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A particle of mass m moves under a force F = −cx^3 where c is a...

A particle of mass m moves under a force F = −cx^3 where c is a positive constant. Find the potential energy function. If the particle starts from rest at x = −a, what is its velocity when it reaches x = 0? Where in the subsequent motion does it instantaneously come to rest?

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Answer #1

1. Potential energy function [as force is negative gradient of potential energy i.e.  F(x) = - dU /dx ]

  

2. From law of conservation of energy, total mechanical energy = sum of kinetic and potential energy remains constant

total energy at x = -a is equal to total energy at x = 0

is the velocity at x = 0

3. Let at x' particle instantaneously comes to rest.

when particle comes to rest, its kinetic energy will be zero. so

all its enrgy becomes equal to maximum potential energy at x = a

  is the position where particle comes to instanteous rest

pls upvote

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