Classical mechanics - Energy balance confussion

In summary, the conversation revolves around the balance of energy in a situation involving initial mechanical energy, rest, and height. The equations Wnc = Delta E and W = Force (dot) distance are relevant, and h / sin(theta) is equal to the hypotenuse of an inclined plane. There is confusion about differentiating between height and distance along the surface, and there may be some incorrect signs. The equations are eventually fixed with the help of Doc Al.
  • #1
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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  • #2
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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  • #3
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.
 
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FAQ: Classical mechanics - Energy balance confussion

What is classical mechanics?

Classical mechanics is a branch of physics that studies the motion of objects and the forces that act upon them. It is based on the laws of motion and gravitation developed by Sir Isaac Newton in the 17th century.

What is energy balance confusion in classical mechanics?

Energy balance confusion in classical mechanics refers to a common misunderstanding about the conservation of energy in a system. It is the idea that the total amount of energy in a system can change or be lost, when in reality, energy is always conserved and can only be transferred between different forms.

How does energy balance confusion occur in classical mechanics?

Energy balance confusion can occur when there are multiple sources of energy in a system and it is not clear how they are interacting with each other. It can also occur when there is a lack of understanding of the different forms of energy, such as kinetic energy and potential energy.

How can energy balance confusion be resolved in classical mechanics?

To resolve energy balance confusion in classical mechanics, it is important to carefully consider all sources of energy in a system and understand how they are interacting with each other. It is also helpful to clearly define and differentiate between the different forms of energy present in the system.

What are some real-life applications of energy balance in classical mechanics?

Energy balance principles are used in many real-life applications, such as designing efficient machines and structures, understanding the motion of celestial bodies, and predicting the behavior of complex systems like weather patterns. It is also crucial in fields like engineering, biomechanics, and astrophysics.

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