of a net external force. The central question is whether the net force does more work during the first doubling of speed or the second, requiring justification of the reasoning behind the answer.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between work and kinetic energy, with some suggesting the use of the work/kinetic-energy theorem. Questions are raised about the specifics of the force and whether values such as mass are provided. There is also an exploration of how to express the work done in terms of consistent variables.

Discussion Status

The discussion is ongoing, with participants offering guidance on relevant principles and equations. There is an acknowledgment of the need to compare the work done during the two phases of speed doubling, but no consensus has been reached on the approach to take.

Contextual Notes

Participants note the absence of specific values such as mass, which may affect the analysis. There is also a mention of the need to clarify how to express work done in terms of the same variables for comparison.

clarkandlarry
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Homework Statement


The speed of a particle doubles and then doubles again because a net external force acts on it. Does the net force do more work during the first or the second doubling? Justify your answer.

Homework Equations


I'm not sure, but i think E = 1/2 mv(squared)


The Attempt at a Solution



Im pretty sure this has something to do with kinetic energy, but the question is asking about the net force doing work. How do I incorporate force into this?
 
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use the work/kinetic-energy theorem
 
were you given any values? like mass...etc but i suspect the 2nd doubling because it would require a greater force to accelerate the particle even more than it has already been.
 
The question asks for how much work the force does. The specifics of the force don't matter, the only thing you want to find is how much work that force does.

Let U_{0,1} represent the work done by the force taking it from the initial speed to double the initial speed.
Let U_{1,2} represent the work done by the force in taking the particle from double the initial speed to quadruple the initial speed.

To compare U_{0,1} and U_{1,2}, you have to get them both in terms of the same variables. So how can you do this?
 
I'm not exactly sure how to do that. I think it has something to do with E = 1/2 mv(squared), but that deals with energy and not work. Is this the equation that I should be using when getting U0,1 and U1,2 in terms of the same variables?
 

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