Potential Energy & Conservative Forces #21

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Homework Help Overview

The problem involves a block being released from a compressed spring and sliding across a surface with friction, where the goal is to determine the compression distance of the spring based on the block's speed after crossing a rough patch.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the energy conservation approach, questioning the correct formulation of the energy equation and the terms involved, particularly the spring energy and friction effects. There are attempts to clarify the meaning of variables and the setup of the problem.

Discussion Status

There are multiple interpretations of the energy equation being used, with some participants correcting each other's formulations. While some participants have arrived at numerical values, there is no consensus on the correctness of these values, and further clarification is sought.

Contextual Notes

Participants express uncertainty regarding the definitions of variables and the proper setup of the energy conservation equation. There is mention of potential arithmetic errors and the need for consistent units in calculations.

UCrazyBeautifulU
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In the figure below a 1.24 kg block is held at rest against a spring with a force constant k = 700 N/m.

Initially, the spring is compressed a distance d. When the block is released it slides across a surface that is frictionless, except for a section of width x = 4.85 cm that has a coefficient of kinetic friction μk = 0.357. Calculate d such that the block's speed after crossing the rough patch is 2.23 m/s.


Sorry I can't post the picture. This was how I was figuring out the problem, but that isn't working.


k ( L_1 + x)^2 - coefficient sign (u_k)mgx = 1/2mv_f^2 + mg(0)

since d= L_1 + x and F= kd

substitute values to get L_1 and then find d

That is how i was doing it but I can't figure it out. Is there a more simple explanation or way to figure out this problem? Thanks.
 
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What's "L_1 + x" supposed to be?

The spring is compressed a distance "d": What's the energy stored in it?

Except for the spring energy term, your energy equation should work fine.
 
I get 0.0641 m when i figure it out my way and that answer is incorrect. Maybe I am doing some math wrong, but I double checked? What answer do you get if you use my above equation?

Are you sure it is the right equation to use?
 
First correct the spring energy term. It should be: 1/2 k d^2.
 
1/2kd^2 - u_k(mgx) = 1/2mv_f^2 +mg(0)

Solve for d

I got d= 0.090595

incorrect answer

can anyone else help me with this one?
 
UCrazyBeautifulU said:
I got d= 0.090595
That's not the answer I get. Check your arithmetic. (Did you use the proper units for distance?)
 
yeah, my math was off. Thanks, i figured it out.
 

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