Use the work-energy theorem to derive an expression for v^2

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Homework Help Overview

The discussion revolves around the application of the work-energy theorem to derive an expression for the square of the velocity (v^2) in a context involving spring forces and friction. Participants are examining the relationships between variables such as spring constant (k), displacement (x or d), and mass (m).

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to manipulate the work-energy theorem but encounters difficulties with their initial equation. Some participants question the definitions of variables k and x, noting potential confusion with the variable d. Others suggest reconsidering the energy changes in the spring during the mass's movement.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the variables involved. There is a recognition of the need to clarify the definitions of k and x, and some guidance has been offered regarding the energy considerations in the spring system.

Contextual Notes

There appears to be missing information in the problem statement, particularly regarding the definitions of k and x, which are crucial for understanding the setup. The original poster's use of variables may lead to confusion, as there are multiple terms that could represent similar concepts.

David112234
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Homework Statement


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Homework Equations


Work energy theorem

The Attempt at a Solution


.5mv2 - .5mv2 = (kx - μmg)d
final velocity is 0

½mv2 =(kx - μmg)d
solve for v2

((kx - μmg)d2)m
When this was wrong I tried integrating Fx but it was still wrong
Capture2.png
 
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I miss a question in this problem statement ?
I miss what ##k## means (but I can guess)
I also miss what ##x## means, which is very important. Note that there is a ##d## already.
 
BvU said:
I miss a question in this problem statement ?
I miss what ##k## means (but I can guess)
I also miss what ##x## means, which is very important. Note that there is a ##d## already.
K is the spring constant
X is supposed to be d, I am just used to using x for position, in answers 3-4 i changed it to d
 
David112234 said:
K is the spring constant
X is supposed to be d, I am just used to using x for position, in answers 3-4 i changed it to d
If x is d, your very first equation is wrong.
Remeber that there is energy in the spring both initially and after the mass has moved distance d. What is the change in that energy?
 

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