# Force between polar molecule and an ion

1. Mar 14, 2015

### Westin

1. The problem statement, all variables and given/known data

Under certain conditions the interaction between a "polar" molecule such as HCl located at the origin and an ion located along the x axis can be described by a potential energy U=−b[PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmmi10/alpha/144/char3D.pngx^2, [Broken] where b is a constant.

What is Fx, the x component of the force on the ion?

Fx=

What is Fy, the y component of the force on the ion?

Fy= 0

2. Relevant equations

U=-b/x^2

3. The attempt at a solution

The y component of the force on the ion was fairly obvious but I am getting stuck on the x component.

I know that the force must me positive but it was incorrect when I tried +b[PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmmi10/alpha/144/char3D.pngx^3[/B][/B] [Broken]

Last edited by a moderator: May 7, 2017
2. Mar 14, 2015

### TESL@

I think you need to know the partial charges and their separation/distance.

3. Mar 14, 2015

### Westin

these are the choices i have
A). +2b/x^3
B). 0
C). +b/x^3
D). -2b/x^3
E). -b/(2x)
F). -b/x^3
G). -b/x

4. Mar 14, 2015

### Staff: Mentor

What is the relation between force and potential?

5. Mar 14, 2015

### Staff: Mentor

Why?

6. Mar 14, 2015

### Staff: Mentor

Why do you say that?

7. Mar 14, 2015

### TESL@

The molecule will rotate in such way that H will be at the farthest and Cl at the closest point to the ion. Then the force will depend on partial charges and the distance between both H and Cl, and ion and molecule.

8. Mar 14, 2015

### Staff: Mentor

On can infer from the equation U=−b/x2 that the molecule is taken as a point dipole with its orientation assumed to be always favorable.

9. Mar 14, 2015

### Westin

Wait, wouldn't the answer be negative because the force on an object is the negative of the derivative of the potential function? The potential energy U is equal to the work you must do against that force to move an object from the U=0 reference point to the position r. The force you must exert to move it must be equal but oppositely directed, and that is the source of the negative sign.

10. Mar 14, 2015

### Westin

I'm almost positive the answer is -b/(2x) after what I just said. Any feedback?

11. Mar 14, 2015

### Staff: Mentor

Again, what is the equation that relates force and potential energy?

12. Mar 14, 2015

### Westin

F = -dU/dx

13. Mar 14, 2015

### Staff: Mentor

Great, now apply that equation to the problem given.

14. Mar 14, 2015

### Westin

Im confused with on how to.. F = −b/x^2 take derive then get -b/2x

15. Mar 14, 2015

### Staff: Mentor

I guess you mean U. What is the derivative of $x^{-2}$?

16. Mar 14, 2015

### Westin

F = -b/x^2 ---> -bx^-2 ---> 2b/x^3 this is it

17. Mar 14, 2015

### Westin

It was incorrect... I have one try left , I don't get what else it could be

18. Mar 14, 2015

### Staff: Mentor

Doesn't this contradict what you wrote earlier?
Before submitting answers, lets check if they make sense...

19. Mar 14, 2015

### Westin

Ahh yes it does,-2b/x^3 should be correct? Im sorry for my personal confusion. I'm in a poor experimental physics class at Michigan state where you have to teach yourself online everything..

20. Mar 14, 2015

### Staff: Mentor

It's ok to be confused. I'm just hoping that you can gain some good habits. From the formula for energy, you can see that the energy increases (decreases in magnitude but with a negative sign) when the ion moves away from the origin, so the force must be directed towards the molecule. That takes care of the sign. Then it is just a question of going back to fundamentals, ie, F = -dU/dx, to get the force. Then you can check that the answer makes sense, considering the physics (force must be directed towards the origin). It's easy to lose track of minus signs, especially in a case like this where you get 3 in a row.