Classical mechanics - Energy balance confussion

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SUMMARY

The discussion focuses on the confusion surrounding energy balance in classical mechanics, specifically when comparing mechanical energy at rest at height h and at height 0. Key equations referenced include the work done by a nonconservative force (Wnc = Delta E) and the relationship between force and distance (W = Force · distance). Participants identified a common error of confusing height with distance along an inclined plane, leading to incorrect calculations. The issue was resolved by correcting the limits in an integral during the deductions.

PREREQUISITES
  • Understanding of classical mechanics principles, particularly energy conservation.
  • Familiarity with nonconservative forces and their impact on mechanical energy.
  • Knowledge of calculus, specifically integration and limits.
  • Ability to interpret and analyze graphical representations of physical problems.
NEXT STEPS
  • Review the principles of energy conservation in classical mechanics.
  • Study the effects of nonconservative forces on mechanical energy.
  • Learn about the mathematical techniques for solving integrals in physics problems.
  • Examine examples of inclined plane problems to clarify the relationship between height and distance.
USEFUL FOR

Students and educators in physics, particularly those studying classical mechanics, as well as anyone involved in solving energy balance problems in physical systems.

JuanC97
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Hi everyone.
I'm confused with the balance of energy in this situation (I'm comparing the mechanical energy, initially, at rest, at a height = h, and then, at the end, at height = 0). It doesn't seem to be fine, maybe I missed something.
I'd appreciate some help - Everything is in the .jpg below.

There are 2 relevant equations:
1. The work done by a nonconservative force is equal to the change in mechanical energy. (Wnc = Delta E)
2. W = Force (dot) distance.
Also, take into account that h / sin(theta) is equal to the hypotenuse of the inclined plane.
 

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It's a bit difficult to follow. And since you put your work in a jpg instead of typing it here, it is hard to comment.

One thing: You seem to mix up the height h with the distance along the surface.
And another: You may have mixed up some signs.
 
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Doc Al said:
You seem to mix up the height h with the distance along the surface

Hmmm, right. y(t) gives me the displacement along the surface (not the height).
Give me some minutes and I'll have the equations fixed.

* EDIT: Doc Al, you were right. I rewrote the equations by hand and everything fits well now, thanks.
I just had to change the limits in one integral at the beginning of the deductions.
 
Last edited:

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