Work, Energy and Power for a Particle moving in a Potential Field

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The discussion revolves around the confusion regarding a particle's motion when its potential energy U(x) equals its total energy E(x), leading to a kinetic energy (KE) of zero. Participants clarify that a particle can indeed stop, using the example of a ball thrown against gravity, which momentarily halts with zero KE. The concept of motion being restricted to a specific region is also highlighted, indicating that the particle's movement is limited under certain conditions. The initial question about the correctness of the book's answer is addressed, confirming that the printed information may be misleading. Understanding these principles is crucial for grasping work, energy, and power in a potential field.
Rongeet Banerjee
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Homework Statement
A particle with total Energy E is moving in a potential energy region U(x).Motion of the particle is restricted to the region when
1.U((x) greater than E
2.U(x) less than E
3.U(x) = E
4.U(x) less than or equal to E
Relevant Equations
Total Energy=Potential Energy+Kinetic Energy
15866407852351629022995.jpg

But yet again my text says that option 4 is correct.
 
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It looks like you got option 4b there!
 
Oh yes I corrected it.
 
I don't understand that how can motion take place if U(x) becomes equal to E(x).KE in that case should be zero.So is the answer printed in my book wrong?
 
Rongeet Banerjee said:
I don't understand that how can motion take place if U(x) becomes equal to E(x).KE in that case should be zero.So is the answer printed in my book wrong?
A particle can stop! Think of a ball thrown up against gravity. It stops instantaneously and at that point its KE is zero.
 
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PeroK said:
A particle can stop! Think of a ball thrown up against gravity. It stops instantaneously and at that point its KE is zero.
Oh so "motion of the particle is resticted to the region "meant that!Truly I am so humbled.
 

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