Why is the Sign of Work and Energy Important?

[jegues]

Homework Statement

There are two problems attached that illustrate my confusions, but my questions is more general than this specific example.

Homework Equations

The Attempt at a Solution

For the first problem where we are asked for the potential energy,

When the dipole moment is parallel to the electric field, it has 0 potential energy.

$$U_{i} = - \vec{p} \cdot \vec{E} = 0$$

When the dipole rotates 60 degrees, the potential energy is not 0.

$$U_{f} = -\vec{p} \cdot \vec{E} = -pEcos\theta$$

The potential enegry given from the formula is negative, but there are only positive answers as possibilities.

I know it is obvious to choose the positive one that corresponds to our answer, but sometimes both negative a positive quantities are listed as possible answers, and I am often confused on which one to choose.

Why is that negative sign in our formula for potential energy, what's its purpose?

For problem number 2 where we are asked for the work,

Initially there is 0 potential energy in the system (perpendicular),

$$U_{i} = 0$$

but then the dipole rotates such that it is parallel to the direction of the field so,

$$U_{f} = -pE$$

Now,

$$W = \Delta U = U_{f} - U_{i} = -pE - 0 = -pE$$

It seems as though the work is negative, but the correct answer is that it is positive.

What am I mixing up?

What do I need to think about and be consistent with to eliminate these sign errors?

Please be as clear as possible. A good example to remember how to determine the sign would be excellent.

Thanks again!

 

[jegues]

Bump, still looking for some help on this, tests tomorrow!