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A good exercise is to solve the motion on an inclined plane at angle ##\theta##. The usual way by looking at tangential motion. Then, convert back to Cartesian coordinates.Atomillo said:
Equations of motion of a point sliding on a line of arbitrary shape
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Homework Help Overview
The discussion revolves around the equations of motion for a point sliding along a curve defined by a function f(x) in a two-dimensional space. The original poster, who is studying Electronic Engineering, is exploring how to derive these equations from principles of conservation of energy, particularly in the context of motion on an inclined plane.
Discussion Character
- Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation, Assumption checking
Approaches and Questions Raised
- The original poster attempts to derive the velocity as a function of time, v(t), from the velocity as a function of position, v(x), using integration. They express concerns about obtaining results that seem to describe free fall instead of motion along the curve.
- Some participants question the validity of treating the motion as one-dimensional when the curve is not straight, suggesting that a two-dimensional approach may be necessary.
- Others raise the need to relate the velocities in the x and y directions and inquire about the implications of conservation of energy in this context.
Discussion Status
The discussion is ongoing, with participants exploring different interpretations of the problem. Some guidance has been offered regarding the relationship between the x and y components of motion, and the need for a more comprehensive understanding of kinetic energy in two dimensions. There is a recognition of the complexity involved in extending one-dimensional concepts to a two-dimensional scenario.
Contextual Notes
Participants are grappling with the implications of defining motion on a curve and the assumptions that come with it. There are references to specific equations and concepts, such as the conservation of mechanical energy and the relationship between the coordinates, which are still being clarified. The original poster expresses uncertainty about their understanding and the correctness of their approach.
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