potential energy

[deepika.physicslover]

force acting on any body is given by the form:
F=-dU/dx
where U is the potsntial energy of the body.
now consider a situation : a ball is thrown upward with a certain finite velocity (no other non-conservetive force acts on it , neglet air friction)
when the ball is at the top of its trajectory i.e. we can equally say that its kinectic energy is zero or its potential energy is maximum.REMEMBER GRAVITAIONAL FORCE IS STILL ACTING ON THE BALL.
F=-dU/dy
so acc to the form mentioned above U is max so force acting on the ball should b zero but obviously gravity is still acting.
SO WHERE THE FALLACY LIES??

[Fu-Kwun Hwang]

Fx=-dU/dx, Fy=-dU/dy

for gravitation potential U=mgy
so Fy=-dU/dy= -d(mgy)/dy=-mg
It is a constant , always point down.
U is maximum, does not imply dU/dy is also zero. 

[deepika.physicslover]

uh........i didn refuse dat da force is constant but m just askin u da reason behind da fallacy
n tell me if U is max y doesn it imply dat da force is zero.......i thin mathematicalyy itz correct 2 say dat ven U is max. dU/dy is zero........the topmost point acts as a maxima for da potential energy curve.
dont u thin so?? n obviously after dat da ball will again start 2 fall .

[Fu-Kwun Hwang]

When U(x) is maximum along x-axis, then dU/dx=0
But it did not imply dU/dy=0;

There is no maximum for U in y direction. U(y)=mgy . It is a line with slope mg.

[deepika.physicslover]

do u want 2 say dat da curve in da situation above will b like dat of an inverted V shaped curve, so in dat case at da topmost point da function is not differetiable dats y F is not equal 2 zero?

[Fu-Kwun Hwang]

May be I know what is your problem now.
The potential energy U(y)=mgy  does not have a maximum value along y direction.
But, it is the particle which has maximum potential energy when it reach the highest point.

It is due to total energy of the particle is conserved: kinetic energy + potential energy = (1/2)mv²+mgh=total energy , which is a constant.

[deepika.physicslover]

yeah , u got dat know, n yes dats bcoz of mechanical energy conservation itz potential energy attains a max. value.m i right in explaining da thin above ,i mean da way i was thinkin.?(da inverted V shaped potential energy curve.........)