Hard potential energy function question

[Lucy Yeats]

Homework Statement

Potential energy function A particle of mass m, starting from x = −∞, approaches
a force region whose potential is given by
V (x) =(ka^2)/((x^2)+(a^2))
where V0 > 0 and a are constants.
(a) Derive an expression for the force on the particle as a function of

Homework Equations

E=F/Q, V=W/Q, E=V/d

The Attempt at a Solution

I tried to substitute it into the equations above, but it didn't work. A friend thought the answer involved calculus, but I'm not sure where to start. Any hints would be much appreciated...

 

[Lucy Yeats]

Is it correct that potential x mass = potential energy?

 

[Lucy Yeats]

Do I need to introduce a constant for the charge, of can I express F without this? Help, please! Thanks! :-)

 

[SammyS]

Is it correct that potential x mass = potential energy?

No.

Check your thread which directly asks this question.

 

[SammyS]

Do I need to introduce a constant for the charge, [STRIKE]of[/STRIKE] or can I express F without this? Help, please! Thanks! :-)

You don't need the charge.

You can express F without introducing a charge.

Do you know how to take the gradient?

F = -▽ V .

Otherwise, F = - dV(x)/dx .

 

[Lucy Yeats]

Thanks SammyS, you post about the gradient answers the question perfectly!

:-)