Graph of a particle in parabolic path

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Homework Help Overview

The discussion revolves around a particle moving along a parabolic path, with participants exploring the implications of a graph that represents potential energy, denoted as V(x), and its relationship to the particle's motion. The subject area includes concepts from mechanics and energy, particularly focusing on potential energy in a gravitational context.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants question the meaning of the y-axis in the graph and whether V(x) represents potential energy. There is discussion about the implications of the graph's parabolic shape and its relation to the particle's equilibrium position and motion. Some participants express uncertainty about distinguishing between different functions that describe the particle's motion.

Discussion Status

The discussion is active, with participants raising questions about the interpretation of the graph and the physical meaning of the variables involved. Some guidance has been offered regarding the relationship between potential energy and the particle's motion, but no consensus has been reached on the exact nature of the graph.

Contextual Notes

Participants are navigating assumptions about the graph's representation, including whether it depicts potential energy or the actual path of the particle. There is also mention of the initial conditions under which the particle is released, which adds complexity to the interpretation.

Jahnavi
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Homework Statement



graph.jpg

Homework Equations

The Attempt at a Solution



I don't understand what is y-axis representing ? What is V(x) ? Is it potential energy ?

Since the graph is a parabola , V(x) = kx2

I don't know how to proceed further .
 

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Jahnavi said:
Is it potential energy ?
I think it must be, given the choice of answers.
 
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haruspex said:
I think it must be, given the choice of answers.

OK . V(x) is zero (minimum ) at x= 0 . x = 0 represents position of equilibrium .

How to distinguish between a) and b) ? Both represent SHM
 
The problem says that the particle follows the parabolic path shown, and the arrow points to the initial position of the particle, from where it is released from rest. Which function corresponds to that initial condition?
 
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ehild said:
The problem says that the particle follows the parabolic path shown, and the arrow points to the initial position of the particle, from where it is released from rest. Which function corresponds to that initial condition?

The parabolic shape in the graph represents the variation of V(x) with x . It does not represent the path .

Is the parabola representing V(x) or the actual path of the particle ? These two are different things

.Or is that the parabola is representing the actual path as well the variation of potential energy ?

If it is the actual path then option B) makes sense as it represents the cosine curve where particle is as it's extreme position.
 
"A particle of mass m is released from rest and follows a parabolic path as shown. " What do you think it means?
You can imagine that the particle moves in a well of parabolic cross section. And the potential energy is proportional to the height,
Anyway, the particle starts from rest. Which graphs starts with zero slop?
 
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Thanks !
 

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