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?
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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